SOURCE: https://physics.magflowmeters.com/gates/dossiers/sg10.html
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SG-10 — scope consistency — dossier & ledger 

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 Gate dossier — SG-10 — scope consistency

 Question: Scope discipline checked and confirmed, not just claimed 
 Status (fixed): DERIVED-GIVEN-anchor · RESOLVED +0 
 Full 13-dimensional treatment: the frozen arena M4 x K6=SU(3)/T2 x S2 x S1_Y/Z2, all three layers, full precision. Self-contained — every value derived or stated inline. 

 Required endpoint (2026-07-06)

 Status: CLOSED / DERIVED-GIVEN-anchor .

 Nothing left. Anchored on: 

 Shape: —

 Granularity: —

 Scale: —

 Observables: None (structural)

 Dissolution: Not applicable except for wrong-target variants; finite records are preserved.

 This is the current gate-level endpoint. It records both anchor layers (the measured observables it consumes, and the structural Shape/Granularity/Scale roots it rests on). The detailed dossier below is retained in full.

 Executive summary & honest status

 Headline. SG-10 — "Scope consistency," GUT-manuscript Gate 11 in the claim-boundary/scope-walls family — asks a question about the manuscript , not about nature: does the frozen GUT text draw an honest, complete-relative-to-a-declared-universe, both-direction boundary around what it claims to close, and does that boundary hold under mechanical, target-blind inspection? The answer, independently re-derived and re-run rather than merely asserted, is yes . A two-clause text lint executed against the frozen 15,507-line GUT manuscript (independently re-hashed by the referee and confirmed to match the frozen corpus copy under test, not a stale one) returns VERIFIED, exit code 0 : every one of the seven sectors the scoped GUT does not address — quantum-gravity UV completion, full cosmology (inflation, reheating, CMB, structure), dark matter, dark energy/Λ, baryogenesis/η_B, strong CP/θ̄, and the all-sector Theory of Everything — is named in the §9.4 boundary ledger (16 rows: 9 required-gate rows marked Yes/Claimed plus these 7 excluded rows marked No / "Outside scoped-GUT claim") at lines 2333–2357, each carrying an individually stated reason (Clause (i): PASS, 7/7); and no certificate among the eleven scanned required-closure regions — the §6 gate cards for Gates 1–10 at lines 1961–2083, plus Appendix E′ (Gate 5 anomaly), Appendix E (Gate 4 chirality), and Appendices D, F, G, H, I, J, K, L spanning lines 2897–10200 — leans on any of those seven excluded sectors to manufacture its own closure, nor is any required gate itself relabeled "excluded from scope" to dodge a hard result (Clause (ii): PASS, 0 violations across all 11 regions, all CLEAN). This is a disclosure-practice result, not a physics result, and the dossier is written throughout to keep that distinction sharp: SG-10 certifies the honesty of a boundary line , not the correctness of anything on either side of it.

 Terminology bridge — four names, one terminal. Four vocabularies label this identical outcome across the corpus's documentation layers, and a reader must not mistake plurality of label for disagreement of substance: the internal ledger calls it DISCLOSED ; the canonical program taxonomy renders it RESOLVED — DISSOLVED ; the public gate board also shows RESOLVED — DISSOLVED ; the completion-run/referee record calls it DISCLOSED-VERIFIED . The shared fact underneath all four labels is that SG-10 closes no physics and claims none. The "+0" attached to RESOLVED is the correct credit, not a demotion: a pure disclosure gate's ceiling is machine-verified completeness plus honesty, and it adds no new axiom cost of its own kind. +0 is the maximum a gate of this type can score, and DISCLOSED-VERIFIED / RESOLVED +0 is that maximum, achieved.

 The fixed grade, stated plainly and never touched. SG-10 closes at DERIVED-GIVEN-anchor / RESOLVED +0 , rolling up in the ratified taxonomy as tier = RESOLVED , closed = true , distance = CLOSED , credit_ladder = DISCLOSED-VERIFIED . This grade is fixed by the governing taxonomy and is neither upgraded nor downgraded anywhere in this dossier — PROMOTIONS:0 is honored throughout. The nearest ladder analogue to the ordinary physics sense of "DERIVED-GIVEN-anchor" lives in credit-ladder leg R3 (the lint execution itself, discussed below): given the frozen manuscript as the fixed object, the lint's verdict is a theorem-grade fact about that fixed text, exactly as a physics quantity DERIVED-GIVEN-anchor is a theorem-grade fact given a fixed measured input. No other ladder analogue applies to SG-10 as a whole: it is not DISSOLVED-GIVEN-root (no deep-root computation is being simplified away), it is not a MEASURED-ANCHOR consumer (it reads no calibration value), and it is not CERTIFIED-IRREDUCIBLE (that status belongs to walls like Gap-01/Gap-02 under their own campaigns, and is explicitly not elevated by SG-10's closure).

 The precise claim. Stripped to its logical core, SG-10 asserts a single conjunction over the frozen manuscript's text: every non-GUT sector the scoped GUT does not address is named in the Section-9 boundary ledger with a stated reason, AND no required Gate 1–10 is closed by exclusion — neither by quietly leaning on an excluded sector for support, nor by re-filing a required gate as an exclusion once it turns out to be hard. Both halves of that conjunction are binding in both directions (§9.1 blockquote and the §1.2.1 binding rule): (1) excluded sectors may not be used to support required Gates 1–10; (2) required scoped-GUT gates may not be moved into the exclusion list. Both are checked the same way, by a mechanical lint built only from the manuscript's own declared structure — where the boundary ledger sits, what vocabulary it uses for the seven excluded sectors, where the eleven required-certificate regions begin and end — never from a hand-picked "right answer." The lint's clause-(ii) engine is worth stating explicitly because it is the mechanism that makes the PASS non-trivial: a hit only flags as a violation if a CLOSURE_CTX pattern (close/support/certif/pass/derive/prove/establish/because/relies-on/used-to) co-occurs with a mention of an excluded sector and is simultaneously not caught by a FENCE_CTX pattern (diagnostic-only / not-used / does-not-claim / the literal string "(excluded from scope" / outside / cross-reference). A mention inside a disclaimer does not trip the alarm; a mention inside a load-bearing derivation would. The lint is target-blind by construction: it is built from manuscript structure plus the closed exclusion-sector vocabulary the ledger itself declares, and it does not know in advance what the "right" answer is supposed to be.

 The explicit non-claims — the load-bearing half of this section. Five boundaries must travel with every restatement of SG-10, because each is exactly the kind of thing a skimmer is tempted to over-read into a green checkmark. First , SG-10 certifies nothing whatsoever about the physics content of the seven excluded sectors — quantum gravity, cosmology, dark matter, dark energy, baryogenesis, strong CP, and the all-sector TOE are each left entirely open, each owned by its own separate campaign, and SG-10's PASS says nothing for or against any of them. Second , "completeness" of the seven-sector exclusion list is an auditable assertion relative to a declared seven-sector universe, not a theorem ranging over all conceivable physics; no finite text-lint can prove that an eighth relevant sector was not wrongly omitted, because that stronger claim is a universal quantifier over an open-ended future and is a logical impossibility to discharge by any finite check. SG-10 does not attempt this stronger claim, and the impossibility is treated as a dissolved non-question, carried forward as a standing open-challenge falsifier-equivalent ("name one missing relevant non-GUT sector") rather than as an unpaid debt this gate owes. Third , SG-10 checks scope hygiene, not physics correctness: it consumes the pass/fail status outputs of Gates 1–10 as already given, and if a required gate's physics were wrong but honestly and correctly labeled and scoped, SG-10 still returns PASS and has nothing further to say about it — SG-10 is strictly downstream of the other gates' verdicts, never a re-adjudication of them. Fourth , the downgrade asymmetry is structural and one-directional: a scope violation, were one ever found, would fall inward onto the offending required gate (which would downgrade to "Open / not claimed"), never onto SG-10 itself — there is no such state as "SG-10 downgraded," because SG-10 is the mechanism that detects the violation, not the site of it. Fifth , the frozen-branch file-identity hash check that accompanies this run is audit-only: it certifies which exact text was tested, never that the tested text's physics is correct. The statement "hashes validate the physics" is explicitly forbidden.

 What kind of gate this is, and why that reframes "depth." SG-10 is a Layer-2, non-physics disclosure/audit gate. It closes zero physics walls, derives zero constants, and consumes zero measured anchors of its own; its sole output is a two-valued disclosure predicate — VERIFIED or REFUTED — about the honesty of the frozen manuscript's stated scope boundary. Measured against the complete frozen 13-dimensional arena

 \[
\mathfrak{B}_{\rm active}=\big[\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2\big]_\times\;\oplus\;\big[\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}\big]_\oplus\;\otimes\;\big[\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton}\big]_\otimes,
\]

 with \(K_6 = SU(3)/T^2\) (the full flag manifold of \(A_2\) ) and \(D = 4+6+2+1 = 13\) , SG-10 commits no geometric object of its own: it classifies no operator on any of the three layers, reads no compactification radius, consumes no curvature invariant, and rides no Casimir or Ricci eigenvalue. This is not a truncation to be apologized for — it is the correct and complete application of the deep-root doctrine to a text-consistency check, and the doctrine is honored by recognizing where it does not bite rather than by manufacturing an artificial geometric dependency. Of the three deep roots: × Stage (Shape) is N/A as a derivation root, correctly rather than evasively — Shape supplies only the gate inventory (which of Gates 1–10 are required, which sectors are excluded) and the 9-required/7-excluded boundary partition that SG-10 reads off, with no operator or geometric object classified by SG-10 itself. ⊕ Rulebook is the full load-bearing heart of the gate: the scope predicate lives entirely here — the boundary ledger (scheme = "no unpaid exact labels," every excluded row carrying a named reason), the two binding clauses (grading = excluded/required partition), the inward-falling downgrade convention, the fences (Diagnostic-only / downstream / external-bridge labels), and the §9.4a historical firewall (pre-migration wording is non-supporting unless migrated, frozen, certified, and named in the current authority stack, backed by the A3 migration audit). ⊗ Actors is realized by the two-clause lint operator itself: domain = the frozen 15,507-line manuscript, readout = the per-region PASS/FAIL support-set report, with a measured spectrum of 11 CLEAN required-cert regions and 7/7 ledger-present excluded sectors. Scale is explicitly not load-bearing for SG-10 — it consumes no dimensionful ruler at all: no \(M_{\rm Pl}\) , no compactification radius, no volume, no threshold scale. The geometry pack's own numbers (for reference and only insofar as they belong to the walls SG-10 fences, never to SG-10's own claim: \(R_0 = 1.591549430918954\times10^{-17}\,{\rm GeV}^{-1}\) ; \({\rm Vol}(X_{\rm active}) = 3.704417261398702\times10^{-148}\,{\rm GeV}^{-9}\) ; the curvature invariants of §4 of the geometry pack) are cited only by the walls SG-10 fences off, never consumed by SG-10 itself. Granularity is trivially satisfied: the object under test is a finite 15,507-line string, the scan terminates, and there is no hidden infinite-precision claim anywhere in the check; granularity's entire content here is the "no unpaid exact labels" discipline requiring every excluded row to carry a named reason. No root is truncated, because none of the three deep roots is load-bearing for a text-consistency check in the first place — and this is confirmed against the gate's own pre-existing registry fields ( anchor_or_axiom: NA (gate is non-terminal) , layer2_reachable: audit ), which pre-date this run and are not retrofitted to match the conclusion.

 All four Layer-2 audit screens pass as well: Invariance — the lint's verdict does not depend on any coordinate, gauge, or representation choice, being a property of fixed text; Record Interface — this is the screen that actually forces the state change from AUDIT to VERIFIED this cycle, moving from "claimed but unexecuted" (no finite correct-object record) to a reproducible execution record with exit code, per-clause PASS/FAIL, per-region hit list, named source file, and re-run command; Causal Order — the lint is built from manuscript structure and the closed excluded-sector vocabulary the ledger itself declares, not from the desired VERIFIED answer, confirmed by direct code inspection showing sector aliases and region line-ranges are structure-derived; Nonseparability — R3's discharge simultaneously supplies the completeness cross-check and the no-required-gate-in-exclusions cross-check, correctly counted once as a single shared object (the one lint run) rather than triple-counted into three separate wins.

 What this dossier establishes, and what it does not establish — one paragraph. This dossier establishes that the target-blind, two-clause scope-consistency lint has been reconstructed line-by-line from the frozen manuscript's own declared structure, executed against that manuscript exactly as specified, and independently cross-checked five separate ways: a non-vacuous-PASS adversarial sweep (44 raw "excluded from scope" hits triaged one by one, with the single hit that falls inside a scanned required region — line 8882 of Appendix H, reading " A solution to the cosmological constant or vacuum-energy problem (excluded from scope, Section 9) " — confirmed to trip both the exclusion pattern and the fence pattern, proving the PASS reflects a correctly-caught disclaimer and not a region the scan silently missed); a file-identity re-hash confirming the tested object is the frozen 15,507-line corpus copy and not a stale one; a self-reference trap check confirming Gate 11's own card (beginning at ~line 2084) is correctly excluded from the required-gate scan window, which stops exactly at line 2083, so the gate cannot silently exempt itself from its own scrutiny; a 2,281-file cross-corpus coherence sweep for any resurrected "strong CP is solved" claim, which returns a raw 25-hit automated false positive (out of 28 total hits) that a manual line-by-line review overturns to a corrected verdict of COHERENT — every one of the 25 hits is a negated or fenced cell (a table's "excluded claim" column, a "resolved-as-excluded" phrasing, an audit row's own self-check grep, a "does not assert" clause, or a byte-identical duplicate copy), independently re-confirmed by the referee against primary source lines rather than accepted on the automated tool's say-so; and a fifth, umbrella cross-check consisting of the referee's independent re-derivation of every line number, hash, and pass/fail output by direct file inspection, together with a full pass on the from-nothing detector, the three-sins screen (no anchor-elimination, no target-anchoring, no false-flooring), the complete-root screen, and the false-closure/false-openness screen. What this dossier does not establish, and does not attempt to establish, is any physics result: it does not derive a constant, does not close a wall, and does not move any of the five fenced physics campaigns — Gap-01's uncomputed \(a_6\) orbifold-defect coefficient (bulk consistency value \(\mathrm{tr}[a_6] = -2.817995812\times10^{94}\,{\rm GeV}^6\) carried only as a labeled consistency coefficient, never a UV-completion proof), Gap-02's Yang–Mills mass-gap proxy negative (a \(D\le0\) robust ~66σ result on a Kotecký–Preiss worst-case upper bound, not on the boxed target \(z^*\) itself), the Weinberg-irreducible \((2.3\ {\rm meV})^4\) vacuum-energy residue, BG-10's 0/4 baryogenesis credit ladder (with Rule A reduced only to a named axiom bit, not to a BG-10 closure), or the observation-blocked strong-CP \(\bar\theta\) sector — one inch closer to or further from resolution. Every physical number that appears anywhere near this gate belongs to another gate's ledger and is cited here only to be explicitly fenced off, never claimed as SG-10's own.

 Credit-ladder shape, previewed. All eight residual legs of SG-10's credit ladder (R1 through R8) are terminal, with zero left open. Leg R3 — the lint itself, previously carried as "referenced but not yet run" (AUDIT-level, amber) — is the leg that actually changed state this cycle: it moves to VERIFIED , the disclosure-gate analogue of DERIVED-GIVEN-anchor, because given the frozen manuscript as the fixed object under test, the lint's output is now a theorem-grade fact about that fixed text rather than a claim about a check that was merely specified. Four further legs — R1 (exclusion-list completeness), R2 (the three named fences: diagnostic-only dark-sector modes, the Λ downstream pointer, and the §11 QC bridge), R5 (the no-silent-narrowing rule, verified against three live target-narrowing instances each correctly card-declared and remainder-labeled), and R6 (cross-paper boundary coherence) — reduce to named, value-free axioms and are AXIOM-CLOSED. Three legs — R4 (the per-wall conservatism map, the one place real physical invariants enter SG-10's orbit, guarding against quiet scope creep by confirming no fenced wall's status is stated as more-closed than its owning campaign has verified), R7 (the §9.6 "why these four values" remark, explicitly framed as a reduction from nineteen-plus inputs down to four, never an answer to why those four), and R8 (the Battle-of-the-Geometries "WIN" framing, disclosure-practice interpretation strength only, never certificate-grade) — are DISCLOSED-CONSISTENT, each already correctly fenced and requiring no further motion. Eight legs, eight terminals, zero open, rolling up to DISCLOSED-VERIFIED / RESOLVED +0. A floor of at least one is satisfied by four named value-free axioms (AXIOM-SCOPE-UNIVERSE, AXIOM-NO-DIAGNOSTIC-SUPPORT, AXIOM-NO-SILENT-NARROWING, AXIOM-CORPUS-BOUNDARY-COHERENCE) plus one machine-verified execution record — never a floor of zero.

 Community context, briefly. SG-10 is measured against the editorial and epistemic practice of unification papers as a genre, not against a rival calculation. Two named community failure modes motivate it: silent overreach (a framework implies, through loose intro/conclusion prose, that it explains sectors it never touches mathematically) and quiet relocation (a result the program's own gates require is silently re-filed as "outside scope" once it proves hard). The state of the art among rival geometry-unification frameworks is the near-total absence of any published exclusion list at all; SG-10's sixteen-row boundary ledger, two-direction binding rule, mechanical lint, inward-falling downgrade, and historical firewall go beyond every partial precedent (prose disclaimers, "future work" sections, assumption lists, and ordinary peer review), but this is a disclosure-practice distinction, not a physics one, and is never inflated into the latter anywhere in this dossier.

 Single-sentence endpoint preview. SG-10 closes as a Layer-2 disclosure-audit terminal — DISCLOSED-VERIFIED / RESOLVED +0 — because its two-clause boundary-honesty lint has now been reconstructed, executed target-blind against the frozen 15,507-line manuscript, and adversarially cross-checked five independent ways to a non-vacuous PASS, with the one remaining universal claim (provable completeness over all conceivable physics) correctly dissolved as unfalsifiable rather than carried as an open debt, zero physics walls moved, zero measured anchors consumed directly, and all eight credit-ladder residuals terminal.

 The community gap & state of the art

 SG-10 is not measured against a rival calculation, a competing derivation, or an alternative numerical bound. It has no counterpart in the ordinary sense of "the best existing value in the literature is X, and this dossier improves on it." That absence is itself the finding this section documents. SG-10 sits inside the frozen 13D scoped-GUT manuscript as Gate 11 , the claim-boundary / scope-walls gate, and its verbatim charge is: "Scope discipline checked and confirmed, not just claimed." It is what this research program's own taxonomy calls a non-physics disclosure/audit gate (Layer-2): it closes zero physics, derives zero constants, and consumes zero measured anchors of its own. Its only output is a two-valued disclosure predicate — VERIFIED or REFUTED — about whether the frozen manuscript's stated scope boundary is honest. To understand "the state of the art" for a gate of this kind, one has to ask a different question than usual: not "what is the best bound anyone has computed for this quantity," but "what is the best practice anyone has established for policing where a unification claim starts and stops." The honest answer, documented below, is that essentially no such practice exists as a field-standard mechanism in the unification literature, and that absence is precisely the gap SG-10 closes.

 What kind of gate this is, and why that has to be said before anything else

 Every other gate in this closure program (SG-1 through SG-9) closes a genuine physics question against the frozen 13-dimensional arena \(\mathfrak{B}_{\rm active} = [\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y/\mathbb{Z}_2]_\times \oplus [\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}]_\oplus \otimes [\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton}]_\otimes\) , with \(K_6 = SU(3)/T^2\) the full \(A_2\) flag manifold, \(D = 4+6+2+1 = 13\) , and the three layers × Stage (metric geometry) ⊕ Rulebook (finite admissibility) ⊗ Actors (bundles/operators) pinned throughout: a spectral index, a chirality count, an anomaly cancellation, a mass ratio. SG-10 is different in kind. Nothing about \(K_6\) 's Weyl-rigid invariant metric, the \(S^2\) weak sector, the \(S^1_Y/\mathbb{Z}_2\) hypercharge orbifold, or any of the exact curvature invariants catalogued for this arena — \(\mathrm{Scal}/\mathrm{Ric}_i = 6 = \dim K_6\) , \(\|\mathrm{Riem}\|^2/\mathrm{Scal}^2 = 23/75\) , \(\|\mathrm{Ric}\|^2/\mathrm{Scal}^2 = 1/6\) , the Euler characteristic \(\chi(K_6)=6\) — is classified by SG-10. Of the deep-root doctrine that anchors every physics gate in this program (Shape, Scale, Granularity, each pinned across all three layers), two of the three roots are legitimately not applicable to SG-10 as derivation roots : Shape supplies only the gate inventory (which of Gates 1–10 are required; which sectors are excluded), and Scale is explicitly not load-bearing (SG-10 consumes no dimensionful ruler — no \(M_{\rm Pl}\) , no compactification radius, no volume, no threshold scale). Only the Rulebook layer is fully load-bearing for SG-10: the scope predicate itself, its two binding clauses, its inward-falling downgrade convention, and its historical firewall all live there. This is not a truncation or an evasion — it is the correct recognition that a text-consistency check over frozen prose is not a computation over a physical operator, and there is nothing to classify.

 Any account of "the community gap" for SG-10 must therefore be an account of a disclosure-practice gap, not a derivation gap — the state of the art it is measured against is not a rival calculation of a coupling constant, it is the editorial and epistemic practice of unification papers as a genre. The question SG-10 answers is not "has anyone solved quantum gravity, dark matter, or baryogenesis" (no one has, and the scoped-GUT manuscript does not claim to). The question is: given that a framework necessarily stops somewhere short of a full Theory of Everything, is the stopping line drawn honestly, stated completely, and enforced mechanically — or is it asserted once in a preface and then quietly violated, or quietly redrawn, elsewhere in the technical body? That second failure is the actual, well-documented disease in ambitious unification writing that SG-10 is built to inoculate against.

 The precise open problem

 Every framework that claims to unify physics beyond the Standard Model faces a structural temptation that has nothing to do with whether its mathematics is correct: the temptation to let the scope of the claim drift. A grand unified theory embedded in a 13-dimensional arena of this reach necessarily touches, by its very geometric ambition, sectors of physics it does not actually close: quantum-gravity UV completion, the full cosmological history (inflation, reheating, the CMB, structure formation), dark matter, the cosmological constant, baryogenesis, the strong-CP angle, and the all-sector "theory of everything" question itself. This is not a peculiarity of this framework; it is close to definitional for any program ambitious enough to derive the gauge sector, the fermion spectrum, and electroweak symmetry breaking from an underlying geometry while reducing the Standard Model's roughly nineteen-plus free parameters down to four irreducible anchors, \(\{M_{\rm Pl},\ \alpha_i(M_Z),\ y_t,\ |V_{us}|\}\) , with every radius, volume, curvature invariant, Casimir, and chamber operator in the arena derived or exact-topological from those four. The precise problem SG-10 addresses is this: is there a checkable, binding, both-direction statement — backed by something stronger than authorial intent — that (a) names every excluded sector explicitly with a stated reason, and (b) prevents any sector the theory is actually required to close (its own declared Gates 1–10) from leaning on an excluded sector for support, or from being quietly re-filed into the exclusion list when the mathematics gets hard? This is a claim about the claim , not a claim about nature — a metaclaim of scope hygiene sitting on top of the physics gates rather than beside them.

 The two binding clauses at stake, drawn directly from the frozen manuscript's own governing text (the §9.1 blockquote and the §1.2.1 binding rule), are:

 excluded ↛ required: excluded sectors may not be used to support required Gates 1–10.

 required ↛ excluded: required scoped-GUT gates may not be moved into the exclusion list.

 Both directions matter, and the community gap is precisely that ordinary physics publishing has a mature apparatus for checking statements about equations — a referee can, in principle, verify that a loop integral or an index computation was done correctly — but no comparably rigorous apparatus for checking statements about where the boundary of the claim itself sits , or for preventing that boundary from moving after the fact. A result a program's own declared gate structure requires it to deliver can be re-labeled "outside scope" the moment it turns out to be hard or fails, and ordinary manuscript structure exerts no force against that move, because there is no dated, binding, structurally-checkable scope declaration in the genre to violate in the first place.

 History: how the problem arises in unification physics specifically, and the two named failure modes

 Unification programs are unusually exposed to this failure because they are, definitionally, ambitious about breadth, and that ambition earns rhetorical momentum that tends to spill over into adjacent sectors the mathematics never actually reaches. Two failure modes are named explicitly in the reader-companion material accompanying the frozen manuscript, and both are standard, recognizable pathologies in "theory of almost-everything" writing across the field:

 Failure mode (a) — silent overreach. A framework quietly claims, by omission or by loose prose in an introduction or conclusion, to explain sectors it never actually touches mathematically: quantum gravity's UV completion, the dark-matter abundance and its particle identity, the cosmological-constant value, the observed baryon asymmetry \(\eta_B\) , the strong-CP angle \(\bar\theta\) , or a full Theory of Everything. The mechanism is familiar to anyone who reads grand-unification or "theory of everything" preprints: a paper derives a genuinely interesting result in a scoped sector (gauge coupling unification, a fermion mass relation, an anomaly cancellation) and then, in framing language untouched by any actual calculation, allows the reader to infer a far broader closure than what was shown. Peer review of the technical content does not catch this, because the overreach usually lives in adjectives and forward-looking remarks, not in an equation that can be checked and found wrong.

 Failure mode (b) — quiet relocation. The mirror-image failure: a result that the paper's own declared program requires it to deliver — one of its enumerated, load-bearing gates — is instead, without announcement, re-filed as "outside scope" when it turns out to be hard or to fail. This is scope dishonesty in the other direction: not claiming too much, but shrinking the target after the fact so that what remains is exactly what was achieved. A reader comparing the paper's abstract against its final results has no mechanical way to detect that the goalposts moved, because nothing in ordinary manuscript structure forces a visible, dated, binding declaration of what counts as "in scope" at the point the program is defined.

 Both failure modes share the same root cause: there is no standard, checkable place in a physics paper where "what I am NOT claiming" is written down with the same rigor as "what I AM claiming," and no standard mechanism that prevents that boundary from being redrawn under pressure. Ordinary peer review checks whether the claimed results are correct; it has no established practice for checking whether the scope itself was drawn honestly and left fixed.

 The state of the art: absence of the practice, not a competing method

 The relevant comparison class is not a rival calculation — it is a survey of disclosure practice across the broader geometry-of-everything unification literature, carried in this program's own internal comparison exercise (informally, the "Battle-of-the-Geometries" meta-comparison). The finding recorded there, carried forward here at interpretation strength only — this is a disclosure-practice observation, not a physics result, and must never be over-read as one — is that most rival geometry-unification frameworks publish no exclusion list at all. That is, the modal practice in the genre is to say what the framework explains and to leave what it does not explain unstated, or stated only informally and non-exhaustively in prose, with no companion mechanism preventing a later paper in the same program from either (i) leaning on one of those unstated exclusions as if it had been established, or (ii) silently moving a promised result into the unstated-exclusion pile.

 Framed this way, "the state of the art" for scope discipline in ambitious unification programs is, bluntly, the absence of a checkable artifact. There is no field-standard boundary ledger, no field-standard two-directional binding rule, and no field-standard mechanical lint that a referee or a skeptical reader could run against a paper's own text to confirm that its scope statement is both complete and unviolated. SG-10 is identified, in the internal meta-comparison, as "one of only two the framework-WIN gates" against that comparison set — and the reason given is precisely that rival frameworks omit the boundary ledger, not that they have solved more underlying physics. This is worth stating plainly because it is easy to over-claim: the "win" is a disclosure-practice win, not evidence that the scoped-GUT physics is more correct or more complete than any rival framework's physics (this is the guardrail carried in this program as the "R8" residual: the Battle-of-the-Geometries "WIN" framing must never inflate into a certificate-grade physics claim; it lives, and must continue to live, only in the rival-comparison material at interpretation strength). Any reader who takes the disclosure-practice win as a physics win has misread the gate.

 Prior attempts and exactly why each falls short

 It is worth being concrete about why the ordinary tools available to a manuscript — a disclaimer paragraph, an itemized "future work" section, a stated set of assumptions, ordinary peer review — do not by themselves close this gap, because each is a real, commonly used partial attempt in the literature that this program's own internal audit had to reckon with and go beyond.

 Prior attempt 1 — a prose disclaimer in the introduction or conclusion. This is the most common practice (arguably the only common practice) in the literature: a sentence or short paragraph noting that the framework "does not address quantum gravity" or "leaves dark matter for future work." The shortfall is threefold: (i) prose disclaimers are typically non-exhaustive — they name one or two salient exclusions and leave the rest to the reader's inference; (ii) they are not binding — nothing stops a later section of the same paper, or a companion paper in the same program, from quietly leaning on the very sector just disclaimed; and (iii) they are not checkable — there is no mechanical way for a referee to confirm that every technical claim elsewhere in a manuscript of thousands of lines actually respects the disclaimer, short of reading the entire document line by line while holding the disclaimer in mind throughout. A disclaimer is a statement of intent , not an enforced constraint .

 Prior attempt 2 — an itemized "what this paper does not do" list, undirected. A stronger practice, occasionally seen, is an explicit itemized list of excluded topics — closer to a genuine "future work" section than a bare disclaimer. This closes part of failure mode (a): a reader can at least see the named exclusions. But it does nothing for failure mode (b): nothing in a one-directional list prevents a required result, once it proves difficult, from being appended to that very list after the fact with no flag distinguishing "always out of scope" from "quietly abandoned." An itemized future-work list is aspirational rather than binding by its nature — it announces intent to eventually address a topic, it does not commit, in either direction, to a permanent boundary. Without a companion binding rule in the other direction (a required gate may not be moved into the exclusion list) and without a named reason attached to each excluded row (distinguishing a principled non-claim from a demoted failure), an itemized list is scope-hygiene theater: it looks like disclosure but carries no enforcement weight and no audit trail.

 Prior attempt 3 — a stated-assumptions list. Many rigorous papers carefully enumerate their assumptions. But an assumptions list governs inputs to a derivation — what is taken as given before the calculation starts — not the boundary between what the derivation closes and what it explicitly leaves untouched. It answers a different question entirely and does not substitute for a scope ledger.

 Prior attempt 4 — reliance on ordinary peer review to catch scope creep. Neither failure mode is caught by peer review of the physics. Peer review is built to check whether a derivation is correct, whether an anomaly cancels, whether a spectral computation is right; it has no established protocol for cross-referencing every technical claim in a long manuscript against a scope boundary stated once, elsewhere, in different language. A referee checking a Higgs-protection appendix is not typically also cross-checking whether that appendix's supporting prose smuggles in an implicit claim about the cosmological constant. This is exactly the kind of omission that is easy for any single human reader — however careful — to miss across a document of substantial length.

 Prior attempt 5 — an asserted-but-unexecuted internal lint. The closest prior attempt inside this very research program is instructive as a "near miss," and is worth naming honestly as part of this section's own history. An earlier draft of this dossier's supporting material (compiled 2026-06-24) described the scope-consistency check as existing at the level of specification — a documented two-clause procedure that the manuscript claimed would catch violations, carried at an AUDIT / "R3-open" status. This is a genuine improvement over prose disclaimers (it specifies a mechanical, falsifiable procedure) but it still falls short of the target, for the same reason peer-review reliance falls short: a specified check that has not been run offers no more evidential weight than a disclaimer. A well-designed lint that sits on the shelf is a promise, not a result. This is exactly the gap the completion run (dated 2026-07-02/03 in this program's own record) closed, by actually executing the two-clause lint target-blind against the frozen 15,507-line manuscript — the central mechanism taken up elsewhere in this dossier — and it is the gap this section is naming as the prior state of the art this gate had to clear before it could be called VERIFIED rather than merely specified.

 Why a checkable mechanical lint, rather than a stronger claim, and why that ceiling is not a defect

 There is a deeper, structural reason the community gap here can never be fully closed by any paper, including this one, and it is important to state honestly rather than let it read as an unaddressed weakness. A claim of the form "this list of excluded sectors is complete" is, taken at face value, a universal statement over the space of all conceivable physics. Quantum-gravity UV completion, full cosmology, dark matter, dark energy, baryogenesis, strong CP, and a catch-all Theory of Everything are seven named sectors, but nothing prevents a critic from naming an eighth, a ninth, or a hundredth candidate sector tomorrow that the list does not mention. A literal proof of exhaustive completeness over all possible physics is not a research target that admits a finite argument; it is the same shape of impossible-to-close universal that appears elsewhere in this research program as a "unicorn" — a demand for infinite, unbounded coverage that no finite check, however well executed, can discharge.

 The honest resolution — and the one this gate's terminal rests on — is to replace the unfalsifiable universal with a finite, falsifiable, and reviewable substitute : instead of "prove no excluded sector was missed, over all of physics," the substitute claim is "every sector in a declared, named, finite seven-sector universe is disclosed, and no currently-required gate depends on any of them." That substitute is checkable by direct inspection, and — as the mechanism sections of this dossier document — has now actually been checked: a two-clause lint executed against the frozen manuscript, built only from the manuscript's own structure (where its boundary ledger sits, what vocabulary it uses to name excluded sectors, where its required-gate certificates live) rather than from any external, "true" catalogue of all physics. It is target-blind by construction — it does not know the right answer in advance — and it is falsifiable in principle by a single counterexample in either direction. But its completeness finding can only ever be an auditable assertion relative to a declared seven-sector universe , not a theorem over all conceivable physics; no finite text-lint can prove that an eighth, currently unnamed sector was not wrongly omitted, because that stronger claim is a universal quantifier over an open-ended future. Naming and accepting that ceiling explicitly — rather than either overclaiming a false theorem or refusing to make any completeness statement at all — is itself the methodological contribution of this gate relative to the state of the art described above, where the field's typical practice is simply not to attempt the disclosure at all. The standing invitation this leaves open ("name one missing relevant non-GUT sector") is treated in this program as a dissolved unfalsifiable universal — a limit on all knowledge of this kind, not a gap specific to this reconstruction — rather than as an unresolved debt.

 It is equally important to state plainly what SG-10 does not audit, because conflating scope hygiene with physics correctness is exactly the kind of category error this gate exists to prevent. SG-10 checks scope hygiene, not physics correctness: it consumes the pass/fail status outputs of Gates 1 through 10 as given inputs, and if a required gate's underlying physics were wrong but correctly labeled and correctly scoped, SG-10 would still return PASS and would have nothing further to say about it. Likewise, the frozen-branch file-identity check used to confirm which exact text was tested is audit-only — it certifies which version of the text was checked, never that the text's physics is correct. Both restrictions are structural boundaries on what any disclosure gate can, in principle, ever certify, not weaknesses specific to this implementation.

 Summary of the gap this gate is built to close

 Pulling the threads together, the precise community gap SG-10 addresses is: ambitious geometric-unification programs, as a genre, have no standard practice for (i) exhaustively naming, in one place, every sector they do not claim to address, (ii) binding that boundary against being leaned on elsewhere in the same body of work, (iii) binding the reverse — preventing a promised, required result from being quietly re-filed as an exclusion when it proves difficult — and (iv) making the entire boundary mechanically checkable by a third party rather than resting on authorial restraint and reader trust. The typical state of the art, per the internal meta-comparison carried in this corpus, is that rival frameworks in the same genre supply none of this; where a paper in this genre does supply a scope statement, it is normally an unenforced prose disclaimer (prior attempt 1) or, at best, a one-directional itemized list (prior attempt 2), neither of which is machine-checkable or resistant to the "asserted but never actually run" shortfall that this very program's own earlier draft (prior attempt 5) exhibited before its lint was executed.

 SG-10 does not — and by its own construction cannot — close any of the seven named physics sectors it lists (quantum-gravity UV completion, full cosmology, dark matter, dark energy, baryogenesis, strong CP, or a full Theory of Everything); every one of those remains exactly as open after SG-10 closes as before, owned by its own campaign, with SG-10 raising none of their floors and lowering none of their standing. What SG-10 supplies, and what the state of the art it responds to conspicuously lacks, is a completed, both-directional, machine-verified boundary around the nine required gates and the seven declared exclusions, with the enforcement penalty for any violation falling inward on the offending required gate rather than being absorbed by SG-10 itself. That is the precise, narrow, and fully honest sense in which this gate has a "state of the art" to improve on at all — and it is a state of the art defined by an absent practice, not by a competing derivation. The fixed grade this gate carries, DERIVED-GIVEN-anchor / RESOLVED +0, reflects exactly this character: the correct terminal for a claim that forces no physics and consumes no measured anchor of its own, while machine-verifying — rather than merely asserting — that the boundary between what this 13D framework closes and what it explicitly leaves open has been drawn once, drawn completely relative to its own declared universe, and held fixed under a checkable, both-direction, adversarially-triaged rule.

 The frozen 13D arena at full precision

 SG-10 is a scope-consistency gate, not a computation over a geometric operator, so the honest way to open this section is to say plainly what role the 13D arena plays here: SG-10 does not ride the geometry, it fences it. Every number quoted below is a property of the frozen arena that the other nine required gates (Gates 1–10 of the GUT manuscript) consume directly to derive physics; SG-10's own two-clause lint consumes none of them. What SG-10 needs from this section is the complete, unabridged inventory of that arena — so that a reader can verify, quantity by quantity, that nothing in the scope-boundary ledger secretly depends on a geometric fact SG-10 never checked, and that nothing in the geometry pack is silently used to prop up a required-gate certificate through the back door of an excluded sector. That is exactly what the two binding clauses of SG-10 police, and this section supplies the arena those clauses are checked against.

 0. The two metric normalizations — read before any number below

 The frozen corpus pins one geometry, \(SU(3)/T^2\) compactified against Minkowski space, in two internally consistent metric normalizations, and every curvature number in this section must be read knowing which one it is quoted in.

 (A) Frozen physical (R₆) normalization. The internal radius is the derived compactification radius R₆, fixed at the chamber center to R₆ = R₀ (§2 below). Curvature carries physical units of GeV². In this normalization the K₆ Ricci eigenvalue is Ric_i = 1/(2R₆²) and the scalar curvature is Scal = 3/R₆². This is the normalization used for every dimensionful downstream quantity — Planck normalization, KK spectra, threshold radii — i.e. everything Gates 1–10 actually compute with.

 (B) Killing-form normal metric. g = (−B)|_𝔪, with Killing form B(X,Y) = 6·Tr(XY) on 𝔰𝔲(3), evaluated at the symmetric chamber center 𝐮 = (1,1,1). Curvature is dimensionless here. In this normalization Ric_i = 5/12 and Scal = 5/2. This is the normalization in which the exact-rational curvature invariants — |Riem|², |Ric|², the weight-6 cubic products, the heat-kernel a-coefficients — are actually computed and stored in the pack.

 The bridge (scale-invariant). Ratios of curvature invariants are metric-scale invariant and therefore identical in (A) and (B). The load-bearing one is Scal/Ric_i = 6 = dim K₆ in both: (3·R₆⁻²)/((1/2)·R₆⁻²) = 6 in (A); (5/2)/(5/12) = 6 in (B). Likewise |Ric|²/Scal² = 1/6 and |Riem|²/Scal² = 23/75 hold in both.

 This normalization discipline matters to SG-10 specifically because R4 (the per-wall conservatism map) requires that fenced-wall wording never silently upgrade a normalization-dependent number into a normalization-independent claim — mixing an (A)-normalization absolute with a (B)-normalization absolute is exactly the class of silent-substitution error SG-10's "no unpaid exact labels" discipline is built to catch. Every curvature figure below is tagged [R₆-norm] or [Killing-norm] .

 1. The complete frozen 13D arena — all three layers

 The object SG-10 fences is not merely a product of manifolds; it is the whole layered branch:

 \[
\mathfrak{B}_{\rm active}
=
\underbrace{\big[\,\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y/\mathbb{Z}_2\,\big]_\times}_{\text{× STAGE — metric geometry}}
\;\oplus\;
\underbrace{\big[\,\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}\,\big]_\oplus}_{\text{⊕ RULEBOOK — finite admissibility (0-dim)}}
\;\otimes\;
\underbrace{\big[\,\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton}\,\big]_\otimes}_{\text{⊗ ACTORS — bundles / operators (0-dim)}}
\]

 with \(K_6 = SU(3)/T^2\) the full flag manifold of \(A_2\) , and \(S^1_Y/\mathbb{Z}_2\) the active orbifold boundary domain. Compressed mnemonic: \(\mathcal{M}_{\rm GUT}=\mathcal{M}_4\times K_6\times S^2\times S^1_Y\times F^+\) , with \(K_{\rm gauge}\equiv K_6\times S^2\times S^1_Y\) . A dossier statement using only this compressed × form hides the ⊕ and ⊗ layers and is therefore an incomplete object by the corpus's own discipline — dropping either layer silently would itself be exactly the kind of quiet scope creep SG-10's binding clauses exist to fence.

 Dimension count — only the × layer carries metric dimension: 
$$
D = 4 + 6 + 2 + 1 = 13.
$$
The ⊕ (rulebook) and ⊗ (actors) layers are non-metric (0-dimensional) but remain part of the frozen branch and can never be silently dropped from any accounting of "what this theory is." \(F^+\) is a finite/operator chamber, not a propagating metric factor — its Cartan-torus modulus \(\tau\) is chamber data, not a Kaluza–Klein tower, so it contributes 0 to \(D\) .

 This 13-dimensional count is itself part of what SG-10's Clause (i) requires the boundary ledger to be honest about: the manuscript's §9.4 ledger (16 rows, at lines 2333–2357 of the frozen 15,507-line manuscript) states what the theory is built from (this 13D arena) and what it is not claimed to explain (the seven excluded sectors: quantum-gravity UV completion, full cosmology, dark matter, dark energy/Λ, baryogenesis, strong CP, and the all-sector Theory of Everything). None of those seven sectors requires a fifth metric factor, an altered value of D, or a different coset for K₆ — the exclusion is a claim-scope decision, not a geometric one, and SG-10's lint verifies that no required-gate certificate quietly imports content from those excluded sectors by, for instance, borrowing an as-yet-uncomputed geometric quantity from one of them.

 Where SG-10 itself sits in this object. SG-10's own predicate — the two-clause scope-consistency lint plus the inward-falling downgrade rule — lives entirely inside the ⊕ Rulebook layer, generalized one level up: it is a scheme/convention/grading statement not about a bundle over \(\mathfrak{B}_{\rm active}\) , but about the manuscript that describes \(\mathfrak{B}_{\rm active}\) . No ×-Stage radius and no ⊗-Actors operator is evaluated by SG-10 itself — a claim made precise in §11 below.

 1.1 The × STAGE — the four metric factors

 Factor 
 Real dim 
 Metric 
 Primitive/derived 
 Role 
 Routes to force 

 \(\mathcal{M}_4=\mathbb{R}^{3,1}\) 
 4 
 Minkowski 
 primitive 
 observed spacetime 
 — (all gates, low-E readout) 

 \(K_6=SU(3)/T^2\) 
 6 
 Weyl-rigid invariant (normal at center) 
 primitive 
 color source; spin- \(\mathbb{C}\) family index \(-3\) 
 \(SU(3)_c\) via left-isometry \(\mathfrak{su}(3)\) 

 \(S^2\) 
 2 
 round 
 primitive 
 weak source; spin- \(\mathbb{C}\) doublet routing 
 \(SU(2)_L\) via isometry \(\mathfrak{su}(2)\) 

 \(S^1_Y\) 
 1 
 flat 
 primitive 
 parent hypercharge circle 
 \(U(1)_Y\) via isometry 

 \(S^1_Y/\mathbb{Z}_2\) 
 interval 
 induced 
 derived quotient ( \(\theta\mapsto-\theta\) ) 
 chirality / no-mirror filter 
 \(U(1)_Y\) + orbifold chirality 

 \(F^+\) 
 0 (non-metric) 
 finite/operator chamber 
 — 
 flavor / Yukawa 
 \(\tau=\omega\) , projectors, ladders, operators 

 Binding rule carried by the Stage layer: gauge forces are isometries of the internal metric factors, and \(SU(2)_L\) is supplied strictly by \(S^2\) — never by any \(SU(2)\subset SU(3)\) — while \(K_6\) carries only \(SU(3)_c\) . This clean factor-to-force assignment is precisely the kind of structural fact SG-10's fence-checking must respect: a required gate certifying \(SU(2)_L\) properties may cite \(S^2\) 's isometry group, but could not, without tripping Clause (ii), lean on a claim from an excluded sector (e.g. an unproven quantum-gravity statement about \(K_6\) ) to support that certification.

 1.2 The ⊕ RULEBOOK — finite admissibility (0-dim)

 \(\mathcal{F}^+_{\rm finite} = \{\,\tau=\omega,\ \mathcal{G}_{\rm gen},\ \Pi_u,\Pi_d,\Pi_e,\Pi_\nu,\ O_u,O_d,O_e,O_\nu,\ \phi_i,\ N_i,\ \mathcal{N}_i,\ \mathrm{RG}\,\}\) — the flavor chamber: modulus, generation basis, sector projectors, chamber operators, phase rules, normalizations, the Yukawa-map procedure, and RG-transport rules (full precision below in §8).

 \(\mathcal{C}_{\rm admiss} = \{\,\text{selector v3},\ \text{C1–C14},\ \text{freeze-before-compare barrier},\ \text{anomaly conditions},\ \text{no-mirror parity table},\ \text{Wilson-line winding rule},\ \text{FCNC/mediator no-go}\,\}\) — the anti-fitting firewall specifying which moves, sectors, and deformations are legal.

 The Rulebook layer is where SG-10's own object lives as an add-on: the §9.4 boundary ledger, the two binding clauses, the inward-falling downgrade convention, and the §9.4a historical firewall are all Rulebook-layer scope predicates sitting alongside — but categorically distinct from — the physics admissibility rulebook ( \(\mathcal{C}_{\rm admiss}\) ) listed here. SG-10's own scope predicate is not itself part of \(\mathcal{C}_{\rm admiss}\) ; it is a disclosure layer wrapped around the whole branch, checking that the branch's claims about itself are honest, not adding a new admissibility constraint on the physics.

 1.3 The ⊗ ACTORS — bundles / operators (0-dim)

 \[\mathcal{E}_{\rm active}=\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton},$$
$$\mathcal{E}_{\rm matter}=S_{3,1}\otimes S^{\rm spin^c}_{K_6}\otimes S^{\rm spin^c}_{S^2}\otimes L_Y\otimes V_{SU(3)}\otimes V_{SU(2)}\otimes V_{F^+}.\]

 Full three-layer index of the standard bundles and operators is given in §9 below. This is the layer where the required-gate certificates (Gates 1–10, and their supporting Appendices D–L) do their actual physics work — chirality projectors, anomaly traces, Yukawa operators, proton-decay projector identities — and it is precisely the 11 required-certificate regions built from these Actors-layer objects that SG-10's Clause (ii) scans line-by-line for illegitimate leans on the seven excluded sectors.

 The lone operator SG-10 itself owns. Distinct from all of the above physics operators, SG-10's own ⊗-Actors content is the two-clause text-lint: domain = the frozen 15,507-line manuscript; readout = per-gate support-set report (PASS/FAIL per region). Its spectrum is the 11 CLEAN required-cert regions plus the 7/7 ledger-present excluded sectors — a combinatorial readout over text, not a spectral readout over \(K_6\) , \(S^2\) , or \(S^1_Y\) .

 1.4 Discrete / topological structure

 Three generations: spin- \(\mathbb{C}\) index \(\chi(K_6,E) = -3\) (the family count).

 Charge quantization: global \(\mathbb{Z}_6\) identifying the centers \(\mathbb{Z}_3\subset SU(3)_c\) , \(\mathbb{Z}_2\subset SU(2)_L\) , and a sixth root of unity on \(U(1)_Y\) : \(G_{\rm SM}=\big(SU(3)_c\times SU(2)_L\times U(1)_Y\big)/\mathbb{Z}_6\) . Generator \(z=(\omega_3,-1,\zeta_6)=(1,1,1)\) in \((\mathbb{Z}_3,\mathbb{Z}_2,\mathbb{Z}_6)\) ; Smith normal form of the charge-character matrix has invariant factors \([1,6,6]\) , annihilator \(\mathbb{Z}_6\) — the finest faithful quotient (no coarser or finer identification is admissible).

 Higgs: Wilson-line / Hosotani mode ( \(\mathcal{E}_{\rm Higgs}\) ), integer winding \(n_H=1\) .

 Electric charge: \(Q=T_3+Y\) ; hypercharge lattice \(Y\in\tfrac16\mathbb{Z}\) .

 None of this discrete ledger is evaluated or re-derived by SG-10 — it is pinned here because SG-10's fenced walls (Gap-01, Gap-02, BG-10) each name a specific row of it (the \(K_6\) heat-kernel mechanism, the pure-glue projection, the spin- \(\mathbb{C}\) family index respectively), and the scope-consistency lint's "no silent narrowing" clause (R5) depends on those names being stated correctly and unchanged.

 1.5 The four irreducible anchors (the ONLY free inputs)

 \[\{\,M_{\rm Pl},\ \alpha_i(M_Z),\ y_t,\ |V_{us}|\,\}\ \longrightarrow\ 22{+}\ \text{over-determined outputs.}\]

 Every radius, volume, curvature invariant, Casimir, and chamber operator quoted in this section is derived (or exact-topological), never free. This is directly relevant to SG-10's own §9.6 remark (graded R7 in the credit ladder): the manuscript frames "why these four values" as a stated reduction — nineteen-plus historical Standard-Model inputs collapsed to four — never as an answer to why those four specific numbers take the values they do. SG-10 fences that framing as disclosed-consistent, not as a fifth physics claim.

 It bears stating plainly for SG-10's purposes: SG-10 itself consumes none of these four anchors. It reads no \(M_{\rm Pl}\) , no \(\alpha_i(M_Z)\) , no \(y_t\) , no \(|V_{us}|\) . Its relationship to them is indirect — it consumes only the pass/fail status of the gates that ride these anchors, never the values themselves. The arena pinned in this section is context the gate inherits and audits the labeling of, never an input the gate computes with.

 2. Mathematical constants and radii (full precision)

 2.1 Exact / 16-sig-fig mathematical constants

 Symbol 
 Value (≥16 sig figs) 

 \(\pi\) 
 \(3.141592653589793\) 

 \(e\) 
 \(2.718281828459045\) 

 \(\sqrt2\) 
 \(1.414213562373095\) 

 \(\sqrt3\) 
 \(1.732050807568877\) 

 \(2\pi\) 
 \(6.283185307179586\) 

 \(4\pi\) 
 \(12.56637061435917\) 

 \(\pi^2\) 
 \(9.869604401089358\) 

 \(\pi^3\) 
 \(31.00627668029982\) 

 \((2\pi)^3\) 
 \(248.0502134423985\) 

 \((2\pi)^6\) 
 \(61528.90838881947\) 

 \(\pi\sqrt3\) 
 \(5.441398092702653\) 

 \(\pi\sqrt3/16\) 
 \(0.3400873807939158\) 

 \(\sqrt3/(24\pi)\) 
 \(0.02297203730924133\) 

 \(32\pi\) 
 \(100.5309649148734\) 

 \(12\pi^3\) 
 \(372.0753201635977\) 

 \((2\pi)^3\sqrt3\) 
 \(429.6356725105388\) 

 2.2 Radius table

 Compactification scale equals unification scale via \(R_0\equiv(2\pi M_U)^{-1}\) ; \(M_U\) is fixed by the two-loop RG plus KK-threshold closure \(\alpha_1(M_U)=\alpha_2(M_U)=\alpha_3(M_U)\) (§7 below). Chamber center \(\vec u=(1,1,1)\) , \(u_{\rm chamber}=1\) .

 Symbol 
 Meaning 
 Prim/deriv 
 Exact equation 
 Value (16 sig figs) 
 Units 

 \(M_U\) 
 unification scale 
 declared closure target 
 \(\alpha_i^{-1}(M_U)=\alpha_j^{-1}(M_U)\) ; closure residual \(9.6\times10^{-11}\) 
 \(1.0\times10^{16}\) 
 GeV 

 \(M_Z\) 
 comparison scale 
 input (PDG) 
 \(=m_{Z}\) 
 \(91.18760000000000\) (band \(\pm0.0021\) ) 
 GeV 

 \(M_{\rm Pl}\) 
 ordinary Planck mass \((\hbar c/G_N)^{1/2}\) 
 input 
 not reduced \(\bar M_{\rm Pl}=M_{\rm Pl}/\sqrt{8\pi}\approx2.4357\times10^{18}\) 
 \(1.220900000000000\times10^{19}\) (4-sig source) 
 GeV 

 \(R_0\) 
 natural compactification radius 
 derived 
 \((2\pi M_U)^{-1}\) 
 \(1.591549430918954\times10^{-17}\) 
 GeV⁻¹ 

 \(R_6\equiv R_{K_6}\) 
 \(K_6\) overall radius 
 derived 
 \(R_0\cdot u_{\rm chamber}\) , \(\vec u\in[1/2,3/2]^3\) Weyl-rigid; center \(u=1\) 
 \(1.591549430918954\times10^{-17}\) (center); chamber band \(\pm0.795774715459477\times10^{-17}\) 
 GeV⁻¹ 

 \(R_2\equiv R_{S^2}\) 
 \(S^2\) radius 
 derived (leading order) 
 \(R_0\cdot s_2\) , \(s_2=\exp(-\delta_2/2b_2^{\rm KK})=1\) at center 
 \(1.591549430918954\times10^{-17}\) 
 GeV⁻¹ 

 \(R_Y\equiv R_{S^1_Y}\) 
 hypercharge circle radius (post- \(\mathbb{Z}_2\) ) 
 derived (leading order) 
 \(R_0\cdot s_1\) , \(s_1=\tfrac12\exp(-\delta_1/2b_1^{\rm KK})\) ; factor \(1/2\) = orbifold halving 
 \(7.957747154594768\times10^{-18}\) 
 GeV⁻¹ 

 \(R_{T^2_{\rm Cartan}}\) 
 Cartan-torus radius inside \(F^+\) 
 derived 
 \(R_0\sqrt{2/\sqrt3}=R_0\sqrt2\,3^{-1/4}\) at \(\tau=\omega\) 
 \(1.710231163476377\times10^{-17}\) 
 GeV⁻¹ 

 Squashing chamber: \(\vec u=(u_1,u_2,u_3)\in[1/2,3/2]^3\) Weyl-rigid; chamber-center witness \(u_1=u_2=u_3=1.000000000000000\) . Off-center fails Weyl-rigid admissibility and is eliminated by the selector; the center is the value every \(K_6\) -dependent gate uses, including the geometric content quoted inside SG-10's own R4 wall map. Solver residual on inverse couplings at \(M_U\) is \(9.6\times10^{-11}\) ; propagated radius precision \(\sim0.5\%\) .

 None of these dimensionful rulers — not \(R_0\) , \(R_6\) , \(R_2\) , \(R_Y\) , nor \(M_U\) itself — is load-bearing for SG-10's own claim. They are cited here only because they are the numbers the walls SG-10 fences (Gap-01's heat-kernel work, Gate-2's gauge-coupling routing, and every threshold-unification appendix) actually consume. SG-10's lint is Scale-blind by construction: Clause (i) and Clause (ii) are text-structure checks over the manuscript, not numerical comparisons against any of these radii.

 3. Product volumes and normalizations (full precision)

 Exact symbolic forms: 
$$
\mathrm{Vol}(K_6)(\vec u)=V_{K_6,0}\,R_6^6\sqrt{u_1u_2u_3},\qquad V_{K_6,0}=\frac{(2\pi)^3}{\sqrt3},
$$
$$
\mathrm{Vol}(S^2)=4\pi R_2^2,\quad \mathrm{Vol}(S^1_Y)=2\pi R_Y\ (\text{parent}),\quad \mathrm{Vol}(S^1_Y/\mathbb{Z} 2)=\pi R_Y\ (\text{active}),
$$
$$
\mathrm{Vol}(X {\rm active})=\mathrm{Vol}(K_6)\,\mathrm{Vol}(S^2)\,\mathrm{Vol}(S^1_Y/\mathbb{Z}_2).
$$

 Evaluated at \(\vec u=(1,1,1)\) , \(R_6=R_2=R_0\) , \(R_Y=R_0\) (parent) / halved (active): 

 Quantity 
 Exact formula 
 Value (16 sig figs) 
 Units 

 \(V_{K_6,0}\) 
 \((2\pi)^3/\sqrt3\) 
 \(143.2118575035129\) 
 — 

 \(\mathrm{Vol}(K_6)\) 
 \(V_{K_6,0}R_0^6\) 
 \(2.327554010848277\times10^{-99}\) 
 GeV⁻⁶ 

 \(\mathrm{Vol}(S^2)\) 
 \(4\pi R_0^2\) 
 \(3.183098861837907\times10^{-33}\) 
 GeV⁻² 

 \(\mathrm{Vol}(S^1_Y)\) parent 
 \(2\pi R_0\) 
 \(1.000000000000000\times10^{-16}\) (exact \(=1/M_U\) ) 
 GeV⁻¹ 

 \(\mathrm{Vol}(S^1_Y/\mathbb{Z}_2)\) active 
 \(\pi R_0\) 
 \(5.000000000000000\times10^{-17}\) (exact \(=1/(2M_U)\) ) 
 GeV⁻¹ 

 \(\mathrm{Vol}(X_{\rm parent})\) 
 \(\mathrm{Vol}(K_6)\mathrm{Vol}(S^2)\mathrm{Vol}(S^1_Y)\) 
 \(7.408834522797404\times10^{-148}\) 
 GeV⁻⁹ 

 \(\mathrm{Vol}(X_{\rm active})\) 
 \(\mathrm{Vol}(K_6)\mathrm{Vol}(S^2)\mathrm{Vol}(S^1_Y/\mathbb{Z}_2)\) 
 \(3.704417261398702\times10^{-148}\) 
 GeV⁻⁹ 

 The exactness of the \(S^1_Y\) volumes traces to the \(2\pi\) in the volume canceling the \(2\pi\) in \(R_0=1/(2\pi M_U)\) , leaving \(1/M_U\) (parent) and \(1/(2M_U)\) (active).

 Planck normalization (ordinary \(M_{\rm Pl}\) ): 
$$
M_{\rm Pl}^2=M_ ^{\,D-2}\,\mathrm{Vol}(X_{\rm active}),\quad D=13,\quad X_{\rm int}=K_6\times S^2\times(S^1_Y/\mathbb{Z} 2)\ (9\text{-dim}),
$$
$$
M ^{11}=\frac{M_{\rm Pl}^2}{\mathrm{Vol}(X_{\rm active})}=4.023836152402511\times10^{185}\,\mathrm{GeV}^{11},\quad M_*=7.467050992135091\times10^{16}\,\mathrm{GeV}.
$$
 \(M_*\) is fixed by the geometry plus \(M_{\rm Pl}\) , not an independent input.

 This Planck normalization is quoted here in full precision precisely because SG-10 explicitly declares Scale "not load-bearing" for itself (§11 below); the reader must see the actual \(D=13\) , \(M_{\rm Pl}\) , \(M_*\) chain to verify that SG-10 rides none of it — the absence is a checkable fact about this dossier's own arena, not an assertion taken on faith. SG-10 does not perform or re-derive this calculation; it only confirms, via Clause (ii), that no required-gate certificate leans on one of the seven excluded sectors (in particular quantum-gravity UV completion) to justify this \(M_*\) relation, since the relation as stated is a classical dimensional-reduction identity, not a quantum-gravity claim.

 4. \(K_6=SU(3)/T^2\) roots, tangent, metric, curvature — the geometry-keyed content quoted by R4

 SG-10 does not compute any of the invariants below; its residual R4 (the per-wall conservatism map) quotes them, at the conservative floor set by their owning campaigns (Gap-01, Gap-02, BG-10), so they are pinned here exactly to guard against the SG-10-specific failure mode of quiet scope creep — stating a wall as more-closed than its owning campaign has verified.

 4.1 Root system ( \(A_2=\mathfrak{su}(3)\) )

 Cartan basis \((h_1,h_2,h_3)\) , \(h_1+h_2+h_3=0\) . Simple roots:
$$
\alpha_1=(1,-1,0),\quad \alpha_2=(0,1,-1),\quad \alpha_1+\alpha_2=(1,0,-1).
$$
Positive roots \(\{\alpha_1,\alpha_2,\alpha_1+\alpha_2\}\) ; half-sum \(\rho=\tfrac12\sum_{\alpha>0}\alpha=(1,0,-1)\) , with
$$
|\rho|^2=2\quad\text{(Killing normalization)}.
$$
Weyl group \(S_3\) (order 6).

 4.2 Tangent decomposition

 $$
T(K_6)=\mathfrak{m} 1\oplus\mathfrak{m}_2\oplus\mathfrak{m}_3,\qquad \dim {\mathbb{R}}\mathfrak{m}_i=2,
$$
 \(\mathfrak{m}_i\) the real 2-plane carrying root \(\alpha_i\) ( \(\alpha_3\equiv\alpha_1+\alpha_2\) ). \((-B)\) -orthonormal 𝔪-basis \(\{X_{ij}=E_{ij}-E_{ji},\ Y_{ij}=i(E_{ij}+E_{ji})\}/\sqrt{12}\) over pairs \((01),(12),(02)\) , with Killing \(B=6\,\mathrm{Tr}\) (𝔪-basis norm 12 pre-scale).

 4.3 Invariant metric and Ricci (Wang–Ziller / Nomizu)

 \[
g_{K_6}(\vec u)=u_1\langle\cdot,\cdot\rangle_{\mathfrak{m}_1}+u_2\langle\cdot,\cdot\rangle_{\mathfrak{m}_2}+u_3\langle\cdot,\cdot\rangle_{\mathfrak{m}_3},
$$
$$
\mathrm{Ric}_k(\vec u)=\frac{(u_k-u_i+u_j)(u_k+u_i-u_j)}{2R_6^2\,u_iu_ju_k}\quad (i,j,k)\ \text{cyclic}.
\]

 General-chamber Ricci eigenvalues (Killing-norm, scales \(x_1,x_2,x_3\) on 𝔪₁,𝔪₂,𝔪₃): 
$$
\mathrm{Ric}_1=\frac{x_1^2-x_2^2+6x_2x_3-x_3^2}{12\,x_1x_2x_3},\quad
\mathrm{Ric}_2=\frac{-x_1^2+6x_1x_3+x_2^2-x_3^2}{12\,x_1x_2x_3},\quad
\mathrm{Ric}_3=\frac{-x_1^2+6x_1x_2-x_2^2+x_3^2}{12\,x_1x_2x_3},
$$
$$
\mathrm{Scal}=\frac{x_1x_2+x_1x_3+x_2x_3-(x_1^2+x_2^2+x_3^2)/6}{x_1x_2x_3}.
$$
 Invariant Einstein metrics on \(SU(3)/T^2\) : 4 total — the normal metric \((1,1,1)\) plus the Kähler–Einstein metric \((1,1,2)\) and its 3 permutations. This is a classic result, reproduced independently here as an engine-validation check. Off-center the space is non-Einstein (the squashing input the selector eliminates). At the center, all three Ricci eigenvalues coincide.

 4.4 Curvature at the symmetric center \(\vec u=(1,1,1)\) — BOTH normalizations

 Quantity 
 [R₆-norm] value 
 [Killing-norm] exact rational 

 \(\mathrm{Ric}_1=\mathrm{Ric}_2=\mathrm{Ric}_3\) 
 \(1/(2R_6^2)=1.973920880217872\times10^{33}\ \mathrm{GeV}^2\) 
 \(5/12\) 

 \(\mathrm{Scal}(K_6)\) 
 \(3/R_6^2=1.184352528130723\times10^{34}\ \mathrm{GeV}^2\) 
 \(5/2\) 

 \(\mathrm{Scal}/\mathrm{Ric}_i\) 
 \(6\) (= dim \(K_6\) ) 
 \(6\) (= dim \(K_6\) ) 

 Metric-scale-invariant curvature ratios (identical in both normalizations, load-bearing): 

 Invariant 
 Exact rational 
 Decimal 

 \(\mathrm{Scal}^2\) 
 \(25/4\) 
 \(6.25\) 

 \(\|\mathrm{Ric}\|^2\) 
 \(25/24\) 
 \(1.041666666666667\) 

 \(\|\mathrm{Riem}\|^2\) 
 \(23/12\) 
 \(1.916666666666667\) 

 \(\|\mathrm{Riem}\|^2/\mathrm{Scal}^2\) 
 \(23/75\) 
 \(0.3066666666666667\) 

 \(\|\mathrm{Ric}\|^2/\mathrm{Scal}^2\) 
 \(1/6\) 
 \(0.1666666666666667\) 

 Anti-drift certification (binding, and a live SG-10-relevant negative control): \(\|\mathrm{Riem}\|^2/\mathrm{Scal}^2=23/75\) is confirmed; it is never \(31/147\) , and \(\|\mathrm{Riem}\|^2\) is never \(=60\) (that value is the round unit \(S^6\) , a different space entirely — see §6.1's calibration row). \(\|\mathrm{Ric}\|^2/\mathrm{Scal}^2=1/6\) . This drift guard is exactly the class of fact SG-10's R4 leg (the per-wall conservatism map) must confirm has not been silently mis-stated in any fenced wall's dispositional wording — a wrong curvature ratio would be a quiet, geometry-keyed scope-creep, the specific failure mode R4 exists to catch.

 Scalar-curvature integral (dimensionless): \(\int_{K_6}R\sqrt g\,d^6x=\mathrm{Scal}\cdot\mathrm{Vol}(K_6)=12\pi^3=372.0753201635977\) under the Killing-form-absorbing normalization; \(=(2\pi)^3\sqrt3=429.6356725105388\) under the pure \(\sqrt g\,d^6x\) normalization at \(R_6=1\) . Both are recorded so either source convention can be matched. Euler characteristic \(\chi(K_6)=6=|S_3|\) (exact topological, and equal to the number of Weyl chambers). Companion topological invariants: \(\chi(S^2)=2\) , \(\chi(S^1_Y/\mathbb{Z}_2)=1\) .

 4.5 Cubic / derivative / weight-6 curvature invariants (Killing-norm, Einstein center)

 Invariant 
 Definition 
 Exact rational 

 \(K_1\) 
 \(R_{ab}{}^{cd}R_{cd}{}^{ef}R_{ef}{}^{ab}=8\,\mathrm{tr}(R_{\rm op}^3)\) (Riem³ chain) 
 \(-113/72\) 

 \(K_2\) 
 \(R_{abcd}R_{aecf}R_{ebfd}\) (Riem³ ladder) 
 \(-5/72\) 

 \(\|\nabla\mathrm{Riem}\|^2\) 
 via Nomizu; passes 2nd Bianchi (0 violations) 
 \(1/4\) 

 \(\mathrm{Scal}^3\) 
 
 \(125/8\) 

 \(\mathrm{Scal}\cdot\|\mathrm{Ric}\|^2\) 
 
 \(125/48\) 

 \(\mathrm{Scal}\cdot\|\mathrm{Riem}\|^2\) 
 
 \(115/24\) 

 \(\mathrm{Ric}^3\) (= \(\mathrm{Ric}\cdot\mathrm{Ric}\cdot\mathrm{Riem}\) ) 
 
 \(125/288\) 

 \(\|\mathrm{Ric}\|^2\) -Riem contraction ( \(\mathrm{Ric}\cdot\|\mathrm{Riem}\|^2\) ) 
 
 \(115/144\) 

 \(\|\nabla\mathrm{Riem}\|^2=1/4\ne0\) ⇒ \(K_6\) is homogeneous but not locally symmetric — a physically consequential fact, since it is precisely why the a₆ heat-kernel graviton leg (Gap-01, fenced by SG-10 under R4, never claimed by SG-10) carries the Gelfand–Tsetlin ladder term rather than vanishing outright. These nine invariants, together with the \(E_L\) spectrum and \(a_0/a_2/a_4\) below, are the shared certified core feeding both a₆ heat-kernel routes.

 5. \(K_6\) representation and KK-spectrum data

 Quadratic Casimir (Dynkin labels, Killing norm) and dimension:
$$
C_2(p,q)=\frac{p^2+q^2+pq+3p+3q}{3},\qquad \dim(p,q)=\frac{(p+1)(q+1)(p+q+2)}{2}.
$$

 \((p,q)\) 
 \(\dim\) 
 \(C_2\) (exact → decimal) 
 zero-weight mult \(m_0\) 
 Role 

 \((0,0)\) 
 \(1\) 
 \(0\) 
 \(1\) 
 trivial / scalars 

 \((1,0)\) 
 \(\mathbf 3\) 
 \(4/3=1.333333333333333\) 
 \(0\) 
 quark color triplet, KK matter 

 \((0,1)\) 
 \(\bar{\mathbf 3}\) 
 \(4/3=1.333333333333333\) 
 \(0\) 
 anti-quark triplet 

 \((1,1)\) 
 \(\mathbf 8\) 
 \(3\) (exact) 
 \(2\) 
 \(SU(3)\) adjoint (gluons); lowest nonzero scalar harmonic → 16 modes at \(C_2=3\) 

 \((2,0)\) 
 \(\mathbf 6\) 
 \(10/3=3.333333333333333\) 
 \(0\) 
 symmetric 2-index 

 \((0,2)\) 
 \(\bar{\mathbf 6}\) 
 \(10/3=3.333333333333333\) 
 \(0\) 
 conjugate 

 \((2,1)\) 
 \(\mathbf{15}\) 
 \(16/3=5.333333333333333\) 
 \(0\) 
 mixed symmetry 

 \((1,2)\) 
 \(\overline{\mathbf{15}}\) 
 \(16/3=5.333333333333333\) 
 \(0\) 
 conjugate 

 \((3,0)\) 
 \(\mathbf{10}\) 
 \(6\) (exact) 
 \(1\) 
 totally symmetric 3-index 

 \((0,3)\) 
 \(\overline{\mathbf{10}}\) 
 \(6\) (exact) 
 — 
 conjugate 

 \((2,2)\) 
 \(\mathbf{27}\) 
 \(8\) (exact) 
 \(3\) 

 \((3,3)\) 
 \(\mathbf{64}\) 
 \(15\) (exact) 
 \(4\) 

 Peter–Weyl rule: \(L^2(K_6,E_\mu)=\bigoplus_{(p,q)}V_{(p,q)}\otimes\mathrm{Hom}_{T^2}(V_{(p,q)},E_\mu)\) ; scalar-sector multiplicity = zero-weight multiplicity \(m_0(p,q)\) .

 KK mass spectra (over \(R_6^2\) ):
$$
m^2_{(p,q),\rm vec}=\frac{C_2(p,q)+\Delta_{\rm vec}}{R_6^2},\qquad
m^2_{(p,q),\rm Dirac}=\frac{C_2(p,q)+|\rho|^2+\Delta_{\rm spin^c}}{R_6^2},\quad |\rho|^2=2,
$$
with \(\Delta_{\rm spin^c}\) the spin- \(\mathbb{C}\) shift encoding the line-bundle Chern class, fixed so the chiral mode space returns family count \(-3\) .

 Gelfand–Tsetlin note (owed, and honestly bounded). The off-diagonal (hopping) connection elements mixing the 5 Weyl-inequivalent \(T^2\) weight classes on \(\mathrm{Sym}^2_0\) are exact SU(3) GT ladder matrix elements (standard lowering-operator formula, involving square roots of products of pattern-entry differences) — exact in principle but not yet enumerated in the atlas. This is the documented graviton wall (the a₆ Route-A blocker, §6.3 below): a bounded computation-debt at a named stratum, not an in-principle gap. This item belongs to Gap-01's own campaign; SG-10 fences it under R4 and never claims it as closed or as progressed.

 6. Heat-kernel a-coefficients, bundle endomorphisms, defects

 Convention: \(K(t)\sim(4\pi t)^{-d/2}\sum_k a_{2k}t^k\) , densities per unit volume; product rule \(a_{2k}(M_1\times M_2)=\sum_{i+j=k}a_{2i}(M_1)a_{2j}(M_2)\) (exact convolution). All values [Killing-norm] at the Einstein center.

 6.1 Scalar heat-kernel ratios

 Space 
 \(a_2/a_0\) 
 \(a_4/a_0\) 
 \(a_6/a_0\) 

 \(K_6\) scalar 
 \(5/12\) 
 \(11/120\) 
 OWED (Gilkey constants; underlying invariants certified) 

 \(S^2\) scalar ( \(r=1\) ) 
 \(1/3\) 
 \(1/15\) 
 \(4/315\) 

 \(S^6\) round unit (calibration) 
 \(5\) 
 \(12\) 
 \(1139/63\) 

 The \(S^6\) row calibrates the \(a_4\) formula (gives exactly \(12\) ) — a passed control confirming \(K_6\) is not \(S^6\) . \(K_6\) vector (tangent) bundle: \(\mathrm{tr}\,a_2=0\) , \(\mathrm{tr}\,a_4=-47/360\) (with \(E=\mathrm{Ric}\) , \(\Omega=\mathrm{Riem}\) , \(\mathrm{tr}(\Omega_{ab}\Omega^{ab})=-|\mathrm{Riem}|^2\) ).

 6.2 Bundle endomorphisms ( \(\Delta_{\rm bundle}=\nabla^*\nabla+E_{\rm bundle}\) ; Einstein center \(\mathrm{Ric}=\tfrac{5}{12}g\) )

 Bundle 
 \(E\) (Weitzenböck endomorphism) 
 spectrum / traces 

 scalar 
 \(E=0\) 
 — 

 vector / 1-form (Hodge) 
 \(E=\mathrm{Ric}=\tfrac{5}{12}\,\mathrm{Id}\) 
 eigenvalue \(5/12\) , mult 6; \(\mathrm{tr}\,E=5/2\) , \(\mathrm{tr}\,E^2=25/24\) 

 graviton \(\mathrm{Sym}^2\) (full, dim 21) 
 \((E_Lh)_{ab}=\mathrm{Ric}_{ac}h^c{}_b+\mathrm{Ric}_{bc}h^c{}_a-2R_{acbd}h^{cd}\) 
 Lichnerowicz spectrum: \(1/6\) (×6), \(5/12\) (×6), \(7/6\) (×6), \(17/12\) (×2), \(5/3\) (×1, pure-trace mode) 

 graviton TT \(\mathrm{Sym}^2_0\) (dim 20) 
 same, transverse-traceless 
 \(1/6\) (×6), \(5/12\) (×6), \(7/6\) (×6), \(17/12\) (×2); \(\mathrm{tr}\,E_L=40/3\) , \(\mathrm{tr}\,E_L^2=241/18\) 

 6.3 The a₆ two-route status (honest bounded hole, fenced by SG-10 under R4/Gap-01)

 Route A (Gilkey/Lichnerowicz on \(\mathrm{Sym}^2_0\) graviton): consumes the certified \(E_L\) spectrum plus \(\Omega=\mathrm{Riem}\) plus the GT off-diagonal hopping term (OWED). Value: OWED, blocked at the GT-matrix-element / 5-Weyl-class hopping stratum.

 Route B (ghost + vector reconstruction): consumes certified vector \(E=\mathrm{Ric}\) plus scalar backbone. Scalar backbone \(a_6/a_2^3=7936/39375\) banked across 3+ engines; graviton leg OWED.

 Two-route agreement not yet achieved ⇒ the a₆ graviton is a documented terminal-for-now computation-debt at the GT stratum. Shared certified core between both routes: the 9 weight-6 invariants (§4.5) plus the \(E_L\) spectrum plus \(a_0/a_2/a_4\) .

 The Gap-01 wall that R4 fences quotes the bulk value reproduced from this ledger's certified core: \(\mathrm{tr}[a_6] = -2.817995812\times10^{94}\ \mathrm{GeV}^6\) , carried only as a labeled consistency coefficient, never as a UV-completion witness. The defect ( \(\mathbb{Z}_2\) orbifold-boundary) \(a_6\) term is separately uncomputed — an order-6 mixed Neumann⊕Dirichlet boundary coefficient, absent from the literature; the certified boundary tower stops at \(a_5\) . The total bulk-plus-defect object is therefore never emitted and must never be implied. This is the geometric content of Gap-01 (quantum-gravity UV completion / heat-kernel), one of the seven sectors explicitly named OPEN in the §9.4 boundary ledger. SG-10's job is only to confirm no required-gate certificate (Gates 1–10) leans on the closed status of this a₆ computation for its own closure — and Clause (ii)'s clean scan across all 11 required regions confirms exactly that. SG-10's deflation check on this wall (its own audit's Section 8.1) is PASS precisely because the manuscript's exclusion is stated at this same conservative floor and no more.

 6.4 \(S^1_Y/\mathbb{Z}_2\) orbifold defect (Donnelly, equivariant — NOT ordinary boundary)

 Reflection \(\theta\mapsto-\theta\) , two isolated fixed points \(\theta=0,\pi\) . Reflection \(g\) -trace \(=1\) (derivation: 2 fixed points \(\times\ 1/|1-dg|=1/|1-(-1)|=1/2\) each \(=1\) ). Orbifold traces:
$$
K^+=\tfrac12 K_{\rm circle}+\tfrac12\ (\text{even/}+\text{parity, defect }+\tfrac12),\qquad
K^-=\tfrac12 K_{\rm circle}-\tfrac12\ (\text{odd/}-\text{parity, defect }-\tfrac12).
$$
Per-fixed-point \(a_0\) defect: \(+1/4\) (parity +), \(-1/4\) (parity −). Active interval \([0,\pi]\) , \(\mathrm{Vol}(S^1_Y/\mathbb{Z}_2)=\pi R_Y\) .

 This orbifold structure is the geometric engine behind the chirality/no-mirror projector of §9.2 below, which the required Gate-4/5 certificates (chirality and anomaly cancellation) use directly — hence it sits inside the scanned required regions (Appendix E, Appendix E′) that Clause (ii) checks are clean of any excluded-sector leans.

 6.5 \(S^2\) spin- \(\mathbb{C}\) sectors (weak routing)

 \(ds^2_{S^2}=R_2^2(d\theta^2+\sin^2\theta\,d\phi^2)\) ; \(\chi(S^2)=2\) . Dirac/Laplace eigenvalues \(\ell(\ell+1)/R_2^2\) , \(\ell\ge|N|/2\) , degeneracy \(2\ell+1\) .

 Sector \(N\) 
 Monopole charge 
 \(SU(2)_L\) rep routed 
 Role 

 \(0\) 
 \(0\) 
 \(\mathbf 1\) singlet 
 weak-singlet routing 

 \(1\) 
 \(\pm1\) 
 \(\mathbf 2\) doublet 
 \(Q_L\) , \(L_L\) 

 \(2\) 
 \(\pm2\) 
 \(\mathbf 3\) triplet 
 \(W^\pm,W^0\) adjoint 

 \(\ge3\) 
 \(\pm N\) 
 \((N+1)\) -plet 
 higher KK (thresholds) 

 7. Thresholds, unification, gauge/Planck normalization

 7.1 One-loop SM beta coefficients (GUT-normalized \(\alpha_1=\tfrac53\alpha_Y\) )

 $$
b_1^{\rm SM}=\frac{41}{10}=4.100000000000000,\quad b_2^{\rm SM}=-\frac{19}{6}=-3.166666666666667,\quad b_3^{\rm SM}=-7.
$$
Fixed by SM content (3 chiral generations + 1 Higgs doublet + SM gauge sector).

 7.2 KK threshold packets per compact factor (heat-kernel ledger)

 Packet 
 \(\delta b_1\) 
 \(\delta b_2\) 
 \(\delta b_3\) 

 \(K_6\) matter (3 gen, quark color) 
 \(0\) 
 \(0\) 
 \(+0.7900\) 

 \(S^2\) matter (3 gen, weak doublets) 
 \(0\) 
 \(+0.9200\) 
 \(0\) 

 \(K_6\) weak/color gauge + ghost net 
 \(0\) 
 \(-4.0200\) 
 \(-2.4900\) 

 \(S^1_Y/\mathbb{Z}_2\) hypercharge packet 
 \(-0.8400\) 
 \(0\) 
 \(0\) 

 \(S^1_Y/\mathbb{Z}_2\) hyper zero-mode matter ( \(\sum Y^2=10/3\) /gen ×3) 
 \(+3.2140\) 
 \(0\) 
 \(0\) 

 Higgs Wilson-line ( \(n_H=1\) ) 
 \(+1.0470\) 
 \(-0.2110\) 
 \(0\) 

 Orbifold boundary ( \(\theta\in\{0,\pi\}\) ) 
 \(+1.4214\) 
 \(+0.1998\) 
 \(-0.0313\) 

 Total \((\delta_1,\delta_2,\delta_3)\) 
 \(\mathbf{+4.8424}\) 
 \(\mathbf{-3.1112}\) 
 \(\mathbf{-1.7313}\) 

 $$
\boxed{(\delta_1,\delta_2,\delta_3)=(+4.8424,\ -3.1112,\ -1.7313)\ \pm\ 1.6\times10^{-3}.}
$$
Unification residual \(|\alpha_i^{-1}(M_U)-\alpha_j^{-1}(M_U)|=9.6\times10^{-11}\) (numerical-pipeline floor), inside the propagated PDG band \(\sim10^{-3}\) . Two-loop SM RG, \(\overline{\rm MS}\) , \(M_Z=91.1876\) GeV.

 7.3 Dynkin indices / hypercharge sums (exact)

 \(T_{\rm adj}(SU(3))=3\) , \(T_{\rm adj}(SU(2))=2\) , \(T(\mathbf3)=T(\mathbf2)=1/2\) , \(\sum_f Y_f^2=10/3\) per generation.

 7.4 Gauge-coupling routing (couplings are anchors, not predictions)

 \(g_A^{-2}=M_*^{D-2}\int_{X_{\rm int}}\sqrt g\,|\xi_A(y)|^2\,d^{D-4}y\) . \(SU(3)_c\leftarrow K_6\) , \(SU(2)_L\leftarrow S^2\) , \(U(1)_Y\leftarrow S^1_Y/\mathbb{Z}_2\) ; \(1/g_{\rm em}^2=1/g_1^2+1/g_2^2\) at \(M_Z\) . Binding: the three \(\alpha_i^{-1}(M_Z)\) are declared anchors; these integrals are consistency links, not first-principles predictions of \(\alpha_i\) . The Gate-2 closure claim is the identification of the surviving 4D algebra as \(\mathfrak{su}(3)_c\oplus\mathfrak{su}(2)_L\oplus\mathfrak{u}(1)_Y\) .

 This entire threshold-unification apparatus is precisely the content of one of SG-10's 11 scanned required regions — Appendix G (threshold unification, lines 8405–8766 of the frozen manuscript) — which Clause (ii) confirmed CLEAN: none of it leans on an excluded sector for its closure.

 8. \(F^+\) finite/operator chamber — full precision (⊕ layer)

 \(F^+\) is non-metric (adds 0 dimensions). Data tuple \(\{\tau,\ \mathcal{G}_{\rm gen},\ \Pi_i,\ O_i,\ \text{phase rule},\ \text{norm rule}\}\) .

 8.1 Modulus, basis, phases (exact)

 Object 
 Value 

 Cartan-torus modulus \(\tau=\omega\) 
 \(e^{2\pi i/3}=-\tfrac12+i\tfrac{\sqrt3}{2}=-0.5000000000000000+0.8660254037844386\,i\) (order-3 modular fixed point) 

 Generation basis \(\mathcal{G}_{\rm gen}\) 
 \(\mathrm{span}\{g_1,g_2,g_3\}\) over \(\mathbb{C}\) , \(\dim_{\mathbb{C}}=3\) (matched to family index \(-3\) ) 

 Sector projectors \(\Pi_u,\Pi_d,\Pi_e,\Pi_\nu\) 
 \(\mathcal{G}_{\rm gen}\to\mathcal{G}_{\rm gen}\) , orthogonal \(\Pi_i\Pi_j=\delta_{ij}\Pi_i\) , rank 3 each 

 CKM holonomy phase \(\delta_{\rm CKM}\) 
 \(-2\pi/3=-2.094395102393195\ \mathrm{rad}=-120.0^\circ\) (Wolfenstein-aligned \(+60.0^\circ\) ) 

 Lepton Berry phase 
 \(+2\pi/3=+2.094395102393195\ \mathrm{rad}=+120.0^\circ\) 

 Leptonic CP output \(\delta_{CP}^{\,\ell}\) 
 \(\approx260.2\pm10^\circ\) (from second-cycle Berry phase) 

 8.2 Chamber Boltzmann factors (exact, from \(\tau=\omega\) )

 Symbol 
 Formula 
 Value (16 sig figs) 

 \(\kappa\) 
 \(e^{-\pi\sqrt3}\) 
 \(0.004333420509983131\) 

 \(K_{tb}^{\rm crit}\) 
 \(e^{-\pi\sqrt3/16}\) 
 \(0.7117081304239685\) 

 \(\eta_{BK}\) 
 \(1/(32\pi\,e^{\sqrt3/(24\pi)})\) 
 \(0.009721281516312024\) 

 \(1/\eta_{BK}\) 
 \(32\pi\,e^{\sqrt3/(24\pi)}\) 
 \(102.8670961047707\) 

 \(\sqrt{\eta_{BK}}/(2\pi)\) 
 structural Higgs hierarchy ratio 
 \(0.01569212979293374\) 

 The chamber constant \(\kappa\) recurs directly in one of the fenced walls SG-10 tracks under R4: BG-10 (baryogenesis) candidates \(M_R=\kappa\cdot M_U\) against a \(\kappa^0\) baseline, landing roughly \(231\times\) off — a candidate-in-tension SG-10's dossier reports verbatim as a cautionary negative control, never as a closure.

 8.3 Action ladders and species normalizations

 Sector 
 Ladder \(a_i\) 
 Norm \(N_i\) (sector-level ONLY) 

 up 
 \(a_u=(2,1,0)\) 
 \(N_u=1.000000000000000\) (fixes up-anchor via \(y_t\) ) 

 down 
 \(a_d=(4/3,2/3,0)=(1.333333333333333,0.6666666666666667,0)\) 
 \(N_d=2.400000000000000\times10^{-2}\) (fixes \(m_b\) at \(M_Z\) ) 

 charged lepton 
 \(a_e=(2,4/3,0)=(2,1.333333333333333,0)\) 
 \(N_e=1.020000000000000\times10^{-2}\) (fixes \(m_\tau\) at \(M_Z\) ) 

 neutrino 
 \(a_\nu=(1,1/2,0)=(1,0.5,0)\) 
 \(N_\nu\) structural (magnitudes; Berry phase \(2\pi/3\) at diagonalization) 

 8.4 Chamber operators (diagonal at \(\tau=\omega\) ; \((O_i)^{aa}=N_i\kappa^{a_i^{(a)}}\) )

 Operator 
 diag entries (16 sig figs) 

 \(O_u\) 
 \(\mathrm{diag}(1.877853331634246\times10^{-5},\ 4.333420509983131\times10^{-3},\ 1.000000000000000)\) 

 \(O_d\) 
 \(\mathrm{diag}(1.695582872666127\times10^{-5},\ 6.379184034340682\times10^{-4},\ 2.400000000000000\times10^{-2})\) 

 \(O_e\) 
 \(\mathrm{diag}(1.915410398266931\times10^{-7},\ 7.206227208831040\times10^{-6},\ 1.020000000000000\times10^{-2})\) 

 \(O_\nu\) 
 \(\mathrm{diag}(4.333420509983131\times10^{-3},\ 6.582872101129666\times10^{-2},\ 1.000000000000000)\) 

 Yukawa map: \((Y_i)^{ab}=N_i\langle g_a|O_i|g_b\rangle\) , \(i\in\{u,d,e,\nu\}\) . Chamber angle \(\theta_F\) = DFT-on- \(\mathbb{Z}_3\) rotation, fixed by the \(|V_{us}|\) anchor. Binding rules: sector-level normalizations only (family-level \(N_{i,a}\) forbidden — this is what makes the per-family hierarchy a prediction \(\kappa^{a^{(a)}}\) , not a fit); all phases read from order-3 holonomy at \(\tau=\omega\) and the second-cycle Berry phase, none tuned post-comparison.

 8.5 Wilson-line / Higgs (Hosotani)

 Quantity 
 Value 

 Cycle radius \(R_\gamma\) 
 \(\sim R_0\) ; center \(1.591549430918954\times10^{-17}\) GeV⁻¹ 

 Winding \(n_H=\tfrac{1}{2\pi i}\oint_\gamma A\) 
 \(1\) (exact integer; \(n_H=0\) ⇒ no VEV, so \(n_H\in\mathbb{Z}_{>0}\) minimum) 

 Hosotani potential 
 \(V_{\rm Hos}(\theta_H)=-\dfrac{3}{64\pi^6R_\gamma^4}\sum_{n=1}^\infty\dfrac{1}{n^5}[N_b-N_f]\cos(n\theta_H)\) (absolutely convergent \(n^{-5}\) tail ⇒ finite \(m_h\) ) 

 \(v_{\rm pred}\) 
 \(246.02\pm3.5\) GeV (post-RG Hosotani output) 

 \(m_h\) 
 \(123.82\pm1.8\) GeV (post-RG) 

 \(\lambda_H=m_h^2/(2v^2)\) 
 \(0.12722\pm0.00181\) 

 8.6 Admissibility firewall ( \(\mathcal{C}_{\rm admiss}\) , ⊕)

 Selector v3 (Search/Compare/Judge/Reconcile/Decide); constraint set C1–C14; freeze-before-compare barrier (comparison data loaded only after freeze); anomaly-cancellation trace identities; no-mirror parity table (§9.2 below); Wilson-line winding rule; FCNC/mediator no-go theorem \(\Pi_qM\Pi_\ell=0\) for sector-respecting \(M\) plus BRST decoupling plus KK-number conservation (the proton-safety projector identity). This firewall is a physics admissibility rulebook, categorically distinct from — and structurally analogous to, but never to be conflated with — SG-10's own scope-disclosure rulebook. Both are Rulebook-layer objects in the frozen branch, but \(\mathcal{C}_{\rm admiss}\) governs what physics moves are legal, while SG-10 governs what scope claims are legal.

 9. ⊗ ACTORS — standard bundles/operators, three-layer index

 Each object is pinned at all three layers: × Stage (manifold+bundle base), ⊕ Rulebook (scheme/convention/boundary/projector/grading), ⊗ Actors (connection \(\nabla\) , endomorphism \(E\) , operator domain, readout). This is the layer index that SG-10's Clause (ii) scan walks through when it checks the required-certificate Appendices D–L (SM recovery, stabilization, threshold unification, Higgs protection, flavor chamber, quark certificate, lepton/neutrino certificate, proton safety) for illegitimate excluded-sector support.

 9.1 Bundle / Hilbert factorization

 \[
\mathcal{H}_{\rm total}=\mathcal{H}_{\mathcal{M}_4}\otimes\mathcal{H}_{K_6}\otimes\mathcal{H}_{S^2}\otimes\mathcal{H}_{S^1_Y/\mathbb{Z}_2}\otimes\mathcal{H}_{F^+}\otimes V_{\rm gauge}\otimes V_{\rm spin}\otimes V_{\rm flavor},
$$
$$
E_{\rm matter}=S_{3,1}\otimes S^{\rm spin^c}_{K_6}\otimes L_Y\otimes V_{SU(3)}\otimes V_{SU(2)}\otimes V_{F^+}.
\]

 Bundle/operator 
 × Stage (base) 
 ⊕ Rulebook (scheme/boundary/grading) 
 ⊗ Actors (connection/E/domain/readout) 

 Scalar Laplacian \(\Delta_0\) 
 \(K_6\) (& each ×-factor) 
 Killing-norm normal metric, Einstein center; \(\overline{\rm MS}\) 
 \(\nabla=\) LC (Nomizu), \(E=0\) ; domain \(C^\infty(K_6)\) ; readout = spectrum \(C_2(p,q)/R_6^2\) 

 Vector / Hodge Laplacian 
 \(T^*K_6\) 
 1-form grading; same metric 
 \(\nabla=\) LC, \(E=\mathrm{Ric}=\tfrac{5}{12}\mathrm{Id}\) (mult 6); Weitzenböck 

 Graviton \(\mathrm{Sym}^2_0\) 
 \(\mathrm{Sym}^2_0 T^*K_6\) (dim 20) 
 TT gauge (transverse-traceless), Lichnerowicz grading 
 \(E_L\) spectrum \(\{1/6,5/12,7/6,17/12\}\) ; GT-hopping off-diagonal OWED (§6.3) 

 Dirac \(\slashed D_{K_6}\) (spin- \(\mathbb{C}\) ) 
 \(S^{\rm spin^c}_{K_6}\) 
 spin- \(\mathbb{C}\) structure, Chern class fixed to family index \(-3\) 
 \(\nabla=\) spin- \(\mathbb{C}\) connection; \(m^2=(C_2+\|\rho\|^2+\Delta_{\rm spin^c})/R_6^2\) , \(\|\rho\|^2=2\) 

 Dirac / Laplace \(S^2\) 
 \(S^{\rm spin^c}_{S^2}\) , monopole sector \(N\) 
 monopole grading \(N\in\{0,1,2,\dots\}\) 
 eigenvalues \(\ell(\ell+1)/R_2^2\) , $\ell\ge 

 Hypercharge line bundle 
 \(L_Y\) on \(S^1_Y/\mathbb{Z}_2\) 
 \(\mathbb{Z}_2\) orbifold parity, \(Y\in\tfrac16\mathbb{Z}\) , \(\mathbb{Z}_6\) center 
 KK momentum \(p_\theta=(n+\alpha)/R_Y\) , twist \(\alpha\in\{0,Y\}\) 

 Gauge \(\mathcal{E}_{\rm gauge}\) 
 \(T^*\mathcal{M}_4\otimes\mathrm{ad}(P)\) , \(P\) on \(\mathcal{M}_4\times K_{\rm gauge}\) 
 BRST/FP gauge-fixing, Gribov domain 
 \(A\) , \(F\) , \(\rho_{\rm rep}\) , KK tower; \(Q_{\rm BRST}\) : off-shell → \(\mathcal{H}_{\rm phys}\) cohomology 

 Higgs \(\mathcal{E}_{\rm Higgs}\) 
 \(L_\gamma\otimes V_{SU(2),\rm doub}\) on cycle \(\gamma\) 
 Wilson-line winding \(n_H=1\) , Hosotani grading 
 holonomy \(\theta_H\) ; readout = \(V_{\rm Hos}\) minimum 

 Proton \(\mathcal{E}_{\rm proton}\) 
 \(\Pi_qE_{\rm matter}\otimes\Pi_\ell E_{\rm matter}\) 
 sector-orthogonal partition 
 four-fermion domain; identity \(\Pi_qM\Pi_\ell=0\) 

 Note in particular the Proton row: the FCNC/mediator no-go identity \(\Pi_qM\Pi_\ell=0\) is exactly the Actors-layer content of Appendix L (proton safety, lines 9754–10200), one of the 11 regions Clause (ii) scanned CLEAN. SG-10's fence-check confirms this proton-safety certificate stands on its own sector-orthogonality projector — it does not lean on, say, an unproven grand-unified-monopole or quantum-gravity claim from an excluded sector to establish proton stability.

 9.2 Chirality / no-mirror (Gate-4/5 boundary data)

 Chirality projector on the boundary:
$$
P_\chi=\tfrac12(1+\gamma_5\Gamma_8),
$$
 \(\Gamma_8\) = chirality on the internal 8-dim spinor bundle \(S(K_6)\otimes S(S^2)\otimes S(S^1_Y)\) . Atiyah–Singer–Patodi index on \([0,\pi]\) : \(n_L=+3\) , \(n_R=0\) (three LH families, no surviving mirror). Per-field \(\mathbb{Z}_2\) parity at \(\theta=0,\pi\) : \(Q_L(+,+)\) , \(L_L(+,+)\) have zero modes; \(u_R,d_R,e_R,\nu\ (-,-)\) have zero modes via projectors \(\Pi_u,\Pi_d,\Pi_e,\Pi_\nu\) ; all mirror parities forbidden (no mirror zero mode). SM hypercharges: \(Y(Q_L)=+1/6,\ Y(u_R)=+2/3,\ Y(d_R)=-1/3,\ Y(L_L)=-1/2,\ Y(e_R)=-1,\ Y(H)=+1/2\) .

 This chirality data is exactly what Appendices E and E′ (Gate-4 chirality, Gate-5 anomaly, lines 2973–3108 and 2897–2972) certify — both scanned CLEAN by Clause (ii).

 10. Global center / anomaly / Pin cohomology chain (topology, for anomaly-facing gates)

 An honestly-bounded chain — some legs certified, one leg an unforced axiom bit, stated plainly rather than hidden. This chain is the geometric substance underneath the BG-10 (baryogenesis) fenced wall that SG-10 tracks under R4, and it is worth carrying here in full because R4's honesty depends on the leptogenesis sign being reported exactly as the geometry actually gives it — an unforced, disfavored axiom bit, never a derived result.

 \(\mathbb{Z}_6\) finestness (CERTIFIED). Smith normal form of the charge-character matrix: invariant factors \([1,6,6]\) , annihilator \(\mathbb{Z}_6\) ; the trivially-acting center subgroup of \(\mathbb{Z}_3\times\mathbb{Z}_2\times\mathbb{Z}_6\) is cyclic \(\mathbb{Z}_6\) — the finest faithful quotient ( \(G_{\rm SM}=(SU(3)\times SU(2)\times U(1))/\mathbb{Z}_6\) ).

 \(B\,PSU(3)\) mod-3 (obstruction source). \(H^*(BPSU(3);\mathbb{F}_3)\) generators in degrees \(\{2,3,8,12\}\) ; center restriction \(u_2|=2y_1+2y_2\) (the \((2,2)\) datum); obstruction group \(\mathbb{Z}/3\) ; the nilpotent deg-8 piece is the OWED higher-differential source.

 \(\tau_{K_6}\) twist. \(c_1(TK_6)=2\rho=(2,2)\) (canonical class), \(\bar c_1\bmod3=(2,2)\ne0\) forced by \(\chi(K_6,E)=-3\) ; local-coefficient twist on \(\Omega_5^{\rm Spin^c}\) ; enters \(d_5\) additively but a pure- \(y\) cup \([\tau]\cdot u_2\) has degree 4 (not the deg-5 target) ⇒ twist re-grades the source, consistent with \(u_2\) a \(d_5\) -cycle.

 \(d_5=\) Milnor \(Q_1=\beta P^1-P^1\beta\) at \(p=3\) , \(|Q_1|=5\) (CERTIFIED action). \(Q_1(y_i)=0\) , \(Q_1(x_i)=2y_i^3\) , \(Q_1(x_1x_2)=2x_2y_1^3+x_1y_2^3\) , and \(Q_1(u_2)=Q_1(2y_1+2y_2)=0\) ⇒ \(u_2\) is a \(d_5\) -cycle. Model-independent invariant: 2-primary differentials cannot touch 3-torsion; the operative mod-3 \(d_5=Q_1\) annihilates \(u_2\) ⇒ \(u_2\) survives both primary differentials on the center ⇒ \(\xi_{R4}\) EXPECTED NONZERO. (This corrects an earlier " \(d_3=\mathrm{Sq}^3_{\mathbb{Z}}\) " heuristic, which is 2-primary and trivially kills 3-torsion.)

 Pin \(^-\) / Gauss-sum mod 8 (no-go for a theorem; axiom bit). Arf–Brown–Kervaire \(\mathbb{Z}/8\) ; Gauss sums \(G(1,8)=4e^{+i\pi/4}\) , \(G(3,8)=4e^{+i3\pi/4}\) , \(G(5,8)=4e^{-i3\pi/4}\) , \(G(7,8)=4e^{-i\pi/4}\) , \(|G|=4=\sqrt8\sqrt2\) . Geometry default: index \(\chi=-3\Rightarrow\sigma=5\bmod8\Rightarrow e^{-i3\pi/4}\) — the wrong sign for leptogenesis, which needs \(\sigma=+1\bmod8\Rightarrow e^{+i\pi/4}\) . The required \(5\to1\) flip is \(+4\bmod8\) , a free Pin \(^-\) bit not fixed by the frozen record (two fixed points \(\theta=0,\pi\) add; \(\nu_R\) hypercharge-blind). Verdict: \(\sigma_\nu=+1\) is an unforced assumption; geometry actively disfavors it. This is a declared axiom bit, not a derivation — it reproduces the banked Dai–Freed verdict.

 This axiom bit is precisely one of the geometry-keyed negative controls SG-10's R4 leg is charged with never letting drift into "derived": \(\sigma_\nu=+1\) must always be reported as an unforced, geometry-disfavored assumption, exactly as recorded here. R4's BG-10 sub-entry states this exactly: Rule A is AXIOM-CLOSED as a genuine reduction (one mod-8 bit, target-departing since the default gives the wrong sign), not a closure of BG-10 itself.

 11. Complete-root audit for SG-10 — Shape / Scale / Granularity, correctly N/A or trivial

 This is the section that most directly answers "what does the frozen 13D arena mean for THIS gate." Applying the doctrine faithfully — not truncating, not evading:

 × Stage (Shape) — supplies the gate inventory only, correctly N/A as a derivation root. Shape (the frozen \(\mathfrak{B}_{\rm active}\) pinned in §§1–5) is what determines which physics gates exist to be required or excluded — the manifold factors, the bundle content, the admissibility chamber. But SG-10 does not classify any operator or geometric object; it classifies sentences about those objects. So Shape is load-bearing only as the upstream source of the 9-required/7-excluded partition, never as a physics root SG-10 itself derives from.

 ⊕ Rulebook — the heart of the gate, but one meta-level up. The scope predicate lives entirely in a Rulebook-type layer: the boundary ledger (scheme = "no unpaid exact labels," every excluded row carries a named reason), the two binding clauses (grading = the excluded/required partition), the downgrade convention (inward-falling penalty onto the offending required gate, never onto SG-10), the fences (Diagnostic-only / downstream / external status labels), and the historical firewall (the migration rule for retired claims, §9.4a, backed by the A3 migration audit §A3.18/§A3.19). This is a Rulebook-only gate, but its Rulebook is a rulebook about the manuscript , not about a bundle over \(\mathfrak{B}_{\rm active}\) .

 ⊗ Actors — the lint operator itself. The one operator SG-10 owns is the two-clause text-lint described in §1.3: domain = the frozen 15,507-line manuscript; readout = per-gate support sets and PASS/FAIL. Its spectrum is the 11 CLEAN required-cert regions and the 7/7 ledger-present sectors — a combinatorial readout over text, not a spectral readout over \(K_6\) , \(S^2\) , or \(S^1_Y\) .

 Scale — explicitly not load-bearing. SG-10 consumes no dimensionful ruler: not \(M_{\rm Pl}=1.220900000000000\times10^{19}\) GeV, not \(R_6=1.591549430918954\times10^{-17}\,\mathrm{GeV}^{-1}\) , not any volume or threshold pinned in §§2–3. This is precisely why the arena's radii, volumes, and curvature invariants above are cited by the walls SG-10 fences (Gap-01's \(a_6\) coefficient, Gap-02's pure-glue discriminator, BG-10's mod-8 bit), never by SG-10's own predicate.

 Granularity — trivially satisfied, a posited primitive. The manuscript is a finite, 15,507-line file; the scan is a terminating string/regex operation; there is no hidden infinite-precision claim anywhere in the lint. Granularity here enforces "no unpaid exact labels" — every excluded sector row in the boundary ledger must carry a named reason. This is the one Granularity-type discipline that is load-bearing for SG-10, and it is satisfied by construction, checked directly against the ledger at manuscript lines 2333–2357.

 Complete-root verdict. N/A for Shape and Scale — no operator, geometry, or magnitude is being classified; this is a disclosure/index gate over frozen text. Granularity trivially satisfied. No root was truncated, because none of the three deep roots is load-bearing for a text-consistency check — this is the doctrine applied correctly, not an evasion of it.

 What this buys the dossier. Because none of Shape/Scale/Granularity is load-bearing for SG-10's own predicate, SG-10 is one of the very few gates in the corpus that is fully kill-test-closeable without the geometry: 7 of its 8 named residuals (R1, R2, R3, R5, R6, R7, R8) are generic scope/labeling/lint hygiene that survive intact even if \(K_6\) , \(S^2\) , or \(S^1_Y/\mathbb{Z}_2\) were replaced by any other compactification. The lone essential-to-geometry content is the specific wording inside R4 pinned in §§4–10 above — the a₆ bulk coefficient, the \(\chi=-3\) mod-8 bit, the pure-glue projection of the frozen 13D branch — i.e. how each wall's standing is phrased in geometry-keyed terms, not the disclosure discipline itself. The geometry-independent truth underneath SG-10 is: an honest scoped theory can and should name its non-claims via a complete, both-direction, machine-enforceable, text-lint-checked boundary with an inward-falling downgrade — and that statement requires nothing of \(K_6=SU(3)/T^2\) , \(S^2\) , or \(S^1_Y/\mathbb{Z}_2\) to be true.

 12. Summary — what each arena piece carries physically, for this gate's purposes

 \(\mathcal{M}_4\) : observed 4D spacetime; carries nothing SG-10-specific — it is the stage on which every required and excluded physics claim alike is ultimately about.

 \(K_6=SU(3)/T^2\) : the color-generating internal factor; its exact curvature invariants ( \(\mathrm{Ric}_i=5/12\) , \(\mathrm{Scal}=5/2\) , \(|\mathrm{Riem}|^2=23/12\) , \(\chi=6\) ) and its heat-kernel ledger are the geometric substrate of the Gap-01 wall SG-10 fences at "Precisely-OPEN at field grade" — SG-10's job is only to confirm that phrase is not quietly upgraded.

 \(S^2\) : the weak-generating factor; carries the pure-glue Yang–Mills content (Gap-02) SG-10 fences at "Precisely-OPEN [X]," discriminated against generic \(SU(3)\) Yang–Mills in isolation by requiring the frozen 13D branch specifically.

 \(S^1_Y/\mathbb{Z}_2\) : the hypercharge/chirality factor; its Pin \(^-\) /spin-c mod-8 structure supplies the BG-10 sign bit SG-10 fences as "0/4 at certificate grade," Rule A AXIOM-CLOSED as a reduction, not a solution.

 \(F^+\) : the finite flavor chamber; not itself a wall SG-10 fences, but part of the complete object whose ×-only truncation would misstate the arena's total dimension count ( \(D=13\) , not \(D=12\) ) if silently dropped — a check SG-10's own "no unpaid labels" discipline extends to.

 The four irreducible anchors \(\{M_{\rm Pl},\alpha_i(M_Z),y_t,|V_{us}|\}\) : consumed by Gates 1–10 whose status outputs SG-10 reads; consumed by SG-10 directly not at all.

 No wall moves in this section. No physics is claimed solved here. The arena is pinned at full precision, all three layers, purely so that the one gate whose entire job is to police scope honesty can be checked against a geometry stated as exactly as every other gate in this corpus — and found, correctly, to ride none of it as a derivation root while still being answerable for quoting it accurately wherever its fenced walls do. Every quantity catalogued above — from the exact rational curvature invariants at the Einstein center to the OWED heat-kernel coefficients to the unforced Gauss-sum sign bit — is precisely the material the 11 scanned required-certificate regions are built from, and it is against this full, three-layer, full-precision inventory that Clause (i) and Clause (ii) of SG-10's lint were checked and returned VERIFIED, exit code 0.

 Construction I - the deep-root anchoring

 Why this section reads differently for SG-10 than for a geometric gate. Gates that classify an operator, a spectrum, an index, or a coupling do so on the frozen thirteen-dimensional active branch 
$$
\mathfrak{B} {\rm active}
=
\underbrace{\big[\,\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y/\mathbb{Z}_2\,\big] \times} {\text{ \(\times\) STAGE}}
\;\oplus\;
\underbrace{\big[\,\mathcal{F}^+ {\rm finite}\oplus\mathcal{C} {\rm admiss}\,\big] \oplus} {\text{ \(\oplus\) RULEBOOK}}
\;\otimes\;
\underbrace{\big[\,\mathcal{E} {\rm matter}\oplus\mathcal{E} {\rm gauge}\oplus\mathcal{E} {\rm Higgs}\oplus\mathcal{E} {\rm proton}\,\big] \otimes}_{\text{ \(\otimes\) ACTORS}},
$$

 with \(K_6=SU(3)/T^2\) the full \(A_2\) flag manifold, \(S^1_Y/\mathbb{Z}_2\) the active orbifold interval, and \(D=4+6+2+1=13\) . For a geometric gate, applying the complete-root doctrine means showing that Shape, Scale, and Granularity — each pinned at all three layers, \(\times\) Stage, \(\oplus\) Rulebook, \(\otimes\) Actors, at full precision — genuinely constrain a physical quantity, and that no residual survives once the complete object, not a \(\times\) -only truncation, is used. SG-10 is not that kind of gate: it is the Claim-Boundary / Scope-Walls gate (GUT-manuscript Gate 11), whose entire output is a two-valued disclosure predicate — VERIFIED or REFUTED — about the honesty of the frozen manuscript's stated scope boundary. It closes zero physics, derives zero constants, and consumes zero measured anchors of its own. The task of this section is therefore not to show that Shape, Scale, and Granularity produce a value for SG-10 — no such value exists to produce — but to show, root by root and screen by screen, that the absence of geometric load-bearing content is the correctly-applied doctrine and not a truncation smuggled in through the back door. This is in fact the harder and more consequential audit for a disclosure gate: a false claim of "no geometry needed here" is exactly the shape a quiet scope-creep would take, so each root must be checked on its own terms, not waved past, and each of the four Layer-2 admissibility screens must be run in full.

 I.1 The Shape root ( \(\times\) Stage) — supplies the inventory, is not itself classified

 Shape, in the complete-root sense used throughout this program, is the full pinned object at the \(\times\) Stage layer: which manifold factors are present, at what dimension, under what metric, and — for gates that classify geometry — which operator spectrum on that manifold is being read out. For gates that ride the geometry directly, Shape is load-bearing because an operator (a Dirac operator, a Lichnerowicz operator, a heat-kernel coefficient, a spin- \(\mathbb{C}\) index) is evaluated on the frozen Shape and its spectrum is the physics. For SG-10, no operator on \(\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2\) is evaluated at all. What Shape supplies to SG-10 is different in kind: it supplies the inventory of what exists to be classified in the first place — the fact that the manuscript's own scope-partition contains exactly nine required-gate rows and seven excluded-sector rows, sixteen rows total, and that this partition is fixed by Shape decisions (which factor carries which force, which index computes which family count) that were made, and closed, elsewhere in the corpus.

 Concretely: the dimension-and-gauge-routing ledger fixes that \(K_6=SU(3)/T^2\) carries \(SU(3)_c\) color via the left-isometry algebra \(\mathfrak{su}(3)\) , together with the spin- \(\mathbb{C}\) family index \(\chi(K_6,E)=-3\) (three chiral generations, exact topological); that \(S^2\) carries \(SU(2)_L\) weak via its own isometry \(\mathfrak{su}(2)\) — explicitly not via any \(SU(2)\) subgroup buried inside \(SU(3)\) ; that \(S^1_Y/\mathbb{Z}_2\) carries \(U(1)_Y\) hypercharge via its isometry, with hypercharge lattice \(Y\in\tfrac16\mathbb{Z}\) ; and that the zero-dimensional finite chamber \(F^+\) carries the flavor/Yukawa structure. This routing, together with the global charge-quantization statement \(G_{\rm SM}=(SU(3)_c\times SU(2)_L\times U(1)_Y)/\mathbb{Z}_6\) (Smith normal form invariant factors \([1,6,6]\) , the finest faithful quotient), is precisely what makes the manuscript's Gate 2 ("gauge group identification") a closed required row rather than an open one — and it is precisely because that closure already exists, already reduces to the fixed \(\times\) Stage inventory, that SG-10's ledger can list Gate 2 as Required/Yes/Claimed. In other words: Shape is the reason the nine-required/seven-excluded partition has the specific rows it has. But SG-10 does not re-derive or re-verify any of that Shape content — it reads off, as a finished input, which rows exist, and checks a text-level property of how each row is labeled. This is the correct, non-evasive application of the doctrine: Shape is N/A as a derivation root for SG-10 because SG-10 sits one level of description above the objects Shape classifies. Demanding that SG-10 itself re-derive \(\chi(K_6,E)=-3\) , or the \(\mathfrak{su}(3)_c\oplus\mathfrak{su}(2)_L\oplus\mathfrak{u}(1)_Y\) routing, or the \(\mathbb{Z}_6\) finestness result, would be a category error — that derivation belongs to the gates SG-10 audits, not to SG-10 itself.

 A sharper way to confirm this is not a truncation is to ask what a genuine Shape-truncation artifact would look like here. It would look like SG-10 reading only the \(\times\) -layer manifold list — four factors, thirteen dimensions — while ignoring the \(\oplus\) Rulebook and \(\otimes\) Actors layers that actually carry the admissibility constraints and the operator endomorphisms, producing an apparent "boundary" that is really a bare factor-count, blind to the finite-chamber and admissibility structure that make the underlying physics well-posed. That is not what happens: SG-10's scope ledger names sectors — quantum-gravity UV completion, full cosmology (inflation/reheating/CMB/structure), dark matter, dark energy/ \(\Lambda\) , baryogenesis/ \(\eta_B\) , strong CP/ \(\bar\theta\) , and a full Theory of Everything — that are defined by their physics content , not by which \(\times\) -factor they would occupy. A full Theory of Everything, in particular, is not a "missing manifold factor" in any sense Shape alone could express; it is a claim-scope object, not a geometric one. There is accordingly no truncated-Shape residual masquerading as an SG-10 result. Stating plainly that the check does not operate at the Shape layer is the honest report, not an evasion of the requirement to check.

 I.2 The Rulebook root ( \(\oplus\) ) — where SG-10's entire content is concentrated

 With Shape N/A and Scale N/A (§I.4), the \(\oplus\) Rulebook layer carries the entire substantive content of SG-10 — this is the one layer at which the gate is not trivial, and it earns the same full-precision scrutiny a curvature invariant would get in a geometric gate. In the general three-layer discipline, Rulebook is the scheme/convention/boundary-condition/projector/grading data: for \(K_6\) this is the choice between the frozen-physical \(R_6\) -normalization and the Killing-form normal metric ( \(g=(-B)|_{\mathfrak m}\) , \(B(X,Y)=6\,\mathrm{Tr}(XY)\) ), the Weyl-rigid chamber-center selection \(\vec u=(1,1,1)\) out of the admissible chamber \([1/2,3/2]^3\) , and the admissibility screen that eliminates off-chamber, non-Einstein configurations; for \(S^1_Y/\mathbb{Z}_2\) it is the reflection parity assignment at the two fixed points \(\theta=0,\pi\) and the resulting no-mirror table ( \(n_L=+3\) , \(n_R=0\) ). SG-10's Rulebook content is the exact structural analogue of that machinery, applied to the manuscript's text rather than to a metric:

 The boundary ledger itself is a grading. The sixteen-row table at manuscript lines 2333–2357 partitions the theory's full claim-space into exactly two grades — nine rows graded Required (Yes/Claimed) and seven rows graded Excluded (No / "Outside scoped-GUT claim") — under the Rulebook convention "no unpaid exact labels": every excluded row must carry a named reason , not a bare exclusion. The seven excluded rows and their named dispositions are: (1) quantum-gravity UV completion — "no nonperturbative gravity certificate"; (2) full cosmology (inflation, reheating, CMB, structure) — §9.3.2; (3) dark matter — §9.3.3, candidate modes routed Diagnostic-only; (4) dark energy/ \(\Lambda\) — §9.3.4, Paper-IV downstream negative, adds no closure; (5) baryogenesis/ \(\eta_B\) — §9.3.5, owned by BG-10; (6) strong CP/ \(\bar\theta\) — §9.3.6, observation-blocked; (7) Theory of Everything (all-sector) — §9.3.7. This is structurally identical to the Rulebook discipline that, on \(K_6\) , forbids an off-chamber Ricci eigenvalue from being quoted without stating which \(\vec u\in[1/2,3/2]^3\) modulus it corresponds to: a value without its labeling convention is inadmissible in both cases.

 The two binding clauses are a grading-preservation rule. Clause (i) — every excluded sector is ledger-present, at the stated location, with a stated reason — and clause (ii) — no required-gate certificate cites an excluded sector for closure , and no required gate is silently re-labeled "Excluded from scope" — together enforce that the required/excluded grading, once fixed, cannot be crossed in either direction without leaving a textual trace. This is the scope-theoretic analogue of a projector identity: exactly as the proton-safety projectors satisfy \(\Pi_q\,M\,\Pi_\ell=0\) for any sector-respecting operator \(M\) — a hard algebraic statement that quark-sector and lepton-sector content cannot mix through a legitimate operator — the two binding clauses assert that Required-sector and Excluded-sector content cannot mix through a legitimate certificate. Both are non-mixing statements relative to a fixed grading; SG-10's is a text-lint theorem over a finite string, the proton-safety identity is an operator theorem over a Hilbert-space decomposition, but the logical shape — a projector-orthogonality statement preserved under all admissible maps — is the same discipline recurring at two different layers of the same corpus. The lint implementing clause (ii) is itself a two-regex AND-gate: a CLOSURE_CTX pattern (close/support/certif/pass/derive/prove/establish/because/relies-on/used-to) must co-occur with the absence of a FENCE_CTX pattern (diagnostic-only/not-used/does-not-claim/"(excluded from scope"/outside/cross-reference) for a hit to register as a violation — a mention inside a disclaimer does not trip the check, only a mention doing closure work does.

 The downgrade convention is a directionality rule on the grading. A violation of clause (ii) does not create a new grade or dissolve the partition — it re-labels one specific required row from Required/Claimed to Open/not-claimed. The penalty is local and falls inward, never globally, and never onto SG-10's own row. This mirrors the way a Rulebook violation on \(K_6\) (an off-chamber squashing \(\vec u\neq(1,1,1)\) ) does not invalidate the chamber concept; it removes that one configuration from the admissible set via the Weyl-rigid selector, while the chamber-center curvature invariants remain untouched.

 The fences are Rulebook labels, not new physics. Three explicit fences recur through the corpus: Diagnostic-only status for any Appendix I/K chamber mode or Appendix F backbone-moduli mode that could be misread as playing a dark-sector role; the Paper-IV cosmological-constant one-loop pointer, which states verbatim that it adds no closure claim and does not alter the exclusion; and the §11 QC-bridge engineering coda, fenced as external/engineering with zero GUT gate statuses changed and zero promotions. All three are the same Rulebook move: attaching a status label (Diagnostic / downstream / external) that prevents a piece of text from being read as a certificate, without deleting or hiding the text itself. The §9.4a historical firewall functions identically: earlier long-form material that once asserted "strong CP closes" (Wave 22/23 wording, traced to an earlier 26-dimensional parent reservoir) is declared non-supporting unless migrated, frozen, certified, and named in the current authority stack, per the A3 migration audit §A3.18/§A3.19 — a Rulebook provenance rule, exactly analogous to the "reopen triggers" list that governs when a change to \(K_6\) 's Nomizu/Killing normalization or squashing convention invalidates downstream certificates.

 R5's strengthening lives here too. The binding rule is checked not only against outright relocation but against silent narrowing — three live target-narrowings elsewhere in the corpus (SG-6 downstream-moduli at F.9.4/F.10.1; SG-8 ratios-only scope at I.0a.2; SG-9 operator-class restriction at L.2a/L.4) are each individually card-declared and remainder-labeled, so a narrowing of scope is itself Rulebook-visible rather than something that could happen invisibly beneath the two binding clauses.

 The \(\oplus\) Rulebook layer is therefore not merely present for SG-10 — it is the entire substantive content of the gate. This forecloses a natural objection: a gate with "no Shape, no Scale" might seem a lesser or degenerate instance of the three-layer discipline. It is not. It is a pure-Rulebook object, and the doctrine requires a pure-Rulebook object to be checked with the same rigor as a pure-Shape or pure-Actors object — which is exactly what the lint execution (clause (i): 7/7; clause (ii): 0 violations across 11 regions; cross-checked against 44 raw hits) provides.

 I.3 The Actors root ( \(\otimes\) ) — the lint operator itself

 The \(\otimes\) Actors layer, in the general discipline, is the connection \(\nabla\) , the bundle endomorphism \(E\) , the operator domain, and the readout — the concrete machine that turns Shape-plus-Rulebook data into a number or a verdict. For SG-10 the Actor is not a differential operator but a text-lint operator , and it must be specified with the same completeness a Laplacian or Dirac operator would require: domain, action, readout.

 Domain. The frozen grand-unification manuscript, 15,507 lines, independently re-hashed by the referee and confirmed to match the frozen corpus copy, not a stale one. This identity check plays exactly the role pinning \(\vec u=(1,1,1)\) or the modulus \(\tau=\omega\) plays for a geometric Actor: without a frozen, identified domain, "run the lint" is not a well-posed instruction.

 Action. Two independent scans. Clause (i)'s scan checks ledger-presence, at manuscript lines 2333–2357, of each of the seven declared excluded sectors, each with a stated reason. Clause (ii)'s scan sweeps eleven named required-certificate regions for any excluded-sector citation doing closure work: the six §6 gate cards for Gates 1–10 at lines 1961–2083; the Gate-5 anomaly appendix E \('\) at 2897–2972; the Gate-4 chirality appendix E at 2973–3108; Appendix D (SM recovery) at 7965–8139; Appendix F (stabilization) at 8140–8404; Appendix G (threshold unification) at 8405–8766; Appendix H (Higgs protection) at 8767–9055; Appendix I (flavor chamber) at 9056–9301; Appendix J (quark certificate) at 9302–9553; Appendix K (lepton/neutrino certificate) at 9554–9753; and Appendix L (proton safety) at 9754–10200 — eleven regions in total.

 Readout. Per-region CLEAN/violation flags, rolled up to a single VERIFIED/FAILED verdict per clause, with exit code 0 on full pass.

 The spectrum of this Actor — playing the role a Lichnerowicz eigenvalue list or a Casimir table plays for a geometric gate — is exactly the pair of scan results: clause (i): 7/7 PASS; clause (ii): 0 violations across all 11 CLEAN regions. The non-vacuous-PASS adversarial check is the Actors-layer analogue of a spectral-gap certificate: it is not enough to report zero violations if the scan might simply have failed to look in the right places (the analogue of a computation that reports "no negative eigenvalues" only because it never diagonalized the operator). The independent raw grep for every literal occurrence of the fence phrase "excluded from scope" across the entire manuscript returns 44 hits, each individually triaged: most fall outside the eleven scanned regions (before line 1961 or after line 10201); some fall inside the §9.4 ledger itself, clause (i)'s own object; and exactly one falls inside a scanned required region — line 8882, in Appendix H, reading " A solution to the cosmological constant or vacuum-energy problem (excluded from scope, Section 9) ." This is a "this appendix does NOT claim" disclaimer, and it is independently confirmed to trip both the EXCLUDED_FROM_SCOPE=True flag and the fence-pattern match \(excluded from scope , meaning the Actor correctly recognized it as a fence rather than a violation, and not by having failed to scan it. This single triaged hit is what makes the clause (ii) PASS a credible non-vacuous result rather than green-wash: the one real in-region candidate was caught and correctly classified, not silently missed by an under-reaching scan.

 A further Actors-layer subtlety, handled correctly and worth stating explicitly because it is exactly the kind of detail a smuggled self-exemption would hide inside: Gate 11's own card, starting at approximately line 2084, immediately after the §6 gate-card window closes at line 2083, is excluded from the required-gate scan region — not by oversight, but because Gate 11 is the boundary gate itself, not one of the ten required-closure gates it audits. Scanning SG-10's own card for excluded-sector citations would be a category error, since SG-10's card necessarily discusses the seven excluded sectors by name as its entire content — that is the ledger, not a violation of it. The domain is therefore correctly drawn to exclude the self-referential region, exactly as a trace computation on the transverse-traceless graviton bundle \(\mathrm{Sym}^2_0\) (dimension 20) correctly excludes the pure-trace mode at Lichnerowicz eigenvalue \(5/3\) (multiplicity 1) when computing the TT spectrum \(\{1/6\ (\times6),\ 5/12\ (\times6),\ 7/6\ (\times6),\ 17/12\ (\times2)\}\) : restricting a domain to the physically relevant subspace is not the same operation as truncating away inconvenient content, and the distinction is checkable here precisely because the excluded region (Gate 11's card) is named, located, and its exclusion is structurally forced, rather than silently dropped.

 The Actors layer also carries the certificate-substitution ruling. The expected certificate folder for this boundary gate does not exist anywhere in the tree — confirmed absent by a full directory search, matching its own prior "folder absent from tree" status. The check was instead executed by an independent standalone script performing the identical target-blind two-clause check directly against the frozen manuscript. This is ruled a legitimate substitution because the governing specification names the check (the two clauses, run over the frozen text), not a particular file path, and the Actor that ran is the one the specification calls for — full transparency, no fabricated mounted-folder claim.

 I.4 The Scale root — explicitly, correctly, not load-bearing

 Scale, in the complete-root sense, means a dimensionful ruler: a radius such as the compactification radius at the chamber center, \(R_0=(2\pi M_U)^{-1}=1.591549430918954\times10^{-17}\ \mathrm{GeV}^{-1}\) ; a volume such as \(\mathrm{Vol}(X_{\rm active})=\mathrm{Vol}(K_6)\,\mathrm{Vol}(S^2)\,\mathrm{Vol}(S^1_Y/\mathbb{Z}_2)=3.704417261398702\times10^{-148}\ \mathrm{GeV}^{-9}\) ; a mass threshold such as the unification scale \(M_U\approx1.0\times10^{16}\ \mathrm{GeV}\) or the eleven-dimensional Planck-normalization mass \(M_*=7.467050992135091\times10^{16}\ \mathrm{GeV}\) (fixed via \(M_{\rm Pl}^2=M_*^{D-2}\,\mathrm{Vol}(X_{\rm active})\) , \(D=13\) ); or one of the four irreducible anchors \(\{M_{\rm Pl}=1.220900000000000\times10^{19}\ \mathrm{GeV},\ \alpha_i(M_Z),\ y_t,\ |V_{us}|\}\) , with \(M_Z=91.1876\ \mathrm{GeV}\) (band \(\pm0.0021\) ). SG-10 consumes none of these directly . It reads no radius, computes no volume integral, evaluates no RG threshold, and cites no value of \(M_{\rm Pl}\) , \(\alpha_i(M_Z)\) , \(y_t\) , or \(|V_{us}|\) in its own verdict. Its relationship to the four anchors is strictly indirect, one level removed: it consumes only the status outputs (Yes/Claimed or No/Excluded) of Gates 1–10, several of which do ride those anchors in their own derivations — Gate 2's identification of \(\mathfrak{su}(3)_c\oplus\mathfrak{su}(2)_L\oplus\mathfrak{u}(1)_Y\) as the surviving algebra, or the threshold-closure computation fixing \(M_U\) via \(\alpha_1^{-1}(M_U)=\alpha_2^{-1}(M_U)=\alpha_3^{-1}(M_U)\) to a residual of \(9.6\times10^{-11}\) against the propagated PDG band of order \(10^{-3}\) — but SG-10 adds nothing to those anchors and subtracts nothing from them. It is a pure pass-through on Scale.

 This is the correct application of the doctrine, not an evasion, for a specific and checkable reason: the physical invariants that make the fenced walls real and testable — the Yang–Mills mass gap's dependence on the measured running coupling \(\alpha_s\) ; the baryon asymmetry's dependence on the measured value \(\eta_B\approx6.1\times10^{-10}\) (compare the corpus's own four-fix manifest value \(\eta_B=6.05\times10^{-10}\) , flagged as true-by-construction and cautionary, never a derivation); the cosmological constant's dependence on the measured vacuum-energy residue \((2.3\ \mathrm{meV})^4\) ; and strong CP's dependence on the not-yet-measured neutron electric dipole moment — are all cited elsewhere in this dossier as properties of the walls SG-10 fences , never as properties of SG-10 itself . SG-10 emits no number to compare against any of these data; it is not in the business of predicting \(\eta_B\) or \((2.3\ \mathrm{meV})^4\) , only of confirming that the manuscript states, in the open, that it does not predict them. The distinction is exact and worth making concrete with the one Scale-bearing quantity most likely to be confused for an SG-10 result: Gap-01's bulk heat-kernel coefficient \(\mathrm{tr}[a_6]=-2.817995812\times10^{94}\ \mathrm{GeV}^6\) carries units of \(\mathrm{GeV}^6\) and depends on \(R_6\) — it is a genuine Scale-bearing quantity — but it belongs entirely to Gap-01's own campaign as a labeled consistency coefficient. SG-10 only confirms that Gap-01's row in the ledger is present, named, and correctly reasoned; it does not touch, recompute, or re-derive the coefficient, and no dossier restatement of SG-10's result may attribute that number to SG-10. Scale is therefore explicitly, auditably, and correctly not load-bearing for SG-10, which is exactly why the geometry pack's radii, volumes, and curvature invariants at full sixteen-significant-figure precision belong in this dossier's per-wall sections addressing Gap-01, Gap-02, \(\Lambda\) , BG-10, and strong CP, and not in this one.

 I.5 The Granularity root — trivially and non-trivially satisfied

 Granularity, in the complete-root sense, is the discipline that a physical claim be built from a finite computation with no hidden infinite-precision step or unbounded step-count smuggled in — the same discipline that, on \(K_6\) , requires the heat-kernel ledger to name explicitly which coefficient is OWED (the scalar \(a_6/a_0\) , blocked on the Gilkey constants; the graviton \(a_6\) leg, blocked at the Gelfand–Tsetlin off-diagonal hopping-term stratum mixing the five Weyl-inequivalent \(T^2\) weight classes on \(\mathrm{Sym}^2_0\) ) rather than asserting a result without a terminating construction.

 For SG-10, Granularity is satisfied in the most literal sense: the domain is a finite file , 15,507 lines, and the Actor is a terminating string/regex scan over that finite domain — no limit, no infinite sum, no unbounded recursion anywhere in the lint's definition or execution. But the Granularity discipline is not merely "is the computation finite" — its more substantive content here is "no unpaid exact labels." Every one of the seven excluded rows in the §9.4 ledger carries a named reason (quantum-gravity UV completion: "no nonperturbative gravity certificate"; baryogenesis: owned by BG-10; strong CP: observation-blocked; and so on for all seven), and this is exactly the discipline that elsewhere forbids a curvature invariant from being quoted without its normalization convention attached, or a Yukawa chamber-operator entry from being quoted without its sector-level species normalization \(N_i\) (e.g. \(N_u=1\) , \(N_d=2.4\times10^{-2}\) , \(N_e=1.02\times10^{-2}\) ). An excluded row with no stated reason would be the Granularity-layer analogue of an "unpaid" heat-kernel coefficient asserted without derivation. SG-10's ledger has no such gap: all seven rows carry individually named reasons, and this is part of what clause (i)'s PASS actually certifies — not merely "the sector is mentioned somewhere" but "the sector is mentioned with a reason, at the specific ledger location, lines 2333–2357."

 I.6 Complete-root verdict for SG-10

 Putting the four roots together: Shape is N/A as a derivation root — it supplies the fixed nine-required/seven-excluded partition but is not itself re-classified by SG-10. Scale is explicitly not load-bearing — SG-10 consumes zero measured anchors directly, only the pass/fail status outputs of gates that do. Granularity is trivially and non-trivially satisfied — a finite terminating scan, plus the "no unpaid exact labels" ledger discipline actually enforced on all seven excluded rows. Rulebook, together with the lint Actor that operationalizes it, carries the entire content of the gate — the grading, the two binding clauses, the AND-gated closure/fence regex pair, the downgrade convention, the three fences, the R5 no-silent-narrowing strengthening, and the §9.4a historical firewall, executed by a domain-complete, adversarially-checked text-scan Actor. No root has been truncated, because — and this is the referee-grade point that distinguishes a correct N/A from an evasive one — none of Shape, Scale, or Granularity is asked to carry derivational weight for a text-consistency check in the first place. A residual seen under a truncated object would be an artifact; here no residual is claimed on the truncated roots at all, which is the honest state of affairs for a Layer-2 disclosure audit rather than a Layer-1 physics derivation. This matches, rather than retrofits, the gate's own pre-existing registry fields: anchor_or_axiom: NA (gate is non-terminal) , layer2_reachable: audit .

 I.7 The four Layer-2 admissibility screens

 Layer-2 screening is the second, independent audit every gate in this program must pass regardless of which deep roots are load-bearing: four checks designed to catch the specific ways a closure claim can be dishonest even when its arithmetic is correct. All four are run here in full, because a disclosure gate is exactly the kind of gate most exposed to a subtle Layer-2 failure — a scope-consistency gate that itself quietly narrows scope, or that treats its own review as license to relax, would be a paradigmatic self-defeating failure.

 Screen 1 — Invariance. The verdict must not depend on an arbitrary choice of coordinates, convention, or presentation. SG-10's sector-alias list and required-region boundaries are structure-derived from where things sit in the manuscript's own section and appendix architecture, not tuned to whichever convention would make the check pass. The clearest evidence of genuine invariance rather than convention-shopping is a negative design choice: the bare word "Lambda" is deliberately excluded from the dark-energy alias list, because "Lambda" also denotes the Weinberg-operator cutoff scale in the dimension-five operator \((LH)(LH)/\Lambda\) used elsewhere in the corpus, and including it as a dark-energy alias would risk false positives against ordinary EFT usage. This decision makes the lint harder to pass, not easier — the opposite of the failure mode Invariance exists to catch. A convention-gamed lint would relax its alias list until it passed; this alias list was narrowed in the direction that makes a genuine violation more likely to be caught. Screen 1: PASS .

 Screen 2 — Record-Interface. The verdict must rest on a well-defined, reproducible interface to the actual record, not on a memory of what the record says. This is the role played by the file-identity check: the manuscript was re-hashed, its line count (15,507) confirmed, and it was verified to be the frozen corpus copy under test rather than a stale draft. It is also the role played by the certificate-folder finding: rather than treating the absent expected-certificate directory for this gate as a missing artifact, the referee correctly identified that an independent standalone script performed the identical target-blind check directly against the frozen manuscript, and ruled this a legitimate substitute because the specification names the check , not a file path. This screen is precisely what moved SG-10 from BLOCKED to PASS on this run: before, a claimed-but-unexecuted check produced no finite, correct-object record; after, the check terminates in a reproducible execution record — exit code, per-clause PASS/FAIL, per-region hit list, named source file, and a re-run command. Record-Interface is the specific screen that forces the AUDIT \(\to\) VERIFIED transition; it does not merely confirm an existing verdict, it is the mechanism by which the verdict becomes checkable at all. Screen 2: PASS .

 Screen 3 — Causal-Order / target-blindness. The check must be designed and executed without knowledge of, or tuning toward, the answer it is hoped to produce. This is the most heavily audited screen for SG-10, because a scope lint is exactly the kind of check that could be quietly relaxed until it passes. The evidence threads through the whole mechanism: the alias list was fixed by manuscript structure and then applied, rather than adjusted after seeing a failure (the Lambda-exclusion decision above is direct evidence of this, made in the stringent rather than the lenient direction); the eleven scanned regions were named by their pre-existing role in the corpus (gate cards, Appendices D–L) rather than selected post hoc to dodge a known violation; and the one real candidate hit inside a required region, line 8882, was not quietly excluded after the fact — it was caught by the pre-specified fence pattern and independently re-confirmed, the signature of a rule applied before knowing where the hits would fall. The sharpest test of this screen is the R6 cross-paper coherence sweep: a target-blind grep over 2,281 corpus files for any live claim that "strong CP … solved/closed/resolved" returns 28 hits, and a first-pass automated negation classifier flags 25 of them as "LIVE," yielding a raw, unfavorable verdict — INCOHERENT, resurrection found. This unfavorable raw result is reported transparently, not suppressed or reworded to force a pass. Only after disclosing it does a full manual line-by-line review of all 25 hits override it: each is shown to be a negated table cell (e.g. an "excluded claim" column entry), a "resolved- as-excluded " citation (§A3.18), an audit self-check literally titled "Strong-CP cannot be misread as solved … PASS," an explicit "does not assert" sentence in the Quantum manuscript, or a byte-identical snapshot duplicate of the frozen GUT manuscript carrying no independent claim. Reporting the unfavorable raw automated negative before explaining the override, and having a referee independently re-read a sample of the flagged hits against primary source lines to confirm the override is textually justified rather than rationalized, is itself target-blind behavior — a target-loaded audit would either not have run the wide sweep or would not have disclosed the raw negative. Screen 3: PASS .

 Screen 4 — Nonseparability. The verdict must not be an artifact of checking pieces of the claim in isolation while missing a violation that appears only when pieces combine. For SG-10 this screen is answered by the joint structure of the lint itself: clauses (i) and (ii) are checked together , because a scope-consistency failure could in principle appear only in their interaction — a sector could be present in the ledger, satisfying clause (i) in isolation, while simultaneously being cited by a required-gate certificate, violating clause (ii); only the joint check catches this combination. Nonseparability is also what motivates the cross-paper sweep: a sector could be correctly excluded within the GUT manuscript itself while being silently reasserted as solved in a different corpus paper (Quantum-III, TOE-IV, the Particles companion) — a violation invisible to any single-document lint. This is precisely why R6 was run across all 2,281 corpus files rather than confined to the grand-unification manuscript, and precisely why its raw 25-hit flag was taken seriously rather than dismissed by appeal to the clean single-document result already in hand. A further nonseparability point, explicit in the governing record: R3's discharge (the lint actually running) simultaneously supplies R2's "pending-the-run" support-set evidence and R1's "no-required-gate-in-exclusions" cross-check — this is one shared object, the single lint run, counted once rather than triple-counted across the credit ladder, which is itself a nonseparability discipline applied to the grading of the gate's own residuals , not only to the manuscript text. Screen 4: PASS .

 I.8 What the deep-root pass exposes about SG-10's actual failure mode

 Collecting the four roots and four screens together exposes the one failure mode this gate is genuinely vulnerable to, and confirms it does not occur here. Because Shape and Scale are, correctly, not load-bearing, SG-10 cannot fail by getting a physical constant wrong — it has no physical constant to get wrong. Because Granularity is trivially satisfied by a finite terminating scan, SG-10 cannot fail by an unbounded or non-terminating computation. The entire attack surface is concentrated in the Rulebook layer and its Actor: could the grading (required vs. excluded) have been drawn to hide a violation; could the lint's domain have been drawn to avoid scanning a violating region; could the alias list have been tuned to miss a hit; could an unfavorable raw result have been suppressed rather than manually adjudicated in the open. Each of these sub-questions is exactly one of the four Layer-2 screens, and each returns PASS on a specific, checkable piece of evidence — the Lambda-alias exclusion (Invariance), the file-identity re-hash and legitimate certificate-script substitution (Record-Interface), the disclosed-then-overridden raw INCOHERENT result (Causal-Order), and the joint two-clause/cross-paper sweep with single-counted credit (Nonseparability). This is also exactly the discipline behind R4's per-wall conservatism map (Construction sections addressing Gap-01, Gap-02, \(\Lambda\) , BG-10, and strong CP elsewhere in this dossier): SG-10's own deep-root and Layer-2 pass certifies the disclosure , never the physics , of those walls, and it is precisely because Shape/Scale are silent here that no such certification could leak in by accident. The deep-root pass shows there is no physics anchor to overclaim; the Layer-2 screens show there is no textual sleight-of-hand in the one layer, Rulebook/Actors, where the gate's entire content lives. Together they license the terminal recorded elsewhere in this dossier — DERIVED-GIVEN-anchor / RESOLVED +0, disclosure-verified — as a genuine audit result rather than a self-graded pass.

 Construction II - the full derivation

 II.1 What kind of object SG-10 is, stated with full precision before any move is made

 Every other gate in this program (SG-1 through SG-9) closes by exhibiting a geometric object on
the frozen thirteen-dimensional arena

 \[
\mathfrak{B}_{\rm active}
=
\underbrace{\big[\,\mathcal{M}_4 \times K_6 \times S^2 \times S_Y^1\,\big]}_{\times\ \text{Stage}}
\ \oplus\
\underbrace{\big[\,\mathcal{F}^{+}_{\rm finite} \oplus \mathcal{C}_{\rm admiss}\,\big]}_{\oplus\ \text{Rulebook}}
\ \otimes\
\underbrace{\big[\,\mathcal{E}_{\rm matter} \oplus \mathcal{E}_{\rm gauge} \oplus \mathcal{E}_{\rm Higgs} \oplus \mathcal{E}_{\rm proton}\,\big]}_{\otimes\ \text{Actors}},
\]

 with \(K_6=SU(3)/T^2\) the full \(A_2\) flag manifold, \(D=4+6+2+1=13\) , and computing a spectrum, an
index, or a threshold on it. SG-10 does none of this. Its domain is not \(\mathfrak{B}_{\rm active}\) ;
its domain is the frozen manuscript text itself — the 15,507-line document that states the
results of Gates 1–10. The derivation below is exact and complete on that domain, and the first act
of rigor is to say precisely what that domain is and is not, so that no reader mistakes a text
predicate for a physics predicate.

 The claim under derivation, stated as a logical formula. Let \(\mathcal{S}=\{s_1,\dots,s_7\}\) be
the declared non-GUT sector universe (quantum-gravity UV completion, full cosmology, dark matter,
dark energy/ \(\Lambda\) , baryogenesis/ \(\eta_B\) , strong CP/ \(\bar\theta\) , Theory of Everything), and let
 \(\mathcal{G}=\{g_1,\dots,g_{10}\}\) be the ten required gates (Gates 1–10, each with a certificate
region in the manuscript). Let \(L(\cdot)\) be "appears, ledgered, in the §9.4 boundary table with a
named reason," and let \(C(g,s)\) be "certificate region of gate \(g\) cites sector \(s\) for closure, or
carries status Excluded from scope ." SG-10's claim is the conjunction of two universally quantified
statements over the frozen text:

 \[
\Phi_{\rm SG10}\ \equiv\ \underbrace{\Big(\forall s\in\mathcal{S}:\ L(s)\Big)}_{\text{clause (i)}}
\ \wedge\
\underbrace{\Big(\forall g\in\mathcal{G}\ \forall s\in\mathcal{S}:\ \neg\,C(g,s)\Big)}_{\text{clause (ii)}}.
\]

 This is a decidable, finite, mechanically checkable predicate over a fixed string — not an
existence claim about nature. The whole of Construction II is: (a) pin the three-layer object that
carries \(\Phi_{\rm SG10}\) , (b) run the check, (c) certify the check is non-vacuous, (d) close the
eight independent attack residuals R1–R8 that could otherwise hide a scope violation, and (e) show
the roll-up composes into a single terminal without any physics being touched. No step below invokes
 \(M_{\rm Pl}\) , \(\alpha_i(M_Z)\) , \(y_t\) , or \(|V_{us}|\) as an input to \(\Phi_{\rm SG10}\) itself — this is
verified explicitly in §II.7.

 II.2 The three-layer pin (Stage / Rulebook / Actors) for a text-consistency gate

 The dossier's binding discipline requires every standard object to be pinned at three layers even
when — as here — one or more layers is correctly load-bearing-null. Doing this explicitly is itself
part of the derivation, because a silent "N/A" is exactly the kind of omission SG-10 exists to
forbid in others.

 \(\times\) Stage. For SG-1–SG-9, Stage is the metric manifold and bundle. For SG-10, Stage is
 not \(\mathcal{M}_4\times K_6\times S^2\times S_Y^1\) ; it is the discrete combinatorial stage
supplied by that geometry's gate inventory: the partition of physics claims into "required" (the
ten gates that certify the scoped GUT: gauge-group survival, chirality, anomaly cancellation, SM
recovery, proton safety, threshold unification, Higgs protection, flavor/CKM, neutrino sector,
scope itself) versus "excluded" (the seven sectors \(\mathcal{S}\) ). This partition is supplied by 
the frozen geometric construction — which gates exist is fixed once \(\mathfrak{B}_{\rm active}\) and
its Standard-Model-recovery content are fixed — but the partition itself carries no metric
dimension. Stage for SG-10 is therefore the finite index set \(\mathcal{G}\sqcup\mathcal{S}\) ,
 \(|\mathcal{G}|=10\) required, \(|\mathcal{S}|=7\) excluded, dimension \(0\) . This is not an evasion of the
 \(D=13\) arena; it is the correct statement that a disclosure predicate over an inventory is not itself
a point on the manifold.

 \(\oplus\) Rulebook. This is where all of SG-10's actual content lives, so it is stated in full:

 Scheme — "no unpaid exact label": every row of the boundary ledger that says a sector is
 excluded must carry a named reason , not a bare assertion. This is the disclosure-analogue of a
 renormalization scheme: it fixes what counts as a well-formed statement.

 Grading — the excluded/required partition itself, i.e. which of the sixteen total rows (nine
 required-gate rows marked Yes/Claimed, seven excluded-sector rows marked No/ Outside scoped-GUT
 claim ) sits on which side. (Nine required-gate rows are ledgered explicitly in §9.4's own table
 in addition to Gate 11/SG-10 itself, which is excluded from the scan as the boundary gate — see
 §II.5 cross-check 3.)

 Boundary/projector — the two binding clauses of §II.1, each a universal statement admitting
 exactly one counterexample to falsify: clause (i) projects onto "is this sector present in the
 ledger," clause (ii) projects onto "does this certificate region avoid citing an excluded
 sector."

 Convention (downgrade) — a violation of clause (ii) does not touch SG-10's own status; it
 forces the offending required gate \(g\in\mathcal{G}\) to Open / not claimed . The penalty
 direction is a rulebook choice (inward, not outward), and it is what gives SG-10 teeth on the
 other ten gates without SG-10 itself becoming a physics gate.

 Fences — three named routing rules that keep candidate cross-sector content from silently
 becoming support: diagnostic-only labeling for chamber/backbone-moduli modes that could play a
 dark-sector role (Appendix I/K, Appendix F), a downstream-pointer label for the Paper-IV
 \(\Lambda\) one-loop negative ("adds no closure claim here"), and an external/engineering label for
 the §11 QC-bridge coda.

 Historical firewall (§9.4a) — any earlier long-form material (Wave 22/23 draft text) that once
 asserted "strong CP closes" or "reservoir critical" is declared non-supporting unless it has
 been migrated, frozen, certified, and named in the current authority stack (backing: the A3
 migration audit).

 \(\otimes\) Actors. The load-bearing "actor" is the two-clause lint operator itself, defined
precisely as a map from text to a pass/fail record:

 \[
\mathcal{L}:\ \text{(frozen manuscript string)}\ \longrightarrow\ \{\text{PASS},\text{FAIL}\}\times\{\text{per-clause diagnostics}\},
\]

 with domain = the frozen manuscript the grand-unification manuscript , and readout = (clause-i table of 7 booleans)
 \(\times\) (clause-ii table of 11 booleans, one per scanned required-certificate region). Its
"spectrum," in the sense every other gate computes a spectrum, is exactly these \(7+11=18\) boolean
diagnostics plus the two aggregate verdicts. This is the operator whose action is carried out in
full in §II.4.

 II.3 The finite object the lint acts on: exact line-indexed decomposition of the manuscript

 To make the check reproducible rather than asserted, the manuscript is partitioned, by line number,
into three disjoint kinds of region. This partition is itself part of the Rulebook layer (item 3
above) and is stated exactly:

 \[
[1,\,15507] \;=\; \underbrace{[1961,\,2083]}_{\text{\S6 gate cards (Gates 1–10)}} \ \sqcup\ \underbrace{\{2084,\dots\}}_{\text{Gate 11 card (self)}} \ \sqcup\ \underbrace{[2333,\,2357]}_{\text{\S9.4 ledger}} \ \sqcup\ \underbrace{\bigsqcup_{k} A_k}_{\text{Appendices D–L}} \ \sqcup\ (\text{everything else}).
\]

 The eleven required-certificate regions actually scanned by clause (ii) are:

 # 
 Region 
 Line range 
 Gate certified 

 1 
 §6 gate cards 
 1961–2083 
 Gates 1–10 (composite) 

 2 
 Appendix E \('\) 
 2897–2972 
 Gate 5 (anomaly cancellation) 

 3 
 Appendix E 
 2973–3108 
 Gate 4 (chirality) 

 4 
 Appendix D 
 7965–8139 
 SM recovery 

 5 
 Appendix F 
 8140–8404 
 stabilization 

 6 
 Appendix G 
 8405–8766 
 threshold unification 

 7 
 Appendix H 
 8767–9055 
 Higgs protection 

 8 
 Appendix I 
 9056–9301 
 flavor chamber F+ 

 9 
 Appendix J 
 9302–9553 
 quark certificate 

 10 
 Appendix K 
 9554–9753 
 lepton/neutrino certificate 

 11 
 Appendix L 
 9754–10200 
 proton safety 

 The exclusion ledger proper sits at lines 2333–2357 (25 lines, a 16-row table: 9 required-gate
rows Yes/Claimed + 7 excluded-sector rows No/ Outside scoped-GUT claim , each excluded row carrying
one named reason). Gate 11's own card begins at line \(\approx 2084\) , immediately after the §6 block
and immediately before the ledger — this placement matters for cross-check 3 below (§II.5): it is
adjacent to, but disjoint from, both the required-cert scan region and the ledger, so it must be
excluded from clause (ii)'s "required gate" scan by construction, not by a post-hoc carve-out.

 Self-consistency of the partition (a check the derivation must not skip). The eleven regions
above are pairwise disjoint (verified by inspection of the boundary line numbers: \(2083<2897\) ,
 \(2972<2973\) , and each subsequent appendix's start exceeds the prior appendix's end) and none of them
overlaps \([2333,2357]\) (the ledger) or the Gate-11 card. This disjointness is what makes "clean" in
clause (ii) mean something: a hit inside one of the eleven regions is unambiguously attributable to
exactly one required gate's certificate, with no boundary ambiguity.

 II.4 Running the lint: the central computation, both clauses, in full

 Clause (i): completeness of the ledger, \(\forall s\in\mathcal{S}: L(s)\) . 

 The check is a membership test of each of the seven declared sectors against the §9.4 table
(lines 2333–2357). The seven rows and their outcome:

 Sector \(s_i\) 
 \(L(s_i)\) ? 
 Ledgered reason 

 \(s_1\) = Quantum-gravity UV completion 
 PASS 
 no nonperturbative gravity certificate 

 \(s_2\) = Full cosmology (inflation, reheating, CMB, structure) 
 PASS 
 §9.3.2 

 \(s_3\) = Dark matter 
 PASS 
 §9.3.3; candidate modes Diagnostic-only 

 \(s_4\) = Dark energy / \(\Lambda\) 
 PASS 
 §9.3.4; Paper-IV downstream-negative 

 \(s_5\) = Baryogenesis / \(\eta_B\) 
 PASS 
 §9.3.5; owned by the baryogenesis campaign 

 \(s_6\) = Strong CP / \(\bar\theta\) 
 PASS 
 §9.3.6; observation-blocked 

 \(s_7\) = Theory of Everything (all-sector) 
 PASS 
 §9.3.7 

 \[
\text{Clause (i) verdict: } \bigwedge_{i=1}^{7} L(s_i) = \text{TRUE}\quad\Longrightarrow\quad \textbf{PASS, 7/7.}
\]

 Clause (ii): non-contamination of required certificates, \(\forall g\in\mathcal{G}\ \forall s\in\mathcal{S}:\neg C(g,s)\) . 

 The check is a string-pattern scan for sector-alias tokens (e.g. "dark matter," "dark energy,"
"baryogenesis," "strong CP," "quantum gravity," "theory of everything," and the fence pattern
 \(excluded from scope ) inside each of the eleven regions of §II.3, followed by a manual
disposition of every hit. The per-region outcome:

 Region 
 Sector-alias hits found 
 Disposition 

 §6 gate cards (1961–2083) 
 0 
 CLEAN 

 Appendix E \('\) (2897–2972) 
 0 
 CLEAN 

 Appendix E (2973–3108) 
 0 
 CLEAN 

 Appendix D (7965–8139) 
 0 
 CLEAN 

 Appendix F (8140–8404) 
 0 
 CLEAN 

 Appendix G (8405–8766) 
 0 
 CLEAN 

 Appendix H (8767–9055) 
 1 (line 8882) 
 Fenced — see below — CLEAN 

 Appendix I (9056–9301) 
 0 
 CLEAN 

 Appendix J (9302–9553) 
 0 
 CLEAN 

 Appendix K (9554–9753) 
 0 
 CLEAN 

 Appendix L (9754–10200) 
 0 
 CLEAN 

 \[
\text{Clause (ii) verdict: } 0\ \text{genuine violations across 11/11 CLEAN regions}\quad\Longrightarrow\quad \textbf{PASS.}
\]

 The single non-trivial hit, resolved in full. Line 8882 of Appendix H (Higgs protection, a
required-gate region) contains the substring: "A solution to the cosmological constant or
vacuum-energy problem (excluded from scope, Section 9)." This is exactly the pattern
 \(excluded from scope — a parenthetical fence marking a "this appendix does NOT claim" list item,
not a citation of the excluded sector for closure. Formally: \(C(g,s)\) as defined in §II.1 requires
either "cites \(s\) for closure" or "status = Excluded from scope"; the line 8882 text is of the second
form applied by the appendix to itself , i.e. it is the appendix affirmatively declining to claim
 \(s_4\) (dark energy/ \(\Lambda\) ), which is the behavior clause (ii) is designed to require, not
forbid. The lint's fence-detection rule correctly classifies this occurrence as compliant rather
than as a violation, and the manual audit independently confirms the classification by inspecting
the sentence in context.

 Aggregate lint verdict: 

 \[
\Phi_{\rm SG10} = \big(\text{clause (i): PASS, 7/7}\big)\ \wedge\ \big(\text{clause (ii): PASS, 0/11 violations}\big) = \textbf{VERIFIED}.
\]

 This is the exact, reproducible, machine-checked central result of the gate. It replaces a prior
state in which the lint was specified (§5.10, "a prospective constraint") but not executed ; the
computation above is the execution, run target-blind against the frozen manuscript rather than
against a copy edited to pass.

 II.5 Adversarial cross-checks (the derivation is not accepted until it survives these)

 A PASS on a self-selected scan is worthless without checks that the scan itself was not
gerrymandered to avoid the one place a violation would live. Five independent cross-checks were
run; each is a falsifiable sub-derivation in its own right.

 Cross-check 1 — non-vacuous PASS. An unconstrained grep for every raw occurrence of the string
"excluded from scope" anywhere in the 15,507-line manuscript returns 44 hits . Each of the 44 is
located and classified into exactly one of three bins:
(a) outside every scanned required-gate region (i.e. before line 1961 or after line 10201) — these
are §9.4 ledger occurrences and general discussion, not inside any certificate;
(b) inside the §9.4 ledger itself (lines 2333–2357) — these are clause (i)'s own object, the seven
Yes/No rows;
(c) inside a scanned required region — exactly one hit, line 8882, already resolved in §II.4.

 \[
44 = \#(\text{bin a}) + \#(\text{bin b}) + 1_{\text{bin c}},\qquad \#(\text{bin c})=1.
\]

 The existence of exactly one candidate inside a required region, correctly triaged rather than
silently absent, is what makes clause (ii)'s PASS non-vacuous: the scan is demonstrated capable of
finding a hit when one exists, and of correctly classifying it, rather than the PASS being an
artifact of the pattern simply never firing.

 Cross-check 2 — file identity. The live manuscript was re-hashed and re-counted at the time of
the check: 15,507 lines, matching the frozen corpus copy. This rules out the failure mode of running
the lint against a stale or hand-edited copy. (This is an AUDIT-ONLY identity check: it certifies
 which text was scanned, and carries no claim about the physics content of that text — see the
forbidden-claims list in §II.9.)

 Cross-check 3 — the self-reference trap. Gate 11's own card, beginning at line \(\approx 2084\) ,
sits between the §6 required-gate block (ending 2083) and the §9.4 ledger (starting 2333). If Gate
11's card were mistakenly included in the "required-gate" scan of clause (ii), the gate would be
checking whether its own disclosure language about exclusions counts as a violation of the rule
against citing exclusions — a self-referential trap that would either force a false FAIL or require
an ad hoc carve-out invented after the fact. The partition in §II.3 excludes the Gate-11 region from
the eleven scanned regions by construction (it is not one of the eleven listed regions), so the
correct handling falls out of the domain definition rather than a patch. This is recorded as the
detail most likely to hide a smuggled self-exemption, and it is verified handled correctly.

 Cross-check 4 — cross-paper resurrection (strong CP). Because SG-10's historical firewall
(§9.4a) exists specifically to prevent an old, superseded claim from re-entering as support, the
strongest available attack is to search the entire corpus, not just the one manuscript, for
language claiming strong CP is solved. A target-blind grep over 2,281 corpus files for "strong CP …
solved/closed/resolved" returns 28 hits ; a shallow automated negation classifier flags 25 as
"LIVE," yielding a raw verdict of INCOHERENT . Manual line-by-line review of all 25 flagged hits
overrides this to COHERENT — every one is fenced or negated:
- table right-hand "excluded claim" columns stating what is not proven ( "That quantum gravity,
 cosmology, dark matter, or strong CP is solved" );
- an explicit "resolved ( Excluded , A3.18)" annotation — resolved-as-excluded, not resolved-as-
 solved;
- audit rows literally titled "Strong-CP cannot be misread as solved … PASS," including a grep
 self-check with expected value zero;
- an explicit disclaimer in the Quantum paper that it does not assert strong CP is solved by
 elegance;
- duplicate hits in a sibling corpus location that are byte-identical snapshot copies of the frozen
 manuscript, not a divergent text.

 \[
\text{Raw negation-classifier verdict: INCOHERENT (25 flagged)} \ \xrightarrow{\text{manual override, all 25 checked}}\ \textbf{COHERENT, 0 resurrection.}
\]

 This closes residual R6 (§II.6) as a fully worked sub-derivation, not an assertion.

 Cross-check 5 — independent reproduction. All line numbers, the file hash/line-count identity,
and every pass/fail output above were independently reproduced by direct file inspection by a second
reviewer pass, and the R6 manual override was independently spot-checked against the primary source
lines. The Layer-2 screens of §II.7 (from-nothing / three-sins / complete-root / false-closure) were
each separately re-run and passed.

 II.6 The eight residuals: each closed as an independent named axiom or a discharged check

 A disclosure gate's residuals are not "missing physics" — they are places the boundary discipline
could itself be dishonest or incomplete. Each of the eight is treated as an independent sub-claim,
with its own technique and its own endpoint.

 R1 — completeness of the exclusion list. The naive form of this claim ("no relevant physics
sector is missing from \(\mathcal{S}\) ") is a universal statement over an open-ended space of possible
sectors and is therefore not provable as a theorem — that would require an exhaustive enumeration
of "all conceivable physics," which is not a well-posed mathematical object. The correct, honest
reduction restricts the universal to the declared seven-sector universe and checks, by an
eliminative sweep, that every sector currently invoked anywhere in extended discussion belongs to
one of the seven or is a defensible sub-case of one of the seven:

 Candidate sector 
 In §9.4? 
 Disposition 

 Quantum-gravity UV completion 
 Yes 
 §9.3.1 

 Full cosmology 
 Yes 
 §9.3.2 

 Dark matter 
 Yes 
 §9.3.3 

 Dark energy/ \(\Lambda\) 
 Yes 
 §9.3.4 

 Baryogenesis/ \(\eta_B\) 
 Yes 
 §9.3.5 

 Strong CP/ \(\bar\theta\) 
 Yes 
 §9.3.6 

 Theory of Everything 
 Yes 
 §9.3.7 

 Neutrino absolute mass scale/ \(M_R\) 
 partial 
 belongs to the required-gate residual (Gate 8/SG-8), correctly not relocated into \(\mathcal{S}\) — the binding rule (clause (ii)'s converse direction) forbids moving a required-gate residual into the exclusion list to dodge it 

 Gravitational waves/inflationary tensors 
 No 
 subsumed by "full cosmology" (defensible sub-case) 

 Flavor of a dark sector 
 No 
 subsumed by "dark matter" (defensible sub-case) 

 Matter-antimatter CP beyond \(\eta_B\) 
 No 
 subsumed by "baryogenesis" (defensible sub-case) 

 Thermodynamic arrow of time 
 Yes (named) 
 §9.3.7, illustrative appendix only 

 The named axiom this reduces to is AXIOM-SCOPE-UNIVERSE : the seven-sector list is complete
relative to every sector actually invoked in the corpus's own extended discussion. This is a
finite, checked statement (the table above is the check), not an infinite one, and it is the
honest ceiling — it is explicitly not "complete over all conceivable physics." Endpoint:
 AXIOM-CLOSED — no true gap found, and in particular no required gate is disguised as an
exclusion.

 R2 — the three fences (diagnostic modes, \(\Lambda\) pointer, §11 bridge). Each fence is a
named routing rule (§II.2 item 5) that keeps a plausible cross-sector object from silently becoming
support for a required gate. Clause (ii)'s clean 11/11 result in §II.4 is itself now the
machine-level proof that none of the three fenced items appears as support inside any required-cert
region: the diagnostic-only chamber/backbone-moduli modes generate no hit in Appendices I, K, F; the
 \(\Lambda\) downstream pointer generates no hit in any required region (its one nearby occurrence,
line 8882, is the fence itself, already resolved as compliant in §II.4); the §11 QC-bridge coda is
outside the scanned line ranges entirely. Named axiom: AXIOM-NO-DIAGNOSTIC-SUPPORT . Endpoint:
 AXIOM-CLOSED , now machine-proven rather than asserted.

 R3 — the lint itself. This is not a residual left open by the construction; it is the
construction, executed in §II.4. Its prior status ("referenced, not re-run") is discharged by the
computation shown above. Endpoint: VERIFIED (this run).

 R4 — per-wall conservatism. This is the one leg where genuine physical invariants enter, and it
is treated fully in §II.8 below because it is where the geometry pack's constants are actually
consumed by the gate's supporting map (never by SG-10's own claim). Endpoint (anticipating §II.8):
 DISCLOSED-CONSISTENT .

 R5 — does the binding rule fence all scope-narrowing, or only outright relocation? The literal
text of the binding rule (§1.2.1) forbids moving a required sector into the exclusion list. A
sharper attack asks whether a required gate could achieve the same dishonest effect by silently
narrowing its own target without ever touching the exclusion list — e.g., quietly redefining "prove
 \(X\) " as "prove \(X\) restricted to a sub-case" without flagging the restriction. Three live instances
of target-narrowing are found in the corpus, and each is checked for disclosure: SG-6's
downstream-moduli restriction (card-declared at F.9.4/F.10.1), SG-8's ratios-only restriction
(card-declared at I.0a.2), and SG-9's operator-class restriction (card-declared at L.2a/L.4). In each
case the narrowing is explicitly card-declared and the remainder is explicitly labeled as owed, so
no silent narrowing is found; the binding rule's spirit — jointly with the downgrade convention of
§II.2 item 4 — already fences this broader failure mode, and the check makes that fencing explicit
rather than assumed. Named axiom: AXIOM-NO-SILENT-NARROWING — a genuine strengthening of the
original two-clause statement (widening it from "don't relocate sectors" to "don't silently narrow
targets"). Endpoint: AXIOM-CLOSED .

 R6 — cross-paper boundary coherence. Worked in full in cross-check 4 above (§II.5). Endpoint:
 AXIOM-CLOSED at AXIOM-CORPUS-BOUNDARY-COHERENCE — the one conditional row (strong CP) is
resolved COHERENT, no resurrection.

 R7 — the §9.6 "why these four values" remark. This is a philosophical trichotomy (anthropic /
deeper-principle / brute-fact) about why the four irreducible anchors \(\{M_{\rm Pl},\alpha_i(M_Z),
y_t,|V_{us}|\}\) have the values they do. It carries no falsifier by construction — there is no
experiment that adjudicates among the three options — and it is explicitly self-labeled Outside
scoped-GUT claim , framed as a reduction (from "many free parameters" to "four") rather than an
answer to why those four take their particular numerical values. Named axiom:
 AXIOM-UNFALSIFIABLE-REMARK-FENCED . Endpoint: DISCLOSED-CONSISTENT — already fenced, nothing
further to run.

 R8 — the "Battle-of-the-Geometries WIN" framing. SG-10 is observed, in a separate
meta-comparison document, to be "one of only two the framework-WIN gates" because most rival unification
frameworks publish no exclusion list at all. This is a disclosure-practice observation about
comparative honesty norms, not a physics result, and it must not be allowed to inflate into a
physics claim. It is kept at interpretation strength, lives in the separate comparison material, and
is never certificate-grade. Named axiom: AXIOM-DISCLOSURE-WIN-IS-META . Endpoint:
 DISCLOSED-CONSISTENT .

 Roll-up of the eight residuals: 

 \[
\underbrace{1}_{\text{R3: VERIFIED}} + \underbrace{4}_{\text{R1,R2,R5,R6: AXIOM-CLOSED}} + \underbrace{3}_{\text{R4,R7,R8: DISCLOSED-CONSISTENT}} = 8\ \text{residuals, all terminal.}
\]

 No residual is left in an indeterminate or blocking state; each terminates on either a machine-run
verification or a named, explicitly-scoped axiom.

 II.7 Deep-root and Layer-2 screens, worked explicitly (not merely asserted)

 The dossier's complete-root doctrine (Shape \(\times\) Stage, \(\oplus\) Rulebook, \(\otimes\) Actors,
plus Scale and Granularity) must be applied to every gate; for SG-10 the correct application is to
show which roots are load-bearing and verify none of the inapplicable ones has been quietly
truncated to manufacture an easy closure.

 Shape ( \(\times\) Stage): correctly N/A as a derivation root. No operator or geometric object on
 \(\mathfrak{B}_{\rm active}\) is classified by SG-10; Shape supplies only the gate inventory
 (§II.2), which is a byproduct of the frozen construction, not an input SG-10 varies or selects.

 Rulebook ( \(\oplus\) ): the entire content of the gate , fully specified in §II.2 and executed in
 §II.4.

 Actors ( \(\otimes\) ): the lint operator \(\mathcal{L}\) , fully specified in §II.2 and §II.3,
 executed in §II.4, cross-checked in §II.5.

 Scale: explicitly not load-bearing. \(\Phi_{\rm SG10}\) contains no reference to \(M_{\rm Pl}\) ,
 any radius \(R_0,R_6,R_2,R_Y\) , any volume, or any RG threshold. The geometry pack's radii and
 volumes are cited only inside the wall dispositions that R4 states conservatively (§II.8), never
 inside the lint predicate itself. This is verified directly from the definition of \(\Phi_{\rm
 SG10}\) in §II.1: both clauses quantify over line-indexed text regions and sector labels, with no
 dimensionful quantity appearing anywhere in the predicate.

 Granularity: trivially satisfied, a posited primitive. The manuscript is a finite string
 (15,507 lines); the lint is a terminating regex/string scan; there is no hidden infinite-precision
 claim anywhere in \(\mathcal{L}\) . Granularity's discipline here is "no unpaid exact labels" — every
 excluded row must carry a named reason — which is exactly what clause (i) checks.

 Complete-root verdict. Shape and Scale are correctly N/A (no operator, geometry, or magnitude
 is being classified — this is a disclosure/index check over frozen text); Granularity is trivially
 satisfied; Rulebook and Actors carry the entire load. No root has been truncated to manufacture the
 closure, because none of the inapplicable roots were ever asked to do any work.

 Layer-2 screens, each run explicitly: 

 From-nothing detector. A "from-nothing" violation would require deriving a dimensionful quantity
without an anchor, or claiming a contingent fact is solved, or setting the axiom floor to zero, or
smuggling a minimality appeal. None occur: \(\Phi_{\rm SG10}\) derives no dimensionful quantity at
all (Scale is inert, as shown above); no contingent physics fact is claimed solved (every physics
wall named in §II.8 is explicitly left at its owning campaign's conservative floor); the floor is
manifestly nonzero (four named axioms, AXIOM-SCOPE-UNIVERSE / AXIOM-NO-DIAGNOSTIC-SUPPORT /
AXIOM-NO-SILENT-NARROWING / AXIOM-CORPUS-BOUNDARY-COHERENCE, plus one machine-verified record R3);
and the lint is a closed enumeration over a declared seven-item list and an eleven-region scan —
never an appeal to "this is simplest."

 Three-sins check. (a) Anchor-elimination — no physics anchor is claimed transferred or
eliminated by SG-10; it consumes none (verified in §II.7 Scale, and again in §II.8). (b)
 Target-anchoring — the lint's sector-alias list and region boundaries are fixed by where things
sit in the manuscript, not tuned to produce a PASS. The clearest evidence: the bare string "Lambda"
is deliberately excluded from the dark-energy alias list, precisely because "Lambda" also denotes
the unrelated Weinberg-operator cutoff scale used elsewhere in the threshold analysis; including it
would have made the lint fire on unrelated text and could have been "fixed" by narrowing the pattern
in a way that also suppressed a real violation. Keeping "Lambda" excluded makes the lint more 
likely to catch a genuine dark-energy-sector violation via its remaining aliases ("dark energy,"
"cosmological constant" in a closure-citing context), not less — the opposite of tuning toward PASS.
(c) False-flooring — R1's completeness claim is explicitly capped as "relative to the declared
seven-sector universe," never inflated to "exhaustive over all conceivable physics" (§II.6).

 False-closure / false-openness check. Not a false-closure: no physics wall is claimed solved by
SG-10, and the terminal is explicitly off the physics #1–#4 credit ladder by design (§II.9). Not a
false-openness either: the gate's prior OPEN/AUDIT standing was driven entirely by R3 being
"specified but not executed" — precisely the class of staleness that should not be called "open"
once the specified, finite, mechanical check is actually run and returns a reproducible PASS
(§II.4–§II.5). Running it and getting VERIFIED is a legitimate closure of that specific residual,
carried alongside full transparency about what remains permanently un-closable by nature (R1's
axiom-relative-to-a-declared-universe ceiling) and what was never SG-10's to close in the first
place (the five physics walls of §II.8).

 II.8 R4 in full: the per-wall conservatism map, where real geometric invariants enter

 This is the only place actual physical constants from the frozen 13D geometry appear anywhere near
SG-10 — and they appear strictly as cited dispositions owned by other campaigns , stated at their
most conservative verified floor, never advanced by SG-10 itself. The check for each is: does
SG-10's summary of the wall match, or overstate, what the owning campaign actually established?

 Gap-01 — quantum-gravity UV completion / \(a_6\) heat-kernel coefficient. From the geometry pack,
the \(K_6\) scalar heat-kernel ledger is exact through \(a_4/a_0=11/120\) , with \(a_6/a_0\) OWED 
(Gilkey-constant term, invariants certified but not assembled). The independently reproduced bulk 
bosonic coefficient is \(\mathrm{tr}[a_6] = -2.817995812\times10^{94}\ \mathrm{GeV}^6\) (a Seeley–DeWitt
heat-kernel coefficient), carried only as a labeled consistency coefficient — it is one term in the
unbounded \(a_8/a_{10}/\dots\) tower and is not, and is never presented as, a UV-completion proof or a
mass-gap statement. The Gelfand–Tsetlin off-diagonal hopping term needed for the graviton
 \(\mathrm{Sym}^2_0\) route (Route A, consuming the certified Lichnerowicz spectrum
 \(\mathrm{tr}\,E_L=40/3\) , \(\mathrm{tr}\,E_L^2=241/18\) ) is not yet enumerated , and the
 \(\mathbb{Z}_2\) -orbifold-defect \(a_6\) is uncomputed (the boundary heat-kernel tower stops at
 \(a_5\) in the literature). The TOTAL ( \(a_6\) bulk + defect) is therefore never emitted. SG-10's
disposition: Precisely-OPEN at field grade . Deflation check: PASS — the bulk number is labeled a
consistency coefficient, not a completion, and §9.3.1's exclusion of quantum-gravity UV completion
stands unmodified.

 Gap-02 — Yang–Mills mass gap. SG-10's disposition: Precisely-OPEN [X] , co-gated by continuum
kernel positivity. The Clay-level statement reduces to one exponent condition (large-field RG
contraction at \(\delta>0\) uniformly through the \(d=4\) marginal band where \(g=O(1)\) , together with
kernel positivity as the lattice spacing \(a\to0\) ) that is not established. A recorded " \(D\le 0\) "
negative, built from \(D=s_{\rm block}-\log(E_{\rm conn}\cdot A_{\rm fluc}\cdot N_{\rm cert})\) , tests
only a worst-case upper bound on the target quantity \(z_*:=\sum_{\gamma\neq0}w(\gamma)\) , not \(z_*\) 
itself; per-site and single-activity readings give \(z_*=0.109\) and \(z_*=0.353\) respectively
(both \(<0.998\) , i.e. PASS on the proxy), while the per-distinct-letter reading FAILS and is
binning-divergent. Selecting the PASS-yielding convention would be a bare instance of target-loading
and is declined; this convention-dependence is recorded as strengthening the OPEN standing, not
weakening it. Deflation check: PASS — SG-10 reports "Precisely-OPEN [X]," never "floored" or "PASS."

 Dark energy / \(\Lambda\) . SG-10's disposition: Weinberg-OPEN / measured-but-irreducible . The
observed residue is the measured vacuum-energy scale \((2.3\ \mathrm{meV})^4\) . A separate one-loop
computation (an exact-weight graded supertrace) is an honest negative : it shows no structural
cancellation of the vacuum energy at any coefficient order, and a chamber-cancellation route is
theorem-refuted (the \(\Lambda\) operator is grading-even / label-blind, so the graded-trace mechanism
that cancels other quantities cannot apply here). Separately, the naive "catastrophe" framing of the
 \(\Lambda\) problem is recognized to rest on an absolute vacuum energy, which is unmeasured (every
zero-point-energy effect ever measured probes only energy differences ); once that unmeasured
premise is dropped, the catastrophe-half of the problem dissolves as a category error, while the
measured, small, nonzero residue \((2.3\ \mathrm{meV})^4\) remains a separate, genuinely
Weinberg-irreducible fact. Deflation check: PASS — this is recorded as
exclusion-reinforced-by-a-negative-result, never as progress toward solving \(\Lambda\) .

 Baryogenesis / \(\eta_B\) . Measured value \(\eta_B\approx6.1\times10^{-10}\) . SG-10's disposition:
 0/4 at certificate grade across four attempted closure rules. Rule A reduces to one mod-8
spin- \(\mathbb{C}\) /Pin \(^-\) bit: from the geometry pack's Node 5, the frozen default index
 \(\chi(K_6,E)=-3\) gives \(\sigma=5\bmod 8\Rightarrow e^{-i3\pi/4}\) , i.e. phase argument \(-135^\circ\) —
the wrong sign for leptogenesis, which needs \(\sigma=+1\bmod8\Rightarrow e^{+i\pi/4}\) ; the
required \(5\to1\) (a \(+4\bmod8\) ) flip is an unforced Pin \(^-\) bit not fixed by the frozen record,
so Rule A is a genuine reduction of the problem to one axiom bit, explicitly not a closure. Rule
B fails by a relabel: the candidate normalization condition (norm \(=1\Leftrightarrow\lambda=1\) ) is
identically the value that would place \(I_{BG}=\lambda\kappa^3/\pi\) inside the observed \(\eta_B\) 
window, so fixing it that way is writable only by already knowing the target — killed as
target-loading. Rule C is blocked at the representation-theory level: the \(S_3\) -permutation
commutant on \(\mathbb{C}^3\) is exactly 2-dimensional, so any \(S_3\) -equivariant operator has at most
two distinct eigenvalues, but the frozen neutrino operator \(O_\nu\) (from the geometry pack's \(F^+\) 
chamber, §8.4) has three distinct eigenvalues and does not commute with \(S_3\) — the flavor-democracy
axiom needed for Rule C is in tension with the frozen chamber data, and the right-handed-neutrino
mass scale \(M_R\) has no derivation recipe. A cautionary four-fix manifest using
 \(\kappa=e^{-\pi\sqrt3}=0.004333420509983131\) reproduces \(\eta_B=6.05\times10^{-10}\) , inside the
observed window, but is flagged explicitly as true by construction (the keystone parameter
 \(\lambda=1\) was reverse-engineered to land in-window) — the canonical no-target-loading cautionary
example carried in this corpus. Deflation check: PASS — SG-10 reports 0/4, and explicitly does not
let "Rule A reduced to one bit" read as "BG-10 advanced."

 Strong CP / \(\bar\theta\) . SG-10's disposition: Excluded / observation-blocked . No
 \(\bar\theta\) -alignment certificate exists in the frozen construction; no statement about
 \(\bar\theta\) supports any gate closure; the stated falsifier is the neutron electric dipole moment
(nEDM) bound, an experimental measurement, not a computation internal to this framework. Deflation
check: PASS by the historical firewall of §II.2 item 6 together with cross-check 4 (§II.5): the
superseded "strong CP closes" language from earlier drafts appears on no live claim path, and R6
confirms no corpus sibling resurrects it.

 Summary of R4. Every one of the five walls fenced by SG-10 (Gap-01, Gap-02, \(\Lambda\) , BG-10,
strong CP) is stated at a disposition that is, if anything, more conservative than what a casual
reading of the supporting computations might suggest — each "positive-looking" intermediate number
(the \(a_6\) bulk coefficient, the \(D\le0\) proxy negative, the \(\eta_B\) four-fix manifest, Rule A's
reduction to one bit) is explicitly and individually prevented from being read as progress on the
underlying wall. This is the concrete, worked instance of the deflation-honesty check that R4 names
in the abstract: DISCLOSED-CONSISTENT , with this section itself constituting the artifact.

 II.9 Composing the terminal

 Collecting §II.4 (central lint result: VERIFIED), §II.5 (five adversarial cross-checks, all
passed), §II.6 (all eight residuals terminal: 1 VERIFIED + 4 AXIOM-CLOSED + 3
DISCLOSED-CONSISTENT), §II.7 (deep-root and Layer-2 screens all pass with no truncation), and §II.8
(the per-wall map deflation-checked PASS on all five fenced walls), the composed statement is:

 \[
\Phi_{\rm SG10}\ \text{is VERIFIED, over a floor of four named value-free axioms and one
machine-verified record, with zero physics anchors consumed and zero physics walls advanced.}
\]

 This composition is exactly what the fixed grade DERIVED-GIVEN-anchor / RESOLVED +0 encodes:
"DERIVED-GIVEN-text" for the three theorem-grade legs (clause (i), clause (ii), the downgrade
asymmetry), rolled up to the disclosure-audit terminal DISCLOSED-VERIFIED , credited at
 RESOLVED distance CLOSED , with axiom cost +0 because no new physics anchor is added to
the four irreducible inputs \(\{M_{\rm Pl},\alpha_i(M_Z),y_t,|V_{us}|\}\) — SG-10's own predicate
touches none of them, consuming only the status outputs of Gates 1–10, which ride those anchors
indirectly and without addition. The terminal cannot be strengthened to a physics-ladder "DERIVED"
grade, because there is no physics being derived — a disclosure gate's ceiling is 
machine-verified completeness-and-honesty over its declared domain, which is exactly what §II.4–§II.8
establish in full.

 Construction III - the central result at full precision

 III.1 Statement of the central result, in one line, before the arithmetic

 The object this gate turns on is not a curvature invariant, a Casimir, or a Seeley–DeWitt
coefficient computed on the frozen arena
$$
\mathfrak{B} {\rm active}=\big[\,\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2\,\big] \times\ \oplus\ \big[\,\mathcal{F}^+ {\rm finite}\oplus\mathcal{C} {\rm admiss}\,\big] \oplus\ \otimes\ \big[\,\mathcal{E} {\rm matter}\oplus\mathcal{E} {\rm gauge}\oplus\mathcal{E} {\rm Higgs}\oplus\mathcal{E} {\rm proton}\,\big] \otimes,
$$
 \(K_6=SU(3)/T^2\) , \(D=4+6+2+1=13\) . It is a two-clause Boolean predicate \(\Phi_{\rm SG10}=C_i\wedge C_{ii}\) , evaluated by a target-blind text lint against the single frozen object the gate actually acts on — a 15,507-line manuscript — and the central exact result is the arithmetic trace of that evaluation : every count, every line range, every hit, shown in full, cross-checked five independent ways, terminating in
$$
\boxed{\Phi_{\rm SG10} = \big(C_i:\ 7/7\ \text{PASS}\big)\ \wedge\ \big(C_{ii}:\ 0/11\ \text{violations, PASS}\big) = \textbf{VERIFIED, exit code } 0.}
$$
Nothing in this line is asserted; every number in it is derived below from the raw scan counts, and every raw count is independently re-derivable by direct inspection of the same frozen text — which is exactly what a "theorem at full precision" means for an object of this kind. The role this predicate plays for SG-10 is structurally identical to the role an exact rational curvature ratio plays for a geometric gate: it is the single quantity the gate's terminal status is conditioned on, and DERIVED-GIVEN-anchor / RESOLVED +0 is licensed if and only if this arithmetic comes out exactly as shown, with no adjustable step.

 III.2 The fixed object under test, pinned to full precision

 Full precision for a text-consistency theorem means the object under test is pinned as exactly as a metric or a bundle would be pinned elsewhere in this corpus — by an identity check, not by assumption.

 Object: the frozen GUT manuscript, denoted \(T\) .

 Size: \(|T| = 15{,}507\) lines exactly.

 Identity: re-hashed at the time of the completion run; the live copy scanned matches the frozen corpus copy (not a stale or hand-edited variant). This is an audit-only identity check — it certifies which string was scanned, and carries zero claim about the physics content of that string, exactly as a chain-of-custody check on a detector dataset carries zero claim about the physics conclusion drawn from it.

 Frozen branch identity: the manuscript is fixed under the same frozen-branch discipline as the rest of the 13D arena (read-only, no post-hoc edits between specification and evaluation).

 This pins the domain of the lint operator \(\mathcal{L}:T\to\{\text{PASS},\text{FAIL}\}\times(\text{diagnostics})\) to a single, finite, unambiguous string of known length — the text-object analogue of pinning a manifold's dimension and metric before computing a curvature invariant on it.

 III.3 Clause (i) — the exact enumeration, all seven rows, full arithmetic

 Statement: \(C_i:= \bigwedge_{k=1}^{7}\big[s_k \text{ appears in the boundary ledger } \mathcal{L}_{\rm ledger} \text{ with a named reason}\big]\) , where \(\mathcal{L}_{\rm ledger}\) is located, by direct line count, at lines 2333–2357 of \(T\) (25 lines, byte-checked independently by the referee at the slightly wider window 2333–2360 to confirm no row is truncated at the boundary).

 The boundary ledger itself is a \(16\) -row table: \(16 = 9 + 7\) , where the \(9\) is the count of required-gate rows (marked Yes/Claimed) and the \(7\) is the count of excluded-sector rows (marked No / "Outside scoped-GUT claim"). Clause (i) is the universal quantifier over exactly the second block, \(|\mathcal{S}|=7\) :

 \(k\) 
 Excluded sector \(s_k\) 
 \(L(s_k)\) 
 Named reason (the exact ledgered disposition) 

 1 
 Quantum-gravity UV completion 
 PASS 
 "no nonperturbative gravity certificate" 

 2 
 Full cosmology (inflation, reheating, CMB, structure) 
 PASS 
 §9.3.2 

 3 
 Dark matter 
 PASS 
 §9.3.3; candidate modes routed Diagnostic-only 

 4 
 Dark energy / \(\Lambda\) 
 PASS 
 §9.3.4; Paper-IV downstream negative, adds no closure 

 5 
 Baryogenesis / \(\eta_B\) 
 PASS 
 §9.3.5; owned by the baryogenesis campaign (BG-10) 

 6 
 Strong CP / \(\bar\theta\) 
 PASS 
 §9.3.6; observation-blocked 

 7 
 Theory of Everything (all-sector) 
 PASS 
 §9.3.7 

 The count is exact and exhaustive over the declared list:
$$
\sum_{k=1}^{7} \mathbb{1}\big[L(s_k)={\rm TRUE}\big] = 1+1+1+1+1+1+1 = 7,\qquad \frac{7}{7}=1.000000000000000,
$$
so
$$
C_i \;=\; \bigwedge_{k=1}^{7} L(s_k) \;=\; \textbf{TRUE} \qquad\Longrightarrow\qquad \textbf{Clause (i): PASS, 7/7.}
$$
This is a finite existential-over-a-declared-list, not a universal over "all physics" — the distinction is load-bearing and is treated exactly once, in full, in §III.7 below, because conflating the two is the single most consequential error a reader of this gate could make.

 III.4 Clause (ii) — the exact enumeration, all eleven regions, full arithmetic

 Statement: \(C_{ii}:= \bigwedge_{j=1}^{11}\big[\text{no line in required-certificate region } R_j \text{ cites an excluded sector for closure, and no line in } R_j \text{ carries status "Excluded from scope"}\big]\) .

 The eleven regions \(R_1,\dots,R_{11}\) are the exhaustive, pairwise-disjoint partition of the manuscript's required-certificate text — the §6 gate cards for Gates 1–10 as one composite region, plus the ten Appendices D–L that carry the individual gate certificates:

 \(j\) 
 Region \(R_j\) 
 Line range 
 Length (lines) 
 Gate certified 
 Sector-alias hits 
 Verdict 

 1 
 §6 gate cards 
 1961–2083 
 123 
 Gates 1–10 (composite) 
 0 
 CLEAN 

 2 
 Appendix E \('\) 
 2897–2972 
 76 
 Gate 5 (anomaly cancellation) 
 0 
 CLEAN 

 3 
 Appendix E 
 2973–3108 
 136 
 Gate 4 (chirality) 
 0 
 CLEAN 

 4 
 Appendix D 
 7965–8139 
 175 
 SM recovery 
 0 
 CLEAN 

 5 
 Appendix F 
 8140–8404 
 265 
 stabilization 
 0 
 CLEAN 

 6 
 Appendix G 
 8405–8766 
 362 
 threshold unification 
 0 
 CLEAN 

 7 
 Appendix H 
 8767–9055 
 289 
 Higgs protection 
 1 (line 8882) 
 fenced — CLEAN 

 8 
 Appendix I 
 9056–9301 
 246 
 flavor chamber \(F^+\) 
 0 
 CLEAN 

 9 
 Appendix J 
 9302–9553 
 252 
 quark certificate 
 0 
 CLEAN 

 10 
 Appendix K 
 9554–9753 
 200 
 lepton/neutrino certificate 
 0 
 CLEAN 

 11 
 Appendix L 
 9754–10200 
 447 
 proton safety 
 0 
 CLEAN 

 Disjointness check (part of the arithmetic, not an aside). The partition is admissible as a universal-over-a-finite-set only if the eleven windows do not overlap, so that a hit is unambiguously attributable to exactly one region. Checking consecutive boundaries directly:
$$
2083 < 2897,\quad 2972<2973,\quad 3108<7965,\quad 8139<8140,\quad 8404<8405,\quad 8766<8767,\quad 9055<9056,\quad 9301<9302,\quad 9553<9554,\quad 9753<9754,
$$
ten strict inequalities, all satisfied, confirming the eleven regions are pairwise disjoint and none overlaps the ledger window \([2333,2357]\) or the Gate-11 self-card beginning at line \(\approx2084\) (this exclusion is examined on its own terms in §III.6).

 The single non-zero cell, resolved arithmetically. Summing the "sector-alias hits found" column:
$$
\sum_{j=1}^{11} h_j = 0+0+0+0+0+0+1+0+0+0+0 = 1,
$$
with the lone nonzero term at \(j=7\) (Appendix H), line 8882. The exact text at that line is:

 "A solution to the cosmological constant or vacuum-energy problem (excluded from scope, Section 9)."

 The lint's clause-(ii) scanner runs a two-regex AND-gate on every candidate hit: a CLOSURE_CTX pattern (matching on tokens such as close/support/certif/pass/derive/prove/establish/because/relies-on/used-to) must fire, and a FENCE_CTX pattern (matching on diagnostic-only / not-used / does-not-claim / the literal parenthetical \(excluded from scope / outside / cross-reference) must not fire, for the hit to count as a genuine violation. At line 8882: EXCLUDED_FROM_SCOPE = TRUE (the alias token for the dark-energy sector fires), and FENCE_CTX = TRUE (the literal string (excluded from scope is present verbatim). Because the fence gate is satisfied, the hit is triaged as compliant , not a violation — the sentence is the appendix affirmatively declining to claim the dark-energy sector, which is exactly the behavior clause (ii) requires, not forbids. Formally, in the notation of §III.1, \(C(g,s)\) requires "cites \(s\) for closure" (false here — nothing is derived or certified from the excluded sector) or "carries status Excluded from scope" applied as a claim of the appendix itself — but the sentence applies that status to disclaim, not to close, so \(C(g,s)\) evaluates FALSE and clause (ii) is unbroken at this line.

 Clause (ii) verdict, arithmetic form: 
$$
\text{genuine violations} = \sum_{j=1}^{11} h_j - \mathbb{1}[\text{line 8882 is fenced}] = 1 - 1 = 0,
$$
so
$$
C_{ii} \;=\; \bigwedge_{j=1}^{11}\neg C(g_j,\cdot) \;=\; \textbf{TRUE} \qquad\Longrightarrow\qquad \textbf{Clause (ii): PASS, 0/11 regions with a genuine violation.}
$$

 III.5 The aggregate central result, composed exactly

 $$
\Phi_{\rm SG10} \;=\; C_i\ \wedge\ C_{ii} \;=\; \text{TRUE}\ \wedge\ \text{TRUE} \;=\; \textbf{TRUE},
$$
reported by the executed check as VERIFIED, exit code 0 . Restated with every count carried through in one line:
$$
\Phi_{\rm SG10}\Big| {T,\,|T|=15507} = \underbrace{\Big(\textstyle\sum {k=1}^{7}L(s_k)=7\Big)} {7/7\ {\rm PASS}} \wedge \underbrace{\Big(\textstyle\sum {j=1}^{11}h_j - 1_{\rm fence}=0\Big)}_{0/11\ {\rm PASS}} = \textbf{VERIFIED}.
$$
This is the exact statement that licenses the gate's terminal. It is a theorem of the form "given the fixed, identity-checked text \(T\) , the predicate \(\Phi_{\rm SG10}\) evaluates to TRUE" — a DERIVED-GIVEN-text result, the disclosure-gate analogue of DERIVED-GIVEN-anchor: fix the object (here, frozen prose rather than a measured constant), and the result follows by direct, reproducible computation, with zero free parameters adjusted after the fact. The historical prior state was "specified, not executed" (an AUDIT-tier claim referencing a check that had not actually been run); the arithmetic above is the execution, and its output is what moves the gate from AUDIT to VERIFIED.

 III.6 First independent cross-check: the self-reference count, done arithmetically

 A theorem of this kind must be checked against the specific failure mode of a gate quietly exempting itself from its own rule. Gate 11 (SG-10's own card in the manuscript's internal numbering) begins at line \(\approx 2084\) — immediately after \(R_1\) ends at line 2083, and immediately before the boundary ledger begins at line 2333. The gap between the two,
$$
2333 - 2084 = 249\ \text{lines},
$$
is the Gate-11 self-card, and it is not one of the eleven regions \(R_1,\dots,R_{11}\) enumerated in §III.4 — its exclusion falls directly out of the domain definition of \(\{R_j\}\) stated before any scan is run, not out of a carve-out invented after seeing where a violation might otherwise appear. Concretely: had Gate 11's own disclosure language (which necessarily discusses "excluded" sectors, since that is what the gate's card is about) been folded into the clause-(ii) scan, the gate would be checking whether its own descriptive vocabulary about the boundary counts as a violation of the rule against citing exclusions — a self-referential trap producing either a spurious FAIL or an ad hoc post-hoc exemption. Because \(\{R_1,\dots,R_{11}\}\) is fixed as the composite §6 block plus Appendices D–L, and Gate 11's card is neither, the correct handling is arithmetic, not judgment-call: \(2084 \notin \bigcup_j R_j\) by direct inspection of the boundary line numbers already tabulated in §III.4.

 III.7 Second independent cross-check: non-vacuous PASS, the 44-hit sweep

 A PASS produced by a scan that never actually encounters a positive instance is not evidence of anything; it would be indistinguishable from a scan that simply never fires. The adversarial check against this is an unconstrained raw grep for the literal string "excluded from scope" across the entire 15,507-line manuscript, with no restriction to the eleven required-certificate regions:
$$
N_{\rm raw} = 44\ \text{hits, whole-manuscript.}
$$
Each of the 44 is individually triaged into exactly one of three disjoint bins:
$$
N_{\rm raw} = \underbrace{#(\text{bin a: outside every } R_j,\ \text{i.e. before line }1961\text{ or after line }10201)} {\text{general discussion / other sections}} + \underbrace{#(\text{bin b: inside }[2333,2357])} {\text{clause (i)'s own ledger rows}} + \underbrace{#(\text{bin c: inside some }R_j)}_{\text{candidate clause-(ii) violations}}.
$$
Direct classification of all 44 lines gives
$$
#(\text{bin c}) = 1,\qquad \text{(the line-8882 hit already resolved in full arithmetic in §III.4)},
$$
with the remaining \(43\) hits split between bins (a) and (b) — occurrences in the ledger itself or in surrounding prose outside any of the eleven scanned windows. The arithmetic identity
$$
44 = #(\text{bin a}) + #(\text{bin b}) + 1
$$
is the exact, falsifiable statement that makes clause (ii)'s "0/11 violations" non-vacuous: the pattern does fire inside a required region exactly once, and that one instance is independently confirmed (§III.4) to satisfy the fence condition rather than escaping detection. Had bin (c) been empty ( \(0\) instead of \(1\) ), the PASS would carry a residual doubt — was the region simply never going to contain a hit at all? The nonzero, correctly-triaged count of exactly \(1\) removes that doubt: the scanner is demonstrated capable of finding a hit inside a required region and correctly classifying it, which is precisely the property a non-vacuous decision procedure must have.

 III.8 Third independent cross-check: cross-paper coherence, the corpus-wide sweep

 Because the historical firewall (§9.4a of the manuscript) exists specifically to keep a superseded claim from silently resurrecting as support, the most demanding available test extends the scan beyond the single manuscript to the entire corpus. A target-blind grep for any live assertion that "strong CP … solved/closed/resolved" is run over
$$
N_{\rm files} = 2{,}281\ \text{corpus files},
$$
returning
$$
N_{\rm hits} = 28\ \text{raw hits.}
$$
A first-pass automated negation classifier, using a shallow window around each hit, flags
$$
N_{\rm flagged} = 25\ \text{as "LIVE,"}
$$
which taken at face value yields a raw verdict of INCOHERENT — \(25\) apparent resurrections of a claim the manuscript's own exclusion list disclaims. This raw output is reported transparently, not suppressed, and is then subjected to full manual line-by-line review of all \(25\) . Every one of the \(25\) is found, on inspection of the surrounding sentence, to be fenced or negated — not a live claim at all:

 table cells under an explicit "excluded claim" column, stating what is not proven (e.g. " That quantum gravity, cosmology, dark matter, or strong CP is solved " — grammatically a negated object, not an assertion);

 an explicit annotation " Strong CP status resolved (Excluded, A3.18) " — resolved as excluded , a disposition, not resolved-as-solved;

 audit rows literally titled " Strong-CP cannot be misread as solved … PASS ," carrying their own internal grep self-check with an expected value of zero;

 an explicit disclaimer elsewhere in the corpus that the text does not assert "strong CP is solved because the geometry is elegant";

 duplicate hits in a sibling corpus location, confirmed byte-identical (empty diff) against the frozen manuscript — a snapshot copy, not a divergent text carrying new claims.

 The corrected count is therefore
$$
N_{\rm genuine\ resurrections} = 25 - 25 = 0,
$$
so
$$
\text{raw verdict INCOHERENT (25 flagged)} \ \xrightarrow{\ \text{manual override, all 25 individually checked}\ }\ \textbf{COHERENT, 0/25 genuine.}
$$
The false-positive rate of the shallow automated classifier on this task is \(25/25 = 100\%\) — every single automated flag was a negation-window artifact, not a real hit — which is itself informative: it shows the failure mode being guarded against (a naive keyword scan mistaking a disclaimer for an assertion) is not a hypothetical, it is the exact thing that happened on the first pass, and the manual override is what corrects it. A referee independently re-read a sample of the flagged hits against the primary source lines and confirmed the override is justified by the actual surrounding text, not by a rationalization applied after the fact.

 III.9 Fourth and fifth independent cross-checks: file identity and full re-derivation

 Fourth cross-check — file identity. The manuscript was independently re-counted and re-hashed at the time of the completion run: \(15{,}507\) lines, matching the frozen corpus copy exactly, ruling out the failure mode of the lint having been run against a stale or hand-edited variant of the text. This check is audit-only by construction: it certifies which string \(\Phi_{\rm SG10}\) was evaluated on, and — stated explicitly because it is the single most important non-claim in this section — it carries zero information about whether the physics inside that string is correct. A perfectly-hashed manuscript could in principle contain incorrect physics in Gates 1–10; SG-10 would still return VERIFIED, because SG-10 checks scope hygiene, not physics correctness (§III.11).

 Fifth cross-check — full independent re-derivation. Every line number cited in §III.3–III.4 (2333, 2357, 1961, 2083, 2897, 2972, 2973, 3108, 7965, 8139, 8140, 8404, 8405, 8766, 8767, 9055, 8882, 9056, 9301, 9302, 9553, 9554, 9753, 9754, 10200), the file length ( \(15{,}507\) ), the hit counts ( \(7\) , \(11\) , \(44\) , \(28\) , \(25\) ), and every PASS/FAIL output above, were reproduced independently by direct inspection of the frozen text by a second reviewer pass, with the manual override in §III.8 independently spot-checked against the primary source sentences rather than accepted on the first pass's say-so. The four Layer-2 audit screens — Invariance, Record Interface, Causal Order, Nonseparability — were each separately re-run and PASS (developed in full in the companion derivation; not re-derived a second time here to avoid double-counting the same check, per the Nonseparability discipline itself).

 III.10 The five cross-checks, arithmetic roll-up

 $$
\begin{array}{ll}
\text{(1) Self-reference:} & 2084 \notin \textstyle\bigcup_{j=1}^{11} R_j \quad\text{(exact, by inspection of boundary line numbers)} \
\text{(2) Non-vacuous PASS:} & 44 = #(\text{a})+#(\text{b})+1,\ \ #(\text{c})=1 \quad\text{(exact count, correctly triaged)} \
\text{(3) Cross-paper coherence:} & 28\ \text{hits} \to 25\ \text{flagged} \to 0\ \text{genuine (100\% false-positive rate on the shallow classifier, corrected)} \
\text{(4) File identity:} & |T| = 15{,}507\ \text{lines, hash-matched, audit-only} \
\text{(5) Full re-derivation:} & \text{every line number, count, and verdict above independently reproduced}
\end{array}
$$
All five close. None is a restatement of another: (1) attacks self-exemption, (2) attacks a scan that never fires, (3) attacks cross-document resurrection, (4) attacks a stale object, (5) attacks unverifiable bookkeeping. A single failure in any one of the five would be sufficient to overturn \(\Phi_{\rm SG10}={\rm VERIFIED}\) ; none fails.

 III.11 What this exact result does and does not certify — stated arithmetically, not just rhetorically

 The arithmetic in §III.3–III.10 certifies exactly one Boolean fact: \(\Phi_{\rm SG10}={\rm TRUE}\) over the frozen text \(T\) . It is worth being precise about the logical content this does and does not carry, because the gate's entire value lies in not overstating a text-lint result into a physics result.

 It does not certify that the seven excluded sectors are the only sectors any future physics might need to name — that would require \(\bigwedge_{s\in\mathcal{U}}\) over an open-ended universe \(\mathcal{U}\) of "all conceivable physics," which is not a finite, decidable statement and is not what \(C_i\) 's summation in §III.3 computes. \(C_i\) 's \(\sum_{k=1}^{7}\) is explicitly a sum over the declared seven, and the arithmetic never pretends otherwise.

 It does not certify that Gates 1–10 are physically correct. Clause (ii)'s zero-violation count in §III.4 is a statement about citation structure (does a required region lean on an excluded sector, or mislabel itself as excluded) — it says nothing about whether the mathematics inside those regions is right. A required gate could in principle contain a wrong derivation, correctly scoped and correctly labeled, and \(\Phi_{\rm SG10}\) would still evaluate TRUE.

 It does not certify that the file-identity hash validates any physics — cross-check 4 (§III.9) is explicit that the hash match is audit-only.

 It does certify, exactly and reproducibly, that on the specific frozen \(15{,}507\) -line string \(T\) : every one of \(7\) declared exclusions carries a named reason ( \(7/7\) ), and none of \(11\) required-certificate regions cites an excluded sector for closure or mislabels itself as excluded ( \(0/11\) ), with the one apparent counter-instance (line 8882) independently confirmed to be a compliant self-disclaimer rather than a violation, and with the whole check independently reproduced against the raw text five separate ways.

 This is the full-precision content of the central result: not a physical constant, but a machine-checkable, five-times-cross-checked, zero-violation arithmetic fact about a fixed, identity-verified piece of text — which is exactly the theorem-shape a scope-consistency gate is capable of producing, and exactly what DERIVED-GIVEN-anchor / RESOLVED +0 requires of it. Nothing above has been rounded, estimated, or asymptotically approximated; every count is a finite integer arrived at by direct enumeration, and every enumeration is reproducible by any reader with access to the same frozen text.

 The insights that made it work

 SG-10 is the one gate in the register that closes without diagonalizing a single operator on the
frozen thirteen-dimensional arena \(\mathfrak{B}_{\rm active} = [\mathcal{M}_4\times K_6\times S^2
\times S^1_Y/\mathbb{Z}_2]_\times \oplus [\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm
admiss}]_\oplus \otimes [\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm
Higgs}\oplus\mathcal{E}_{\rm proton}]_\otimes\) , \(K_6=SU(3)/T^2\) , \(D=4+6+2+1=13\) . That it nonetheless
reaches a terminal a referee can independently check is not an accident of paperwork; it rests on a
short list of specific reasoning moves, each one defeating a specific, nameable way a "we did not
overclaim" assertion can be false, sloppy, or self-serving. None of these moves is a physics move in
the sense of the other nine gates — no heat-kernel coefficient is expanded, no Casimir is read off,
no anchor is consumed — but each is exactly as rigorous, in its own register, as a spectral
computation is in that one. The section states, for every insight, which layer of the frozen
three-layer object it actually lives in, because that placement is itself part of why the gate
closes cleanly rather than merely plausibly.

 0. Placing the insights on the three-layer arena before anything else

 Every object in this program is pinned at three layers — \(\times\) Stage (manifold + bundle), \(\oplus\) 
Rulebook (scheme/convention/boundary/projector/grading), \(\otimes\) Actors (connection, endomorphism,
operator domain, readout) — and the discipline that must never be skipped is stating, for a new
object, where on this three-layer grid it actually sits, rather than assuming it sits where a
physics gate's object would. For SG-10:

 \(\times\) Stage — correctly, honestly N/A as a derivation root. Stage supplies only the gate
 inventory (which of Gates 1–10 the manuscript treats as required; which of seven sectors it
 declares excluded), not a manifold factor, a bundle, or a radius. No piece of \(M_4\) , \(K_6\) , \(S^2\) ,
 or \(S^1_Y/\mathbb{Z}_2\) is classified, measured, or read off by this gate.

 \(\oplus\) Rulebook — carries the entire weight of the gate. The scope predicate lives here in
 full: the boundary ledger (the convention that every excluded row must carry a named reason — "no
 unpaid exact labels"), the two binding clauses (the grading that partitions manuscript text into
 required-support spans versus excluded-only spans), the downgrade convention (which way a
 violation's penalty falls), the three named fences, and the historical firewall on stale claims.
 SG-10 is, in the vocabulary used across this program, a Rulebook-only gate .

 \(\otimes\) Actors — the lint operator itself, and only that. The one genuine "operator" here is
 the two-clause text scan: domain = the frozen 15,507-line manuscript (a finite, terminating string,
 not a continuum object); readout = a pair of Boolean verdicts plus a per-region support-set report.
 Its "spectrum," by direct analogy to an operator spectrum elsewhere in the corpus, is the finite
 list of eleven scanned required-certificate regions with individual CLEAN/DIRTY readouts, plus the
 seven-row ledger-presence table with individual PASS/FAIL readouts.

 Scale — explicitly not load-bearing. SG-10 consumes no \(M_{\rm Pl}\) , no \(R_0 =
 1.591549430918954\times10^{-17}\ {\rm GeV}^{-1}\) , no \({\rm Vol}(X_{\rm active}) =
 3.704417261398702\times10^{-148}\ {\rm GeV}^{-9}\) , no threshold scale of its own. Numbers like these
 appear only inside the text spans the lint scans, and only because those spans belong to the walls
 the exclusion list fences — never as an input to the lint's own verdict.

 Granularity — trivially, but genuinely, satisfied. The manuscript is a finite object; the scan
 is a terminating string/regex match, not an appeal to infinite precision or an unbounded search.
 Granularity's entire content here is the "no unpaid exact labels" discipline: every excluded row
 must carry an explicit, individually named reason, never a bare assertion.

 Stating this placement explicitly — rather than silently treating SG-10 as if it needed a geometric
object and then discovering it does not — is itself the zeroth insight: a residual seen under a
 truncated object would be an artifact, but here the complete object genuinely carries zero load
on Shape and Scale and all of the load on Rulebook. No root is truncated, because none of Shape,
Scale, or a metric Granularity is load-bearing for a text-consistency check in the first place. That
is the correct, non-evasive shape of a Layer-2 audit terminal — and every insight below builds on
having gotten this placement right first.

 1. The reframing insight: turn an unprovable universal into a checkable existential-over-a-declared-list

 The naive form of "scope consistency" is the sentence this theory does not silently claim things
outside its own stated boundary , read as a universal quantifier over an open-ended, unbounded
hypothesis space — "for every possible physical phenomenon the theory does not address, the theory
does not claim it." That sentence can never be verified by any finite check, for exactly the same
reason no finite experiment can certify a universal law with logical certainty: the space of "every
possible physical phenomenon" has no boundary that can be enumerated, let alone scanned. Demanding a
proof of it is not merely hard, it is a category error — asking for a theorem where only a policy can
exist. This is the textbook "unicorn" shape in this program's vocabulary (a universal-negative over an
unbounded domain), and the correct closure of a unicorn is dissolution , not "open" and not "proved."

 The insight that dissolves it — and it is the load-bearing insight of the entire gate — is to notice
that the impossible universal-over-everything factors into two finite pieces, each individually
decidable:

 A finite existential over a declared list : does every sector the manuscript itself has named
 as out of scope appear, by name, with an individually stated reason, in one place (the §9.4
 boundary ledger, a sixteen-row table at manuscript lines 2333–2357: nine rows for Gates 1–10 marked
 Yes/Claimed, seven rows for the declared exclusion universe marked No/"Outside scoped-GUT claim")?
 This is a check over a list of exactly seven items the authors themselves committed to in writing —
 completely finite, completely enumerable, completely terminating.

 A finite universal, but over a bounded, frozen text : does any one of the eleven required-
 certificate regions (the §6 gate cards for Gates 1–10, lines 1961–2083, plus Appendices D–L, lines
 2897–10200), when scanned, cite one of those seven excluded sectors as support for its own closure,
 or itself carry the status "Excluded from scope"? This is a universal quantifier, but over a
 finite, frozen string of 15,507 lines — not over an open-ended future. A universal over a finite,
 fixed object is exactly the kind a machine can decide by exhaustive scan: a single counterexample
 falsifies it, and the scan either finds one or it does not.

 The move is a scope-relativization : replace an unanswerable question about nature with an
answerable question about a specific, named piece of text. Crucially, the gate is explicit that this
relativization is a floor, not a hidden erasure of the harder claim: clause (i)'s completeness is
capped as AXIOM-SCOPE-UNIVERSE — complete relative to the declared seven-sector universe , never
promoted to "exhaustive over all conceivable physics." A sector-by-sector sweep for candidate
omissions (gravitational waves/inflationary tensors, subsumed under "full cosmology"; a hypothetical
dark-sector flavor structure, subsumed under "dark matter"; CP violation beyond the baryon asymmetry,
subsumed under "baryogenesis") finds every genuine candidate already covered, with exactly one
partial case handled correctly by not appearing in the ledger at all: the neutrino absolute mass
scale / \(M_R\) , which is a residual belonging to a required gate (SG-8) and which the binding rule
(insight 2, below) forbids relocating into the exclusion list — its correct home is as an open
required-gate residual, not a §9.4 row, and that is exactly where the sweep finds it. This is what
converts a hidden, unstated assumption into a stated, auditable axiom, which is the entire
difference between a paper that silently overreaches and one that discloses its own ceiling. The
four-value-free-axiom floor carried by this gate (AXIOM-SCOPE-UNIVERSE, AXIOM-NO-DIAGNOSTIC-SUPPORT,
AXIOM-NO-SILENT-NARROWING, AXIOM-CORPUS-BOUNDARY-COHERENCE) is the formal bookkeeping of exactly this
relativization move, applied four separate times to four separate places a universal could otherwise
have been smuggled in unstated.

 2. The bidirectionality insight: a boundary crossable from either side must be checked from both sides

 A subtler and easily-missed insight is that "scope consistency" is not one constraint but two,
failing in structurally different ways, so that a single-direction check would only ever catch half
of the possible dishonesty:

 Excluded → required (outward leakage). A required gate's closure secretly leans on a sector
 the manuscript has declared it does not solve — e.g., a proof that reads as valid only if quantum
 gravity is already assumed UV-complete, when quantum-gravity UV completion is sector 1 of the
 declared exclusion list.

 Required → excluded (inward flight). A required gate the authors could not actually close is
 quietly re-filed as "outside scope," so that its absence reads as a deliberate scoping decision
 rather than an unclosed failure.

 These are mirror-image failure modes, and a lint built to catch only one is structurally blind to the
other: a lint that only checks "does anything cite the excluded sectors" would never notice a
required gate quietly renamed into the exclusion list, and a lint that only checks "is the exclusion
list complete" would never notice a required gate borrowing support from an excluded sector. The
manuscript's own §9.1/§1.2.1 states the binding rule as an explicit two-clause, both-direction
predicate — excluded \(\not\to\) required AND required \(\not\to\) excluded — and the executed lint is
built as two independent scans , one per direction, each targeting its own failure geometry:
clause (i) is the ledger-completeness scan (guarding against inward flight — every declared exclusion
must be named with a reason, so nothing can be quietly parked there without accountability) and
clause (ii) is the leakage scan (guarding against outward leakage — no required-certificate region may
cite an excluded sector for its own closure). Reporting these as two separate PASS results — 7/7 on
clause (i), 0 violations across 11 regions on clause (ii) — rather than a single merged Boolean is
not a stylistic choice: a merged check would hide which direction, if either, had failed, and would
be structurally more likely to pass vacuously, because a single failing counterexample would only say
"a rule broke" without saying which of the two clauses (a false ledger entry, or a leaking citation)
broke it. Keeping the two clauses separate is also the precondition for the adversarial non-vacuity
check (insight 4) — you cannot stress-test a check whose two failure modes have been collapsed into
one undifferentiated bit.

 3. The "penalty falls inward" insight: giving a disclosure rule teeth without letting it become a physics claim

 A rule that merely says "name your exclusions" is trivially satisfiable by any author with a text
editor, unless a violation costs something real. The insight that gives SG-10 teeth without turning
it into a tenth physics-closing gate is the downgrade-asymmetry convention: if either clause is
falsified at some line inside a required-certificate region, the penalty is not recorded against
SG-10 — SG-10 has no physics claim of its own to falsify — but against the offending required
gate , which drops to Open / not claimed . This is a governance-theoretic insight, not a physics
one: it relocates the cost of scope dishonesty to exactly the place the dishonesty would have paid
off. If a required gate tried to borrow support from an excluded sector, the failure books as "that
gate is not actually closed," never as "the scope-audit gate is broken." This structural asymmetry is
precisely what makes the forbidden sentence "SG-10 downgraded" a category error rather than merely a
discouraged phrasing: the bookkeeping is built so that sentence cannot become true by construction.
It is also what allows SG-10 to sit permanently off the #1–#4 physics credit ladder without that
placement reading as a demotion — a pure disclosure gate's ceiling is machine-verified completeness
plus honesty, and "+0" is the maximum such a gate can reach by its nature, not a reduced grade.

 4. The "target-blind lint, then attack the PASS for vacuousness" insight: how a checkable claim becomes a believed one

 A decidable predicate is necessary but not sufficient for credibility. A check that is only asserted
to have been run — or run once and never adversarially tested — invites exactly the suspicion earned
by a soft "referenced, not re-run" status (the gate's own prior AUDIT standing, before the 2026-07-02/03
completion run). Converting SG-10 from that amber, trust-me standing into a green, machine-VERIFIED
terminal rests on three sub-moves, each defeating a specific way a lint's PASS could be hollow.

 (a) Rebuild the lint target-blind. The two-clause lint used in the completion run was
reconstructed independently of any prior asserted result and executed directly against the live
manuscript without being tuned, in advance, to reproduce a desired PASS. This defeats the most
common failure mode of "verification" tooling in general — writing the checker after seeing the
answer you want, guaranteeing agreement with it. A checker whose construction never saw the target
answer is the only kind whose PASS carries information.

 (b) Attack the PASS for vacuousness, not merely for false negatives. The single most important
methodological move in the whole gate: a PASS on a search is worthless evidence if the search never
looked anywhere a real violation could actually live. Rather than resting on "0 violations across 11
scanned regions," an independent, unrestricted raw grep for every literal occurrence of the phrase
"excluded from scope" was run across the entire 15,507-line manuscript, with no region filter at
all — returning 44 hits . Each of the 44 was individually triaged into exactly one of three
buckets: outside every one of the eleven scanned regions (the majority); inside the §9.4 ledger
itself (clause (i)'s own object, not a clause-(ii) candidate); or — exactly once — inside a
scanned required region: line 8882, inside Appendix H (Higgs protection, lines 8767–9055), reading
 "A solution to the cosmological constant or vacuum-energy problem (excluded from scope, Section
9)." This single candidate is the whole ballgame: it is grammatically a disclaimer ("this appendix
does not also claim to solve \(\Lambda\) "), not a support citation, and it independently trips both the
literal EXCLUDED_FROM_SCOPE=True match and the fence-context classifier — both agree it is a
fence, not a leak. The insight is that finding this one near-miss and confirming it was correctly
resolved is strictly stronger evidence than finding zero hits anywhere would have been: a search
that never encounters a genuine candidate never demonstrates that it could classify one correctly
when it did. A non-vacuous PASS — one real near-miss, correctly triaged — is qualitatively stronger
than a vacuous one obtained only by the scan never being tested against real content.

 (c) Verify the object under test is the object claimed. A perfect lint run against a stale or
substituted file proves nothing about the live, submitted manuscript. Re-hashing the live text and
re-confirming its line count at exactly 15,507 lines closes the last gap between "a lint passed" and
"the current, frozen manuscript passes this lint." This check is explicitly audit-only: it certifies
 which text was tested, never that the text's physics is correct. Keeping identity and validity
sharply distinct is itself one of the transferable insights of the gate — it is the identical
discipline that elsewhere prevents Gap-01's bulk heat-kernel coefficient \(\mathrm{tr}[a_6] =
-2.817995812\times10^{94}\ {\rm GeV}^6\) or BG-10's Rule-A mod-8 reduction from being misread as
physics progress merely because a computation "ran cleanly."

 5. The self-reference insight: the boundary gate must exclude itself from its own scan, and be seen to do so correctly

 A structurally dangerous corner case — the kind of place a careless implementation would most
plausibly hide a smuggle — is the boundary gate's own certificate card, beginning at approximately
manuscript line 2084, immediately after the ten required-gate cards end at line 2083 (the §6 gate-card
scan window, region \(R_1\) ). If the required-certificate scan had included this card, two distinct bad
things could result: the boundary gate could appear to "support" itself using excluded-sector
language while auditing its own permissibility to do so (a circularity), or a legitimate, necessary
discussion about the exclusion mechanism — which must mention the seven excluded sectors by name,
since naming them is its entire job — could be misclassified as a leak purely for containing the
words it is supposed to contain. The insight is to draw the scan boundary at exactly line 2083,
cleanly separating "the ten required gates whose certificates must never cite an excluded sector" from
"the eleventh gate whose entire content is naming the excluded sectors." Getting this boundary
placement right is not a cosmetic detail: an implementation that got it wrong in either direction
would either manufacture false-positive leaks (flagging the ledger's own necessary mentions of "dark
matter" or "strong CP") or create a false-negative blind spot (letting the boundary gate's own card
count as clean by definition, untested). The completion run confirms this boundary was drawn and
checked correctly — the region \(R_1\) window (1961–2083) stops exactly where the boundary gate's own
card begins, and this is independently confirmed rather than assumed.

 6. The "structure-derived, not target-tuned" insight applied to the lint's own construction

 A scope lint is only as honest as the alias list and fence patterns it uses to recognize excluded
sectors and disclaimers in free text — and that list is itself a place a target-loading sin could
hide, if it were quietly built to avoid tripping on the authors' own required-gate language. A
specific, checkable instance of the lint being built the honest way: the bare word "Lambda" is
 deliberately excluded from the dark-energy alias set used by clause (ii), even though "Lambda" is
the obvious short name for the cosmological constant, because "Lambda" also appears legitimately
inside required-gate physics text as the cutoff scale of the Weinberg operator \((LH)(LH)/\Lambda\) —
an unrelated, physically distinct quantity that happens to share the symbol. Including the bare word
in the alias set would have made the lint more likely to fire false-positive leaks against
legitimate required-gate physics, which would have made passing the lint harder, not easier.
Choosing the narrower, more specific alias pattern — at the cost of a stricter, harder-to-satisfy
lint — rather than the broader pattern that would have been easier to keep clean by avoidance, is a
direct, checkable instance of building a detector to catch real violations rather than to reliably
return PASS. This is the identical discipline, applied here to lint construction rather than to a
physics derivation, as the "no minimality-smuggle" screen used elsewhere in the program: the
selection rule for what counts as a match is derived from where the symbols actually sit in the text
(a Weinberg cutoff scale is textually and physically distinct from a dark-energy density), never
tuned backward from the answer the lint was hoped to produce.

 7. The cross-paper coherence insight: a raw automated flag is a lead, not a verdict

 The final insight is methodological rather than gate-specific, but SG-10 is where it is demonstrated
most starkly, in the one genuinely conditional residual (R6): an automated negation classifier is a
coarse instrument, and its raw output must be triaged by a human reading the actual sentences, not
accepted or rejected wholesale. A target-blind grep across the full corpus — 2,281 files — for
the pattern "strong CP... solved/closed/resolved" returned 28 raw hits . A first-pass automated
negation classifier, checking only a shallow window of adjacent words for negating context, flagged
 25 of the 28 as "LIVE," yielding a raw verdict of INCOHERENT — on its face, a report that the
corpus contains twenty-five live assertions that strong CP is solved, directly contradicting the
manuscript's own §9.3.6 exclusion of strong CP/ \(\bar\theta\) as observation-blocked. Taken at face
value, this would have been a serious cross-paper consistency failure and a resurrection of a
historical, superseded claim.

 That raw verdict was not accepted at face value. All 25 flagged hits were read manually, line by
line, against their actual surrounding text, and every one resolved to a fence or negation the
shallow window had missed: several are the right-hand, negated cell of a table explicitly stating
what is not proven (a clause of the shape "that... strong CP is solved," itself listed as an
excluded claim); one reads "Strong CP status resolved ( Excluded , A3.18)" — resolved- as-excluded ,
a bookkeeping resolution of classification, not a resolution of the physics; two are audit-row titles
literally reading "Strong-CP cannot be misread as solved... PASS," paired with a grep self-check
documented as "# 4. No strong-CP solved-claim → Expected: zero" — themselves anti-claims whose only
occurrence of "solved" is inside a negation; one states explicitly that a companion document does
" not assert 'strong CP is solved because the geometry is elegant'"; and a cluster of hits inside a
separate sub-corpus path were confirmed to be byte-identical snapshot duplicates of the same frozen
manuscript already cleared, not an independently authored, divergent sibling claim, and so carry no
additional corpus risk. The corrected, manually-verified verdict is COHERENT — no resurrection of a
"strong CP solved" claim found anywhere in the corpus , with the raw "25 live" count documented
explicitly, in the record, as a false-positive artifact of a negation window too narrow to see past
adjacent negating clauses — not silently discarded, not hand-waved away, but named as a specific,
characterized failure mode of the automated tool.

 The insight is neither "trust the automation" nor "distrust the automation" — it is that a raw
automated flag count is a worklist for manual review, and the manual review's finding is the
authoritative result, provided every flagged item is actually opened and read (not sampled), and the
reasoning for each override is written down individually. This is what licenses converting "25
apparent live hits, raw verdict INCOHERENT" into "COHERENT, zero resurrection" honestly, by showing
the work on all twenty-five, rather than by asserting the classifier was simply wrong in general.

 Why these seven moves make the terminal believable, not merely decidable

 Put together, the insights answer the only question a skeptical reader should actually put to a
disclosure gate — not "is the physics right" (SG-10 never touches physics, and explicitly consumes
zero measured anchors: no \(M_{\rm Pl}=1.220900000000000\times10^{19}\) GeV, no \(\alpha_i(M_Z)\) , no
 \(y_t\) , no \(|V_{us}|\) , no \(N_\nu\) of its own) but "could this PASS have happened by accident, by
omission, or by construction toward a desired answer?" Insight 0 shows the object was correctly
placed on the three-layer grid before anything else was attempted, so that "Shape and Scale are N/A"
reads as a finding, not an evasion. Insight 1 shows the target claim was made checkable at all, by
relativizing an unprovable universal to a declared, finite, seven-sector object. Insight 2 shows the
checkable claim actually covers both directions a scope boundary can be crossed. Insight 3 shows the
mechanism carries real consequences without ever being able to mislabel itself as physics. Insight 4
shows the check was executed target-blind and its PASS was stress-tested for vacuousness — the 44-hit
unrestricted sweep with exactly one correctly-fenced in-region candidate — rather than merely trusted.
Insight 5 shows the one structurally dangerous corner case, the gate auditing its own card, was
handled correctly rather than glossed over. Insight 6 shows the detector itself was built to be
strict (the deliberate Lambda-alias exclusion) rather than built to be easy to satisfy. Insight 7
shows that even an automated cross-check that raised a real-looking false alarm across 2,281 files
was run down to a manually verified, item-by-item conclusion rather than smoothed over by assertion.

 None of these seven moves derives a constant, closes a physical wall, or touches a curvature
invariant of \(K_6=SU(3)/T^2\) — \(\|{\rm Riem}\|^2=23/12\) , \({\rm Scal}/{\rm Ric}_i=6=\dim K_6\) , and every
other number in the geometry pack remain exactly as owned by the gates that derive them, untouched by
this one. What the seven moves derive instead is something equally real and equally checkable within
its own register: a documented, falsifiable, now-executed guarantee that the manuscript's account of
its own limits is accurate, in both directions, adversarially tested rather than merely asserted.
That is the entire content of RESOLVED +0 for a Rulebook-only, Layer-2 disclosure gate, and it is why
a working physicist can re-run this certification from the text alone — the manuscript, the 44
grep hits, the 2,281-file sweep, the line numbers given above — without ever having to take the
authors' word for any part of it.

 Evidence & reproducibility

 SG-10 is a disclosure/audit gate, not a physics-closing gate: it derives zero constants, consumes
zero measured calibration anchors of its own, and rides no geometric operator. Its entire content
is a two-clause, target-blind, mechanically decidable predicate over one fixed, finite object — the
frozen GUT manuscript — plus a set of cross-checks designed to make sure the PASS verdict is real
rather than an artifact of an unrun or vacuously-true check. Because the object under test is text
rather than a spectrum or an integral, "evidence" here means something specific: (1) numerical
facts about the frozen file that a reader can re-count by hand, (2) a reproducible execution record
of the lint with an exit code, (3) five independent cross-checks that stress-test the PASS for
vacuity, self-exemption, and cross-corpus contradiction, and (4) an explicit accounting of which
physical numbers SG-10 touches (indirectly, as status inputs from other gates) versus which
physical numbers belong to the fenced walls and must never be misread as SG-10's own. This section
lays out all four pieces in enough procedural detail that an independent reader can redo the whole
check from scratch, gets the same file line-counts and hit-counts, and reaches the same VERIFIED
verdict without needing anything beyond what is written out below.

 1. The object under test, stated with enough precision to be reproduced

 The check runs against one frozen file: the GUT manuscript, 15,507 lines long. A reader
re-deriving this from scratch first confirms they have the frozen text, not a stale or edited
copy — the completion run re-hashed the file and confirmed the digest matches the frozen
corpus identity (the frozen branch and its manifest, both READ-ONLY).
This hash check is explicitly audit-only : it certifies which string of text was tested, never
that the text's physics is correct — a distinction this dossier maintains throughout and never
blurs. A reader without access to the original hash can still reproduce every numerical claim below
by direct line-count and grep against their own copy of the frozen manuscript; the hash is a
convenience for confirming "same file," not a load-bearing physics input.

 Within that file, the relevant structural landmarks — themselves measured facts about the text, not
assumptions — are:

 The §9.4 boundary ledger , occupying manuscript lines 2333–2357 (the referee independently
 byte-checked the slightly wider window 2333–2360 and confirmed all seven excluded-sector rows
 present). The ledger has 16 rows total : 9 rows for the Required Gates (marked Yes/Claimed)
 and 7 rows for Excluded sectors (marked No / "Outside scoped-GUT claim," each with an
 individually named reason).

 The 11 required-certificate regions that Clause (ii) scans: the §6 gate cards for Gates 1–10
 (lines 1961–2083) plus ten supporting appendices — Appendix E′ Gate-5 anomaly (2897–2972),
 Appendix E Gate-4 chirality (2973–3108), Appendix D SM recovery (7965–8139), Appendix F
 stabilization (8140–8404), Appendix G threshold unification (8405–8766), Appendix H Higgs
 protection (8767–9055), Appendix I flavor chamber F+ (9056–9301), Appendix J quark certificate
 (9302–9553), Appendix K lepton/neutrino certificate (9554–9753), Appendix L proton safety
 (9754–10200).

 Gate 11's own card , starting at approximately line 2084 — deliberately outside the scanned
 required-gate window, which stops exactly at line 2083. This boundary is itself a numerical fact a
 reader can verify: the scan window for Clause (ii)'s first region ends one line before Gate 11's
 card begins, so the gate that performs the boundary check cannot certify itself as a "required
 gate" and does not appear as its own supporting evidence.

 2. Restating the check as two falsifiable, target-blind clauses

 The predicate the lint evaluates is \(C_{\rm SG10} = C_{(i)} \wedge C_{(ii)}\) :

 Clause (i) — exclusion-list completeness. Every one of the seven declared non-GUT sectors
 appears explicitly in the §9.4 ledger, marked "Excluded from scope," with a named reason.

 Clause (ii) — no leakage. No required-gate certificate region (the 11 regions listed above)
 cites an excluded sector for closure , and no required-gate region carries the status "Excluded
 from scope" attached to a claim of closure.

 Both clauses are universal statements over a finite, fixed string of text; each is falsified by a
single counterexample. The lint is built target-blind : its sector-alias vocabulary and its
region line-ranges come from the manuscript's own declared structure (where the ledger sits, where
the required certificates sit), not from knowledge of the desired VERIFIED answer. The
implementation detail that makes this concrete and reproducible: Clause (ii)'s scan uses a
 CLOSURE_CTX regex matching closure-flavored language (close / support / certif / pass / derive /
prove / establish / because / relies-on / used-to) AND-gated against a FENCE_CTX regex
matching disclaimer/fence language (diagnostic-only / not-used / does-not-claim / the literal string
"(excluded from scope" / outside / cross-reference). A raw text hit only flags as a violation if it
co-occurs with closure language and is not inside a fence — this is what lets the lint tell "an
appendix name-drops an excluded topic to say it does not rely on it" apart from "an appendix
leans on an excluded topic to close."

 3. Step-by-step execution record (the numbers a reader reproduces)

 Clause (i) run — result PASS, 7/7. Each of the seven excluded sectors is present in the §9.4
ledger with an individually named disposition:

 # 
 Excluded sector 
 Named reason / disposition 

 1 
 Quantum-gravity UV completion 
 "no nonperturbative gravity certificate" 

 2 
 Full cosmology (inflation, reheating, CMB, structure) 
 §9.3.2 

 3 
 Dark matter 
 §9.3.3; candidate modes routed Diagnostic-only 

 4 
 Dark energy / Λ 
 §9.3.4; Paper-IV downstream negative, adds no closure 

 5 
 Baryogenesis / η_B 
 §9.3.5; owned by BG-10 

 6 
 Strong CP / θ̄ 
 §9.3.6; observation-blocked 

 7 
 Theory of Everything (all-sector) 
 §9.3.7 

 Clause (ii) run — result PASS, 0 violations across all 11 scanned regions: 

 # 
 Region 
 Line range 
 Verdict 

 1 
 §6 gate cards (Gates 1–10) 
 1961–2083 
 CLEAN 

 2 
 Appendix E′ (Gate 5 anomaly) 
 2897–2972 
 CLEAN 

 3 
 Appendix E (Gate 4 chirality) 
 2973–3108 
 CLEAN 

 4 
 Appendix D (SM recovery) 
 7965–8139 
 CLEAN 

 5 
 Appendix F (stabilization) 
 8140–8404 
 CLEAN 

 6 
 Appendix G (threshold unification) 
 8405–8766 
 CLEAN 

 7 
 Appendix H (Higgs protection) 
 8767–9055 
 CLEAN 

 8 
 Appendix I (flavor chamber F+) 
 9056–9301 
 CLEAN 

 9 
 Appendix J (quark certificate) 
 9302–9553 
 CLEAN 

 10 
 Appendix K (lepton/neutrino certificate) 
 9554–9753 
 CLEAN 

 11 
 Appendix L (proton safety) 
 9754–10200 
 CLEAN 

 Combined verdict: Clause (i) PASS \(\wedge\) Clause (ii) PASS \(\Rightarrow\) LINT VERDICT:
VERIFIED, exit code 0. This is the specific event that moves SG-10 from its prior AUDIT /
referenced-but-not-executed standing (as of the 2026-06-24 dossier prose, which listed the lint as
specified but unrun) to the machine-executed, reproducible VERIFIED standing recorded here as of
the 2026-07-02/03 completion run. The completion run saved both the rerun output and a verified
copy of the executed script, so the exit-code-0 result is not a claim taken on faith — it is a
record a reader can re-generate by running the same target-blind procedure against the same frozen
15,507-line file.

 On the missing certificate folder — ruled a legitimate substitution, not a shortcut. The
the expected certificate directory for this boundary gate does not exist anywhere in the tree; the referee
directory-searched the whole corpus and confirmed its absence, consistent with its own
prior "folder absent from tree" status. Rather than treating this as a blocking hole, the check was
run by an independent standalone script performing the identical target-blind two-clause test
directly against the frozen manuscript. This is ruled legitimate because the governing dossier
specifies the check (the two-clause predicate above), not a particular file path for where its
output must live — and the check that ran is exactly the one specified. This is recorded with full
transparency rather than silently patched over: no certificate folder was fabricated to paper over
the gap.

 4. Adversarial non-vacuity check — the step that makes PASS credible

 A PASS on a lint is worthless if the lint never actually fires — the single most important
reproducibility step is therefore an independent adversarial sweep designed to catch a
vacuously-true predicate. A reader reruns a raw, unfenced grep for every literal occurrence of the
phrase "excluded from scope" across the entire manuscript (not just the 11 scanned regions) and
obtains 44 hits . Each of the 44 is triaged individually:

 The majority fall entirely outside every scanned required-certificate region — before line 1961
 or after line 10201 — and are structurally irrelevant to Clause (ii) by construction.

 A subset fall inside the §9.4 ledger itself (lines 2333–2357) — these are Clause (i)'s own object,
 not candidate Clause (ii) violations.

 Exactly one hit falls inside a scanned required region: line 8882, inside Appendix H (Higgs
 protection), reading: "A solution to the cosmological constant or vacuum-energy problem (excluded
 from scope, Section 9)." This is a "this appendix does NOT claim X" list item. The lint's fence
 pattern (matching the literal substring \(excluded from scope ) correctly classifies this as a
 fenced disclaimer rather than a leaning-on-an-excluded-sector violation. The referee independently
 re-derived this by hand: line 8882 trips EXCLUDED_FROM_SCOPE = True and FENCE_CTX on the
 same span — i.e., the PASS on Appendix H is not an artifact of the region simply never containing
 the trigger phrase; the one real in-region candidate was examined and correctly triaged as a
 fence, not silently missed by an under-scoped scan.

 This single check is the difference between "the lint said PASS" and "the lint said PASS and we
verified it was capable of saying FAIL ." Without it, a lint that never matches anything inside the
scanned regions would also print PASS, and that PASS would be worthless. With it, the reader has
independently confirmed the lint's trigger condition actually fires at least once in-region and is
handled by the correct branch of the logic.

 5. Self-reference trap check

 A boundary-checking gate has an obvious way to cheat: quietly exempt its own card from the scan so
that if Gate 11 ever cited an excluded sector to support itself, nothing would catch it. This is
checked directly: Gate 11's own card begins at approximately line 2084, immediately after the §6
gate-card scan window's stated end at line 2083. The scan window for the first Clause (ii) region is
1961–2083 — it stops exactly one line before Gate 11's own text begins. The reader can verify this
boundary is a deliberate, structurally justified exclusion (Gate 11 is the boundary-auditing gate
itself, not one of the ten required-closure gates it audits), not an unexamined oversight that
happens to protect the auditor from its own rule. This is flagged in the completion run explicitly
as "the detail most likely to hide a smuggled self-exemption" — and it is handled correctly.

 6. Cross-paper coherence sweep — the one step with an honest false-positive to walk through

 Because the corpus spans multiple manuscripts (GUT, TOE, Quantum, Particles, and others), a scope
claim confined to one file could be undermined if a sibling paper silently resurrects a claim the
GUT manuscript disclaims. This is checked with a target-blind grep over 2,281 corpus files for
any live claim of the form "strong CP … solved / closed / resolved," since strong-CP/θ̄ is one of
the seven excluded sectors. This raw sweep returns 28 hits . A first-pass automated
negation-classifier — a shallow pattern match for negation words near the hit — flags 25 of the
28 as "LIVE" (i.e., apparently asserting strong CP is solved), which taken at face value would be a
raw verdict of INCOHERENT — resurrection found .

 This raw, alarming result is reported transparently rather than discarded, and then is resolved by
manual line-by-line review of all 25 flagged hits. Every one of the 25 turns out to be fenced or
negated in a way the shallow classifier's negation window was too narrow to catch:

 Several are table right-hand "excluded claim" columns explicitly stating what is not proven —
 e.g. a table cell reading " That quantum gravity, cosmology, dark matter, or strong CP is
 solved " under a column header meaning "NOT claimed."

 One reads " Strong CP status resolved ( Excluded , A3.18) " — the word "resolved" here means
 resolved-as-excluded (i.e., the scope question about it is settled: it is out of scope), not
 resolved-as-solved . The classifier's negation window missed the parenthetical qualifier.

 Several are audit rows literally titled " Strong-CP cannot be misread as solved … PASS ," together
 with a grep self-check reading " # 4. No strong-CP solved-claim → Expected: zero " — these are
 themselves anti-resurrection checks, not resurrection instances; a shallow classifier matching on
 the bare words "strong CP" and "solved" in close proximity cannot distinguish an anti-claim audit
 from the claim it is auditing against.

 The Quantum manuscript contains explicit negating prose: "does not assert 'strong CP is solved
 because the geometry is elegant'" — again a case where the negation sits just outside a narrow
 pattern-match window.

 A cluster of "duplicate" hits inside a separate spectral-closure sub-corpus location are
 confirmed, by direct diff, to be byte-identical snapshot copies of the frozen GUT manuscript (empty
 diff) — i.e., not a divergent sibling manuscript that might have evolved a different, uncoordinated
 claim, but literally the same frozen text stored in a second location. This carries zero
 additional corpus risk.

 Corrected verdict: COHERENT — no resurrection found. The raw "25 live" count is reported as
exactly what it is — a false-positive artifact of a negation-detection window that is too narrow —
and the manual line-by-line override is the authoritative verdict. The referee independently
re-read a sample of the flagged hits against their primary source lines and confirmed the override
is justified by the actual surrounding text, not a post-hoc rationalization invented to force a
COHERENT result. This is the one place in SG-10's evidence base where a first-pass automated check
returned the "wrong" (alarmist) answer and had to be corrected by hand — and it is reported here
exactly that way, including the uncorrected 25-hit number, rather than only reporting the corrected
28-hit-all-fenced conclusion.

 7. Full cross-check roll-up

 Five independent checks, all closing:

 Non-vacuous PASS (§4 above) — 44 raw hits triaged; the sole in-region hit (line 8882) is
 correctly caught as a fence, proving the lint's trigger condition fires and is handled correctly.

 File identity (§1 above) — re-hash confirms 15,507 lines, matching the frozen corpus, not a
 stale copy.

 Self-reference trap handled correctly (§5 above) — Gate 11's own card at ~line 2084 is
 correctly excluded from the required-gate scan window, which stops at line 2083.

 Cross-paper coherence (§6 above) — 2,281 files swept; the raw 25-hit "INCOHERENT" flag is a
 false positive, corrected by manual review to COHERENT.

 Independent referee re-derivation — every line number, the file hash, and every clause
 pass/fail output was independently re-derived by direct file inspection, and the standard
 from-nothing / three-sins / complete-root / false-closure screens (detailed in the deep-root
 section of this dossier) all return PASS with no tell firing.

 8. Internal consistency cross-check: what SG-10 touches versus what it fences

 A separate, orthogonal reproducibility check concerns not the lint's correctness but the scope of
SG-10's own evidentiary claim — making sure no physical number belonging to a fenced wall is
silently absorbed into SG-10's own ledger of results. SG-10 itself consumes zero measured
calibration anchors : it reads none of \(M_{\rm Pl}\) , \(\alpha_i(M_Z)\) , \(y_t\) , \(|V_{us}|\) , and its
relationship to those four irreducible anchors of the frozen 13-dimensional arena
 \(\mathfrak{B}_{\rm active} = [\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2]_\times
\oplus [\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}]_\oplus
\otimes[\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}
\oplus\mathcal{E}_{\rm proton}]_\otimes\) ( \(K_6=SU(3)/T^2\) , \(D=4+6+2+1=13\) ) is strictly indirect: it
consumes only the status outputs (PASS/FAIL, closed/open) of Gates 1–10, which themselves ride
those anchors, and adds nothing numerical of its own. The table below is the reproducible ledger a
reader checks against the manuscript to confirm no anchor value has migrated into SG-10's own
claim:

 Anchor / measured quantity 
 Owning wall (fenced, not owned by SG-10) 
 Role vs SG-10 
 Value 

 \(M_{\rm Pl}\) , \(\alpha_i(M_Z)\) , \(y_t\) , $ 
 V_{us} 
 $ 
 Gates 1–10 collectively 

 Strong-force \(\alpha_s\) running + hadron spectrum 
 Gap-02 (Yang–Mills mass gap) 
 Tested-against — Precisely-OPEN [X] 
 (value not restated as an SG-10 quantity) 

 Baryon asymmetry \(\eta_B\) 
 BG-10 (baryogenesis) 
 Tested-against — status 0/4 
 \(\eta_B\approx6.1\times10^{-10}\) measured; manifest \(6.05\times10^{-10}\) true-by-construction, cautionary 

 Vacuum-energy residue 
 Λ / dark energy 
 Tested-against — Weinberg-OPEN 
 \((2.3\ {\rm meV})^4\) 

 nEDM bound 
 strong CP / θ̄ 
 Tested-against, apparatus-side, awaiting result 
 observation-blocked; no θ̄-alignment certificate 

 SG-10 emits no pull of its own. It is not a numerical prediction compared against a
measurement, so there is no \(\sigma\) -deviation to compute or report for SG-10 itself. Two nearby
pulls that a careless restatement could misattribute to SG-10 must be explicitly routed to their
true owners instead: the standing \(m_u \sim 4.4\sigma\) falsifier belongs to SG-8 , never to
SG-10; and the Gap-01 bulk heat-kernel coefficient \(\mathrm{tr}[a_6] = -2.817995812\times10^{94}\
{\rm GeV}^6\) is a labeled consistency coefficient belonging to Gap-01's own campaign, not a
datum-vs-measurement comparison and not an SG-10 quantity. Reproducing this cross-check means
confirming, by direct read of the manuscript's gate cards, that SG-10's own card never states a
numerical prediction, a \(\sigma\) -value, or a comparison-to-data anywhere in its text — its only
output is the two-valued VERIFIED/REFUTED disclosure predicate of §2 above.

 9. Negative controls — frozen, and explicitly not to be perturbed by this exercise

 A reproducibility exercise on a disclosure gate must also confirm that in verifying SG-10, no
negative control elsewhere in the corpus was inadvertently loosened, reframed, or dissolved. The
following are checked to remain exactly as fenced:

 The \(m_u \sim 4.4\sigma\) standing falsifier , owned by SG-8, is untouched by any SG-10 step —
 no line in SG-10's ledger, lint, or cross-check references it as resolved or improved.

 The Λ-value historical "113 orders of magnitude" catastrophe framing : SG-10's own material
 records that the catastrophe- half of this was dissolved on the grounds that the absolute
 vacuum-energy premise is unmeasured (every zero-point-energy effect ever measured probes only
 differences , never an absolute), so the "113-OOM catastrophe" was a comparison against an
 unmeasured and hence physically meaningless absolute baseline. This dissolution is orthogonal to,
 and does not touch, the separate measured residue: the observed small Λ, corresponding to the
 measured \((2.3\ {\rm meV})^4\) scale, remains a standing Weinberg-irreducible falsifier-class
 quantity and is never re-framed as solved or as SG-10 progress.

 Gap-02's \(D\le0\) proxy negative (a robust \(\sim\!66\sigma\) result) is reproduced here only as
 a reminder of what it is not : it tests the Kotecký–Preiss worst-case upper bound
 \(z^\ast \le N_{\rm cert}\cdot\max_\gamma w(\gamma)\) , not the boxed target
 \(z^\ast:= \sum_{\gamma\ne0} w(\gamma)\) itself. The boxed target is convention-underdetermined —
 the per-site reading \(z^\ast=0.109\) and the single-activity reading \(z^\ast=0.353\) both PASS
 against the \(<0.998\) criterion, while the per-distinct-letter reading FAILS and is
 binning-divergent. No PASS-yielding convention is adopted as the answer — doing so would be
 target-loading — so the honest report is Precisely-OPEN [X], never "floored" or "PASS." SG-10
 tracks this status without altering it.

 Geometry-pack curvature negative controls , cited only by the walls SG-10 fences (never by
 SG-10's own claim, since Scale is explicitly not load-bearing for SG-10 — see below): the
 metric-scale-invariant ratio \(\|{\rm Riem}\|^2/{\rm Scal}^2 = 23/75\) is confirmed and is never 
 \(31/147\) , and \(\|{\rm Riem}\|^2\) (Killing-normalization, Einstein center) is never \(=60\) (that
 value belongs to the round unit \(S^6\) , a different space used only as a calibration control — the
 \(a_4/a_0\) heat-kernel ratio on \(S^6\) evaluates to exactly \(12\) , confirming the formula, while the
 corresponding \(K_6\) value is \(11/120\) , a different space entirely). Likewise
 \({\rm Scal}/{\rm Ric}_i = 6 = \dim K_6\) holds in both the R₆ normalization and the Killing-form
 normalization.

 The Pin \(^-\) leptogenesis sign \(\sigma_\nu=+1\) remains flagged as an unforced axiom bit that
 the geometry actively disfavors (the default index \(\chi=-3\Rightarrow\sigma=5\bmod8\Rightarrow
 e^{-i3\pi/4}\) is the wrong sign; leptogenesis needs \(\sigma=+1\bmod 8\Rightarrow e^{+i\pi/4}\) , a
 \(+4\bmod8\) free bit not fixed by the frozen record) — never written anywhere as derived.

 10. How a reader re-derives the whole result from scratch — the reproduction recipe

 Stripped to a procedure, independent of any saved output, a reader with only the frozen manuscript
text in hand reconstructs SG-10's VERIFIED verdict as follows:

 Confirm the manuscript is the frozen version (line count 15,507; hash match if available).

 Locate the §9.4 boundary ledger (lines 2333–2357) and count rows: confirm 16 total, 9 marked
 Required/Claimed, 7 marked Excluded/"Outside scoped-GUT claim," each excluded row carrying an
 individually distinguishable named reason (not a generic boilerplate reason repeated seven times).
 This reproduces Clause (i) = PASS, 7/7.

 Identify the 11 required-certificate regions by their section/appendix headers and record their
 line ranges (§6 gate cards 1961–2083; Appendices E′, E, D, F, G, H, I, J, K, L as tabulated in
 §3 above). Within each region, scan for any excluded-sector alias term (quantum gravity, dark
 matter, dark energy/Λ, baryogenesis/η_B, strong CP/θ̄, full cosmology, Theory-of-Everything)
 co-occurring with closure-flavored language and not fenced by a disclaimer pattern. Confirm zero
 such co-occurrences across all 11 regions. This reproduces Clause (ii) = PASS, 0/11 violations.

 Combine: Clause (i) \(\wedge\) Clause (ii) \(\Rightarrow\) VERIFIED, exit code 0.

 Run the adversarial non-vacuity check: raw-grep "excluded from scope" over the whole file (44
 hits expected), triage each by whether it falls in a scanned region, and confirm the sole
 in-region hit (line 8882) is fence-tagged, not a bare closure claim.

 Confirm the Gate 11 self-reference boundary: verify the required-gate scan window ends at line
 2083, one line before Gate 11's own card begins at ~2084.

 Run the cross-paper sweep: grep "strong CP.*(solved|closed|resolved)" (or equivalent) across the
 full corpus (2,281 files expected), obtain 28 hits, and manually inspect each to confirm every one
 is either a negated/fenced statement, an anti-resurrection audit row, or a byte-identical
 duplicate copy of the frozen GUT manuscript. Confirm zero genuine live resurrection claims.

 Cross-check the anchor ledger of §8 above by scanning SG-10's own gate card for any numerical
 prediction, \(\sigma\) -value, or direct anchor citation; confirm there is none, and confirm the
 nearby pulls ( \(m_u\) , \(\mathrm{tr}[a_6]\) ) are attributed to SG-8 and Gap-01 respectively, not to
 SG-10.

 Confirm the negative controls of §9 above are unperturbed: no line anywhere asserts \(m_u\) 
 resolved, Λ solved, Gap-02's mass gap closed, or strong CP solved.

 Every step above is finite, decidable, and returns the same PASS/count on any faithful copy of the
frozen manuscript — there is no free parameter, no fitted threshold, and no step that depends on
which physicist runs it. This is what licenses calling the VERIFIED verdict a reproducible
machine record rather than an assertion: an independent party re-running steps 1–9 against the
frozen text obtains the identical 15,507-line count, the identical 16-row ledger, the identical
7/7 and 0/11 clause results, the identical 44/1 non-vacuity triage, the identical 28/0 cross-paper
triage, and therefore the identical VERIFIED, exit-code-0 terminal verdict.

 11. What this evidence base does and does not license

 Consistent with the fixed grade, this evidence base licenses exactly one claim: the two-clause
scope-consistency predicate, executed target-blind against the frozen manuscript, is VERIFIED. It
does not license, and the reproduction recipe above cannot be stretched to produce, any of the
following: that the seven excluded sectors are provably the complete set of all sectors any
observer could ever consider relevant (that is a universal claim over open-ended future physics,
structurally undecidable by a finite lint, and is carried instead as a named axiom,
AXIOM-SCOPE-UNIVERSE, with a standing open invitation — "name one missing relevant non-GUT
sector" — rather than as a proof); that any of the five fenced physics walls (quantum-gravity
UV/ \(a_6\) , the Yang-Mills mass gap, the Lambda residue, baryogenesis/ \(\eta_B\) , strong CP/ \(\bar\theta\) ) has
advanced, closed, or been reinterpreted as solved (each remains exactly at its own owning
campaign's most conservative verified floor, per the conservatism map cross-checked in this
dossier's companion sections); or that the file-identity hash check constitutes a physics
validation of any kind (it is audit-only, confirming which text was tested, never that the text's
claims are true). Within those honest boundaries, the evidence is complete, independently
reproducible, and terminal: 5/5 cross-checks close, 0 open threads remain in the lint's own
execution, and the sole raw alarm the process generated (the 25-hit automated cross-paper
"INCOHERENT" flag) is resolved by transparent manual review rather than hidden or asserted away.

 Open gaps & the specialist closure path

 0. What "open" means for a Layer-2 disclosure gate, stated precisely before the catalogue

 SG-10 sits off the physics ladder by construction: it is the scope-consistency / claim-boundary
gate over the frozen GUT manuscript, not a computation over any operator living on the thirteen-
dimensional arena \(\mathfrak{B}_{\rm active} = [\mathcal{M}_4\times K_6\times S^2\times
S^1_Y/\mathbb{Z}_2]_\times \oplus [\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm
admiss}]_\oplus \otimes [\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm
Higgs}\oplus\mathcal{E}_{\rm proton}]_\otimes\) , \(K_6 = SU(3)/T^2\) , \(D = 4+6+2+1 = 13\) . Pinning the
gate against all three layers of that arena — \(\times\) Stage, \(\oplus\) Rulebook, \(\otimes\) Actors —
is not a formality here; it is the actual content of the "no truncated object" discipline, because
the honest finding for SG-10 is that two of the three deep roots (Shape and Scale) are
legitimately not load-bearing for this gate at all , and stating that correctly (rather than
either forcing a fake geometric derivation or silently skipping the check) is itself part of what
this section has to get right.

 Concretely: the \(\times\) Stage layer supplies SG-10 nothing beyond an inventory — which of Gates
1–10 are required, and which seven non-GUT sectors are declared out of scope. No metric factor, no
Ricci eigenvalue, no Casimir, no heat-kernel coefficient is classified or consumed by SG-10's own
claim. The \(\oplus\) Rulebook layer is where the entire gate actually lives: the scope predicate
 \(C_{\rm SG10}\) is a rulebook object end to end — the sixteen-row boundary ledger (nine required-gate
rows, seven excluded-sector rows, each excluded row carrying a named reason), the two binding
clauses (excluded sectors may not support required gates; required gates may not be relabeled as
exclusions), the inward-falling downgrade convention (a violation penalizes the offending required
gate, never SG-10 itself), and the historical firewall (pre-migration wording is non-supporting
unless explicitly migrated, frozen, certified, and named in the current authority stack). The
 \(\otimes\) Actors layer is the two-clause text-lint operator itself: domain = the frozen
15,507-line manuscript, connection = none (there is no differential-geometric connection here; the
"actor" is a finite-state regex/membership scan), endomorphism/readout = a per-region PASS/FAIL
report over eleven required-certificate regions plus a 7/7 ledger-presence check. Scale is
explicitly not load-bearing: SG-10 consumes no \(M_{\rm Pl}\) , no compactification radius \(R_0 =
1.591549430918954\times10^{-17}\ \mathrm{GeV}^{-1}\) , no volume \(\mathrm{Vol}(X_{\rm active}) =
3.704417261398702\times10^{-148}\ \mathrm{GeV}^{-9}\) , no curvature invariant — those numbers belong
only to the walls SG-10 fences (Gap-01, Gap-02, \(\Lambda\) , BG-10), never to SG-10's own predicate.
Granularity is trivially satisfied: the object under test is a finite string, the scan terminates,
and the only "granularity" content is the discipline that every excluded row must carry a named
reason (no unpaid exact labels).

 Given that framing, an "open gap" in SG-10 can only be one of two things: (i) a residual that
reduces to a named, value-free scope or labeling axiom , permanently open by the shape of the
claim it makes (a universal statement, an unfalsifiable aside, a standing cross-check discipline);
or (ii) a mechanical run that either has or has not actually been executed , where the fix is not
a derivation but an act of target-blind execution against the fixed text. Every specialist
"attacking" this section is not hunting for missing geometry — there is none to find here by
design — but for dishonesty or incompleteness in a claim boundary : an unnamed eighth sector, a
required result quietly leaning on an excluded one, a required result quietly re-filed as excluded,
or a lint that is specified but never actually run. The credit-ladder roll-up for this gate already
stands at 8/8 residuals terminal (1 DERIVED-GIVEN-text, 4 REDUCED-TO-AXIOM, 3
DISCLOSED-CONSISTENT), so nothing catalogued below blocks the fixed terminal
 DERIVED-GIVEN-anchor / RESOLVED +0 . What follows is nonetheless a full working inventory of
every open object, written so a future specialist can pick up any one of them without having to
reconstruct the boundary logic from scratch.

 1. R1 — Completeness of the seven-sector exclusion list (permanently open, by construction — the deepest residual in this gate)

 (a) The precise open object. The §9.4 boundary ledger, at manuscript lines 2333–2357, names
seven excluded sectors, each with an individually stated reason: (1) quantum-gravity UV completion —
"no nonperturbative gravity certificate"; (2) full cosmology (inflation, reheating, CMB, structure
formation); (3) dark matter, with candidate modes explicitly routed Diagnostic-only; (4) dark
energy/ \(\Lambda\) , with the Paper-IV one-loop negative flagged as adding no closure; (5)
baryogenesis/ \(\eta_B\) , owned by the BG-10 campaign; (6) strong CP/ \(\bar\theta\) , observation-blocked;
(7) a catch-all Theory-of-Everything (all-sector) exclusion. The open claim under test is that this
seven-row list is complete — that no eighth, currently-unnamed non-GUT sector is silently
touched by the manuscript's claims without being disclosed here.

 (b) Why it is hard, and the specific trap. Read at face value, "this list is complete" is a
 universal statement over the space of all conceivable physics — not a finite enumerable set but
every sector a critic could name tomorrow, in five years, or in a subfield that does not yet exist.
This is exactly the shape of object this research program elsewhere labels a "unicorn": a demand
for unbounded, infinite-precision coverage that no finite check can discharge, structurally
identical to demanding a proof that no undiscovered eighth force exists. The trap for a specialist
here is twofold and symmetric. First, attempting to prove the universal by exhaustive case-work
over "all of physics" is a project that cannot terminate — any dossier claiming to have completed it
would be committing a false-flooring failure (claiming a floor of zero residual risk where none is
achievable). Second, and just as damaging, is the opposite error: refusing to make any 
completeness statement at all, on the grounds that the universal cannot be proven, and thereby
leaving the boundary ledger with no stated confidence whatsoever — that would be an under-claim
that throws away real, checkable content. The correct move, already taken and already reflected in
the fixed grade, is to substitute the impossible universal with a finite, falsifiable, target-
blind claim relative to a declared universe : completeness relative to the named seven-sector
list , checked by direct inspection against the manuscript text, never completeness over all
conceivable physics . Getting that substitution phrased correctly — an honest ceiling, not a
theorem and not a shrug — is the entire technical content of R1.

 A second, narrower trap sits inside the same residual and is worth flagging explicitly because it
is the one most likely to actually trip a future reviewer: confusing a required-gate residual 
with an exclusion-list candidate . The neutrino absolute mass scale / right-handed mass \(M_R\) 
(owned by SG-8) is hard and currently unresolved, but it is not a §9.4 row, and correctly so — it
is part of a gate the manuscript still claims to be actively closing, not a sector the manuscript
disclaims touching. The binding rule (clause ii) forbids relocating a hard required-gate residual
into the exclusion list merely because it resists closure. Any future edit that quietly moved \(M_R\) ,
or any other struggling required-gate residual, into §9.4 would be the precise failure mode SG-10
exists to catch, not a legitimate narrowing of scope — and would itself falsify R1's sibling clause
(ii), not strengthen R1.

 (c) What closes it, target-blind — and what a refuting result looks like. R1 cannot be upgraded
from AXIOM-SCOPE-UNIVERSE to a proven theorem; that upgrade path is definitionally unavailable,
because the object being claimed is a universal quantifier over an open-ended set. What can 
strengthen R1, without ever crossing into false completeness, is the standing mechanism already
built into its own construction: publish the finite sector-by-sector completeness witness (the
per-wall conservatism map, section 4 below, together with the enumeration protocol in (d)) and
carry an explicit, permanent, open invitation — name one currently unlisted, relevant non-GUT
sector that this framework silently relies on. A genuine refutation of R1 would look like exactly
that: a critic naming a concrete eighth sector — for instance, a well-posed physics question such as
the neutron-lifetime anomaly, primordial black hole abundance, or some other established open
problem not on the seven-row list and not a specialization of one of the seven — cited to a specific
manuscript line or appendix where a required gate actually relies on it without disclosure. Such a
finding would falsify R1 immediately, and — via the same inward-falling downgrade mechanism used
everywhere else in this gate — the penalty would land on whichever required-gate certificate
improperly leaned on the undisclosed sector, never on SG-10's own terminal. Conversely, the success
criterion for R1 remaining closed at its current terminal is simply that no such named sector
survives continued adversarial reading — the same standard any open, honestly-stated scientific
claim is held to, made explicit rather than left implicit.

 (d) Machinery to start from. There is no calculation to perform here; the starting point is an
 enumeration protocol , mechanical and reviewable without any new mathematics. For any candidate
sector a critic proposes, apply a three-way test in order: (i) is it already a named row, verbatim
or under a stated synonym; (ii) if not verbatim, is it a specialization already subsumed by a named
row — three such subsumptions are already defensible on inspection (gravitational-wave/inflationary
tensor modes fall under "full cosmology"; a hypothetical dark-sector flavor structure falls under
"dark matter"; matter–antimatter CP phenomena beyond \(\eta_B\) itself fall under "baryogenesis"); (iii)
if the candidate clears neither (i) nor (ii), does any required-gate certificate in the manuscript
actually rely on it for closure. Only a "yes" on (iii) combined with "no" on both (i) and (ii)
constitutes a genuine counterexample; anything else is a non-event. This protocol is exactly the
kind of finite, terminating, structure-derived check the rest of the lint machinery (R3 below) is
built from, and a future specialist needs nothing beyond careful reading to run it.

 (e) Leverage. R1 is the axiom the entire disclosure architecture is ultimately checked against,
so every survived adversarial naming attempt strengthens confidence in the whole gate without ever
changing its terminal, which is already fixed at AXIOM-CLOSED for this residual. R1 has essentially
no downstream leverage of its own — nothing else in the corpus is unblocked by R1 moving, because
the dependency runs the other direction: R1's own continued standing depends on the other nine
required gates continuing to report their pass/fail status honestly, not the reverse. Its practical
value to a future specialist is as a standing falsifier with a stated bounty : the single cleanest
way to attack SG-10 as a whole is to try to name sector number eight.

 2. R3 — The scope-consistency lint itself (the residual that was genuinely open, now discharged by an actual run)

 (a) The precise open object, as it stood before this completion run. The manuscript's load-
bearing mechanism for this entire gate is a claim that scope violations are caught by a mechanical,
scriptable, target-blind, two-clause text lint — not by authorial restraint or editorial promise.
Clause (i): every excluded sector named in §9.4 must appear explicitly, marked "Excluded from
scope," with a named reason. Clause (ii): no required-gate certificate (the §6 gate cards for Gates
1–10, plus Appendices D through L) may cite an excluded sector for closure, or carry the status
"Excluded from scope" on a required-gate row itself. Prior to this campaign (dossier prose dated
2026-06-24), this lint was recorded at AUDIT / R3-open — the two-clause procedure was fully
 specified , with an explicit implementation description (a CLOSURE_CTX regex — matching
close/support/certif/pass/derive/prove/establish/because/relies-on/used-to — AND-gated against a
FENCE_CTX regex — matching diagnostic-only/not-used/does-not-claim/"(excluded from scope"/outside/
cross-reference), so that a mention only flags as a violation if it co-occurs with closure language
and is not already inside a disclaimer — but had never actually been executed against the live,
frozen manuscript.

 (b) Why an unrun lint is a real, non-trivial gap and not a formality. It is easy to under-weight
this distinction, so it is worth stating plainly: a specification that a check would pass, if run,
carries essentially no more evidential weight than a well-argued prose disclaimer — it is a promise
of a result, not the result itself. The specific trap named directly in the community-gap analysis
for this gate, and repeated here because it is the central methodological point of R3, is treating
"we designed a rigorous target-blind check" as equivalent to "we ran the rigorous check on the live
text and it returned a verdict." Those are two different epistemic states. Conflating them is
precisely the "referenced, not re-run" failure mode this research program's own honesty discipline
exists to catch rather than to launder — it is the same class of false-openness/false-closure risk
flagged elsewhere in this program under the BS-10 designation: a claimed-but-unexecuted check
produces no finite, correct-object record, and calling it closed before it is actually run would be
green-washing, not certification.

 (c) What closed it, target-blind, with the exact reproducible result and the refutation
criterion. This campaign (2026-07-02/03) closed R3 by reconstructing and actually running the
two-clause lint, target-blind, against the frozen, re-hashed 15,507-line manuscript:

 Clause (i): PASS, 7/7. All seven declared excluded sectors are ledger-present at lines
 2333–2357, each individually marked "Excluded from scope" with a named reason (Section 1 above
 restates the seven).

 Clause (ii): PASS, 0 violations across 11 CLEAN required-certificate regions. The eleven
 scanned regions, with exact line ranges, were: the §6 gate cards for Gates 1–10 (1961–2083);
 Appendix E \('\) , Gate 5 anomaly (2897–2972); Appendix E, Gate 4 chirality (2973–3108); Appendix D,
 Standard-Model recovery (7965–8139); Appendix F, stabilization (8140–8404); Appendix G, threshold
 unification (8405–8766); Appendix H, Higgs protection (8767–9055); Appendix I, flavor chamber F+
 (9056–9301); Appendix J, quark certificate (9302–9553); Appendix K, lepton/neutrino certificate
 (9554–9753); Appendix L, proton safety (9754–10200). Every one of the eleven returned CLEAN.

 Overall verdict: VERIFIED, exit code 0. 

 The refutation criterion for this specific run is concrete and was actively tested for, not merely
assumed absent, via a dedicated adversarial non-vacuous-PASS check : an independent raw grep for
every literal occurrence of the string "excluded from scope" anywhere in the whole manuscript
returned 44 hits , each individually triaged into exactly one of three buckets — (i) outside every
scanned required region entirely (before line 1961 or after line 10201); (ii) inside the §9.4 ledger
itself, i.e. clause (i)'s own object, not a violation candidate; or (iii) the single remaining case,
at line 8882, inside Appendix H , reading "A solution to the cosmological constant or vacuum-
energy problem (excluded from scope, Section 9)" — correctly identified as a "this appendix does
NOT claim" list item, caught cleanly by the lint's own fence pattern \(excluded from scope , and
independently confirmed to trip both the EXCLUDED_FROM_SCOPE=True flag and the FENCE_CTX check
simultaneously. This is the detail that makes the PASS credible rather than an artifact of a region
simply never being examined: the one genuine in-region candidate that existed was correctly
triaged as a disclaimer, not silently missed. Had line 8882 instead read something like "Appendix
H's Higgs-mass protection argument additionally relies on a resolution of the cosmological constant
(excluded from scope, Section 9) to bound the top-loop correction," clause (ii) would have failed at
that exact line, and the correct consequence — by the inward-falling downgrade rule — would have
been a downgrade of Gate 6 (Higgs protection) to Open / not claimed , never a downgrade of SG-10
itself.

 Two accompanying checks close out R3's credibility. A file-identity cross-check : the live
manuscript was re-hashed and reconfirmed at 15,507 lines matching the frozen corpus, not a stale
copy. A self-reference trap check : Gate 11's own card, which begins at approximately line 2084
(immediately after the §6 scan window closes at line 2083), is correctly excluded from the
required-gate scan — it is the boundary gate itself, not a required-closure gate, and including it
would risk a smuggled self-exemption; the scan window's boundary at exactly line 2083 handles this
correctly. And a certificate-folder substitution , ruled legitimate: the expected certificate directory
for this boundary gate does not exist anywhere in the working tree (confirmed by an
exhaustive directory search), matching its own prior "folder absent" status; the check was instead
executed by an independent standalone script performing the identical target-blind test directly
against the frozen manuscript — a faithful instantiation of the specified check, not a fabricated
substitute, since the governing specification names the check , not a particular file path.

 (d) Machinery to start from for any future re-run (e.g. after a manuscript edit). The lint is a
finite two-pass text scan, with no open-ended search anywhere in it — which is exactly why it
belongs to the Granularity leg of the deep-root audit (trivially satisfied) rather than to any
physics root. Pass one: a fixed-string / regex membership test of the seven canonical sector names,
plus their defensible subsumed synonyms from the section-1(d) protocol, against the §9.4 table
region, expecting 7/7. Pass two: for each of the eleven required-certificate line ranges above, scan
for the fence-pattern co-occurrence test — a CLOSURE_CTX hit (close/support/certif/pass/derive/
prove/establish/because/relies-on/used-to) that is not simultaneously inside a FENCE_CTX hit
(diagnostic-only/not-used/does-not-claim/ \(excluded from scope /outside/cross-reference) — with
every raw hit from a supplementary whole-manuscript "excluded from scope" grep individually
triaged by the three-way bucket test from (c). This is deterministic, terminating, and fully
reproducible by anyone with the frozen text and no additional physics.

 (e) Leverage. R3 is the single highest-leverage residual catalogued in this entire section,
because discharging it is what converts the whole disclosure mechanism from asserted to
 evidenced — it is the event that licensed moving the gate's own terminal from an amber
AUDIT/referenced-not-run standing to the current DISCLOSED-VERIFIED / RESOLVED +0. Nothing in the
physics program depends on R3 (SG-10 sits off the physics ladder entirely), but every other
non-permanent residual in this section is now machine-proven rather than merely argued , because
clause (ii)'s clean eleven-region support-set report is the direct, shared evidentiary basis for
R2's "no diagnostic-mode leaked into a required certificate" claim and for R5's "no silent
narrowing went undeclared" claim (Section 5 of the Layer-2 nonseparability screen: this is one
shared object, counted once, not triple-counted across R2/R3/R5). R3 closing is therefore the
load-bearing event this whole section reports; R2 and R5 are, in a precise sense, corollaries of R3
having actually been executed rather than independent achievements.

 3. R2 — The three fenced leak paths (diagnostic-only modes, the \(\Lambda\) downstream pointer, the §11 QC-bridge coda)

 (a) The precise open object. Three specific locations in the manuscript are structurally at
risk of leaking an excluded sector into a required-gate claim, and each is guarded by an explicit
status label rather than by authorial care alone: (i) any Appendix I/K flavor-chamber \(F^+\) mode, or
any Appendix F backbone-moduli mode, that could plausibly resemble a dark-sector candidate is routed
to a Diagnostic-only status and recorded in §9.4 as never usable for gate support; (ii) a
downstream pointer to the Paper-IV computed one-loop cosmological-constant negative states verbatim
that it "adds no closure claim here and does not alter this section's exclusion"; (iii) the §11
QC-bridge engineering coda is fenced by the scope lint as external/engineering, with the explicit
record "zero GUT gate statuses changed; zero promotions," backed by a data-use firewall (the
freeze-before-compare barrier inside \(\mathcal{C}_{\rm admiss}\) ) preventing any post-hoc comparison
from leaking back into a gate status.

 (b) Why this needs a check distinct from R1 and R3. R1 asks whether the exclusion list is
complete; R3 asks whether the lint itself runs clean end to end. R2 asks a narrower, structurally
different question: are there specific, named places where a sector adjacent to an exclusion — a
candidate object that resembles a dark-matter or dark-energy candidate without ever being formally
claimed as one — could be mistaken for, or silently converted into, required-gate support. This is
the subtlest failure mode catalogued in this gate, because it requires no explicit sentence claiming
closure at all; it only requires a diagnostic-only object being used downstream as though it were
certified, without anyone updating its status label at the point of use.

 (c) What closes it, and the exact refutation criterion. R2 is now AXIOM-CLOSED as
AXIOM-NO-DIAGNOSTIC-SUPPORT, and critically, this is no longer a separate hand-argued claim — it is
 machine-proven directly by R3's clause (ii) clean support-set report . If any Appendix I/K/F
diagnostic-only mode, the \(\Lambda\) downstream pointer, or the §11 coda had in fact been cited as
support inside any of the eleven scanned required-certificate regions, clause (ii) would have
registered a violation at that exact line, and it did not. The refutation criterion is therefore
mechanically identical to R3's own: a future specialist would falsify R2 by finding a line inside
one of the eleven required-certificate regions where a diagnostic-only mode, the \(\Lambda\) pointer,
or the QC-bridge coda is cited to support a Gates-1–10 closure claim with no accompanying fence
phrase. None was found in the target-blind re-run.

 (d) Machinery. Identical scanning machinery to R3's clause-(ii) sweep, plus one targeted
secondary check specific to R2: an explicit search confirming each of the three known fence phrases
("Diagnostic only," the Paper-IV downstream-pointer sentence, and the §11 "zero promotions"
statement) appears at its claimed location and actually governs the object it purports to govern —
not merely that the phrase exists somewhere in the document.

 (e) Leverage. R2's closure, riding entirely on R3, retires the specific concern that a dark-
sector-adjacent chamber mode or the \(\Lambda\) one-loop negative could quietly migrate from
"interesting but explicitly unclaimed" into "cited as support" without a visible manuscript edit
ever occurring. This has direct leverage on keeping Gap-01's dark-matter-adjacent chamber modes, the
 \(\Lambda\) /BG-10 boundary, and the §11 engineering coda all honestly non-load-bearing for the physics
gates — which is, in turn, exactly what keeps the per-wall conservatism map in Section 4 below
trustworthy rather than aspirational.

 4. R4 — The per-wall conservatism map (the one place a real physical invariant enters this gate, and the one place "quiet scope creep" could hide)

 (a) The precise open object. SG-10 computes no physical wall's status itself; it only restates 
each fenced wall at its owning campaign's most conservative, independently verified floor, and
checks that the restated disposition has not silently drifted toward "more closed" than its owner
has actually shown. This is the mirror image of the usual target-loading failure this research
program screens for everywhere else: instead of "did we tune a derivation to hit a desired number,"
R4 asks "did we, merely by the act of summarizing an external wall in this gate's own prose,
accidentally describe it as more resolved than its owner has certified." Five walls are checked here,
and every one is stated below at its true, campaign-owned conservative floor with the exact geometric
content it actually rests on, so a future reader can verify no upgrade has been smuggled in.

 Gap-01 — quantum-gravity UV completion, the \(a_6\) heat-kernel coefficient. Conservative
 disposition: precisely-open at field grade. The bulk coefficient \(\mathrm{tr}[a_6] =
 -2.817995812\times10^{94}\ \mathrm{GeV}^6\) is independently reproduced and carried only as a
 labeled consistency coefficient — one term in the unbounded \(a_8/a_{10}/\ldots\) Seeley–DeWitt tower,
 never a UV-completion or mass-gap proof (this is the "MO-12 binding" named explicitly in the gate's
 own governing material). The certified lower rungs of the \(K_6\) scalar heat-kernel ladder are
 \(a_2/a_0 = 5/12\) and \(a_4/a_0 = 11/120\) [Killing-norm]; \(K_6\) scalar \(a_6/a_0\) itself is OWED on
 the Gilkey constants. On the graviton side, two independent routes have been attempted and do not
 yet agree: Route A (Lichnerowicz \(E_L\) spectrum on the transverse-traceless \(\mathrm{Sym}^2_0\) 
 bundle, dimension 20) consumes the certified spectrum \(\{1/6\ (\times6),\ 5/12\ (\times6),\ 7/6\
 (\times6),\ 17/12\ (\times2)\}\) with traces \(\mathrm{tr}\,E_L = 40/3\) and \(\mathrm{tr}\,E_L^2 =
 241/18\) , but is blocked on the owed Gelfand–Tsetlin off-diagonal hopping term connecting the
 five Weyl-inequivalent \(T^2\) weight classes — an exact SU(3) ladder-operator matrix element,
 computable in principle from the standard formula (a square root of a product of pattern-entry
 differences) but not yet enumerated in the atlas; this is a direct consequence of \(K_6\) being
 homogeneous but not locally symmetric ( \(\|\nabla\mathrm{Riem}\|^2 = 1/4 \ne 0\) [Killing-norm],
 which is exactly why the graviton leg carries a nontrivial ladder term at all rather than vanishing
 as it would on a symmetric space). Route B (ghost-plus-vector reconstruction) consumes the
 certified vector endomorphism \(E = \mathrm{Ric} = \tfrac{5}{12}\mathrm{Id}\) and a scalar backbone
 \(a_6/a_2^3 = 7936/39375\) , banked across three or more independent computational engines, but its
 own graviton leg is likewise OWED. The \(\mathbb{Z}_2\) orbifold-defect \(a_6\) (the order-6 mixed
 Neumann \(\oplus\) Dirichlet boundary coefficient at the two fixed points \(\theta=0,\pi\) ) is separately
 uncomputed and absent from the literature , with the certified boundary tower currently stopping
 at \(a_5\) . Consequently the total (bulk \(+\) defect) is never emitted and must never be implied to
 exist. The specific trap R4 screens for: letting the bulk number's 16-significant-figure precision
 (genuinely reproduced independently) read as though it closes anything about UV completeness. It
 does not — the §9.3.1 exclusion stands unmodified, and the deflation check is a clean PASS.

 Gap-02 — Yang–Mills mass gap (observation-locked-real). Conservative disposition:
 precisely-open [X] , co-gated by the continuum-kernel-positivity residual. The Clay problem
 here reduces to whether the recorded robust \(\sim66\sigma\) negative — computed via \(D = s_{\rm
 block} - \log(E_{\rm conn}\cdot A_{\rm fluc}\cdot N_{\rm cert})\) — actually tests the boxed Clay
 target. It does not: it tests the Kotecký–Preiss worst-case upper bound \(z_\ast \le N_{\rm
 cert}\cdot\max_\gamma w(\gamma)\) , which is a proxy , not the boxed target \(z_\ast:=
 \sum_{\gamma\neq0} w(\gamma)\) itself. The boxed target is convention-underdetermined: the per-site
 reading gives \(z_\ast = 0.109\) and the single-activity reading gives \(z_\ast = 0.353\) , both passing
 against the \(<0.998\) criterion, while the per-distinct-letter reading fails and is
 binning-divergent. The specific trap here — explicitly declined in this campaign — would be
 picking the convention that passes and reporting only that one; instead, the target-specification
 defect itself is treated as strengthening the honest open standing, not as something to paper
 over with a favorable binning choice. Deflation check: PASS — this wall reads precisely-open,
 never "floored" or "PASS," anywhere SG-10 touches it.

 Dark energy / \(\Lambda\) (Weinberg-irreducible). Conservative disposition: Weinberg-open /
 measured-but-irreducible. Paper IV's computed one-loop certificate is an honest negative: an
 exact-weight graded supertrace shows no structural cancellation at any coefficient order, and the
 chamber-cancellation route is theorem-refuted because the \(\Lambda\) operator is grading-even and
 label-blind. The subtlety this campaign states explicitly, because it is the cleanest
 audit-the-implicit-assumption case in the whole gate: the historical "113-orders-of-magnitude
 catastrophe" rests on an absolute vacuum-energy premise that is in fact unmeasured — every
 zero-point-energy effect ever measured (Casimir-type effects included) probes only differences in
 vacuum energy, never an absolute value — so the catastrophe-half of the cosmological-constant
 problem dissolves once that unmeasured absolute-energy premise is dropped; it was a fake wall
 built on a premise nobody has ever measured. What does not dissolve, and remains a live,
 Weinberg-irreducible residue, is the observed small residue: the measured \((2.3\ \mathrm{meV})^4\) 
 vacuum-energy density. The trap R4 screens against: letting the dissolved catastrophe-half read as
 progress on the surviving measured residue. It must not, and the deflation check records this
 explicitly as "exclusion reinforced by a negative," never as progress toward solving \(\Lambda\) .

 BG-10 — baryogenesis / \(\eta_B\) (observation-locked-real, measured \(\eta_B \approx
 6.1\times10^{-10}\) ). Conservative disposition: 0 of 4 rules closed at certificate grade. Rule
 A is AXIOM-CLOSED as a genuine reduction — the continuum CP phase collapses to a single mod-8
 spin-c/Pin \(^-\) bit (named BG10-Axiom-SpinC-QP) — but the geometry's own default topological index
 \(\chi(K_6,E) = -3\) gives \(\sigma \equiv 5 \bmod 8\) , which via the certified Gauss sums
 \(G(1,8)=4e^{+i\pi/4}\) , \(G(3,8)=4e^{+i3\pi/4}\) , \(G(5,8)=4e^{-i3\pi/4}\) , \(G(7,8)=4e^{-i\pi/4}\) 
 (all with \(|G|=4=\sqrt8\sqrt2\) ) yields a Gauss-sum phase of \(e^{-i3\pi/4}\) — the wrong sign for
 leptogenesis, which requires \(\sigma \equiv +1 \bmod 8 \Rightarrow e^{+i\pi/4}\) . The required
 \(5\to1\) flip is a \(+4\bmod8\) free Pin \(^-\) bit not fixed by the frozen record , so this is a
 structure-first datum that departs from the phenomenological target rather than a fit to it — it
 is explicitly not a BG-10 closure, only an honest axiom reduction of Rule A. Rule B is
 RELABEL_FAIL: the candidate normalization requiring \(\lambda = 1\) is identically the value that
 places \(I_{\rm BG} = \lambda\kappa^3/\pi\) inside the observed \(\eta_B\) window only by already
 knowing the target — killed outright as target-loading. Rule C is BLOCKED_INPUTS: an
 \(S_3\) -permutation-commutant argument on \(\mathbb{C}^3\) has at most two distinct eigenvalues, but the
 frozen neutrino-sector operator \(O_\nu\) has three distinct eigenvalues and does not commute with
 \(S_3\) , and the right-handed mass scale \(M_R\) has no known construction recipe (the manifest entry
 \(D_N = \mathrm{diag}(1,0,0)\) is by-construction, not derived). A cautionary four-fix manifest exists,
 \(\eta_B = 6.05\times10^{-10}\) , landing in-window, but is flagged explicitly as true by
 construction — its keystone parameter was reverse-engineered to hit the target — and is carried
 as this program's own canonical worked cautionary example of target-loading, never as a result. The
 companion chamber Boltzmann factor \(\kappa = e^{-\pi\sqrt3} = 0.004333420509983131\) gives a
 candidate \(M_R = \kappa\cdot M_U\) that sits roughly \(231\times\) off the corpus's own \(\kappa^0\) 
 baseline — a candidate-in-tension, not a result. The trap R4 screens against here is precisely the
 one the cautionary manifest itself illustrates: letting "Rule A reduced to an axiom" be misread as
 "BG-10 advanced." It must not be, and the deflation check is a clean PASS at 0/4.

 Strong CP / \(\bar\theta\) (observation-blocked). Conservative disposition: excluded /
 observation-blocked. No \(\bar\theta\) -alignment certificate exists anywhere in the corpus, and no
 statement about \(\bar\theta\) supports any closure claim. The operative falsifier is a future nEDM
 measurement, apparatus-side and external to this framework. Deflation check: PASS, reinforced both
 by the §9.4a historical firewall and by R6's cross-paper coherence sweep (Section 6 below).

 (b) Why this is hard, and it is a discipline problem, not a computation. Each of these five
walls is owned by a different campaign inside the same broader corpus, each with its own partial
successes — the reproduced bulk \(a_6\) number, Rule A's genuine mod-8 reduction, the \(\Lambda\) 
catastrophe-half dissolution — and each carries a real temptation to describe those partial
successes, quoted out of their fenced context, in language that sounds like more progress than was
actually certified. The named failure pattern is "quiet scope creep": stating a wall as
more-closed-than-its-owner-has-verified, the mirror image of BG-10's own target-loading trap but
applied to prose rather than to a derivation.

 (c) What closes it, target-blind, and what a refuting result looks like. There is no single
closing action for R4 taken as a whole — it is a standing, per-wall discipline. The "closer," each
time, is structural: whenever one of the five owning campaigns changes a wall's disposition
(bounds Gap-01 further, produces a positivity proof or disproof for Gap-02, produces a new \(\Lambda\) 
result, advances a BG-10 rule, or a nEDM measurement lands), this map is the place that must be
updated to match — and SG-10 itself never leads that update, it only mirrors it (the
downgrade-asymmetry structural rule again: penalties and upgrades alike flow from the owning
campaign inward to this map, never the reverse). A refutation of R4 would look like a future
statement describing one of these five walls in more-closed language than its owning campaign's own
verified status supports — for example, calling Rule A's mod-8 reduction "BG-10 closed," calling
the \(\Lambda\) catastrophe-half dissolution " \(\Lambda\) solved," or calling the Gap-02 per-site
 \(z_\ast\) convention pass "the mass gap proven." Any of those would be a genuine SG-10-relevant
failure of this gate's own disclosure discipline, distinct from and independent of whatever the
underlying physics campaign has actually shown.

 (d) Machinery. No new mathematics — the machinery is a cross-reference discipline : every
wall-status sentence anywhere near the boundary material is checked word for word against its
owning campaign's own most conservative stated floor, with any phrase that could be read as
closing-language flagged and rewritten to match that floor exactly. This is why the wording above is
deliberately qualified rather than terse — "precisely-open at field grade," "co-gated by," "true by
construction," "wrong sign for leptogenesis" — each qualifier is load-bearing, not decorative.

 (e) Leverage. R4 has zero leverage on any of the five underlying physics walls themselves — none
of them move because of anything SG-10 does. Its leverage is entirely on the credibility of the
disclosure gate : a single failure here would not merely reopen one wall's status, it would call
into question every other conservatism statement anywhere in this corpus, by demonstrating that
stated floors cannot be trusted to track owning campaigns' actual verified results. Keeping R4 clean
is disproportionately valuable relative to its own zero physics content.

 5. R5 — Does the binding rule fence all scope-narrowing, or only outright wholesale relocation?

 (a) The precise open object. The two binding clauses as originally framed govern (i) excluded
sectors being leaned on for required-gate support, and (ii) required gates being moved wholesale
into the exclusion list. A narrower, subtler failure mode sits between these two: a required gate's
 target itself being quietly narrowed — redefined to a smaller claim than originally scoped —
without a visible, dated, binding declaration of the narrowing at the point it happens. The open
question is whether the existing binding-rule language, as originally stated, actually fences this
narrower failure mode, or only the cruder wholesale-relocation failure that clause (ii) mechanically
scans for.

 (b) Why this is a genuine, non-obvious residual. Wholesale relocation is easy to catch
mechanically — it is exactly what clause (ii) is built to find. Silent narrowing is harder to catch
precisely because it produces no §9.4 row and no "Excluded from scope" status tag anywhere: by
construction a narrowed target still reports as "claimed," merely a smaller claim than before, with
no textual marker distinguishing "this gate was always scoped this narrowly" from "this gate's scope
was quietly reduced from something larger." A literal reading of the original two clauses, both keyed
to the explicit exclusion-list mechanism, could miss this failure mode entirely, since neither clause
is keyed to target language inside a gate that still reports as claimed.

 (c) What closes it, target-blind, and the refutation criterion. Direct inspection in this
campaign found three live instances of target-narrowing already present in the corpus , and —
critically — each is individually card-declared and remainder-labeled rather than silent: SG-6's
downstream-moduli narrowing (declared at manuscript locations F.9.4/F.10.1), SG-8's ratios-only
narrowing (declared at I.0a.2), and SG-9's operator-class narrowing (declared at L.2a/L.4). Because
every actually-occurring narrowing carries its own explicit card declaration and an explicit
statement of what remains un-closed (the "remainder"), the existing binding rule together with the
inward-downgrade convention were found to jointly fence silent narrowing already — every live
instance found is visible, not hidden. This licenses a genuine strengthening of R5's own statement:
the binding rule, originally read narrowly as "do not relocate a whole sector," is widened, on this
evidence, to "do not silently narrow a target," and R5 is closed at AXIOM-NO-SILENT-NARROWING. The
refutation criterion for a future specialist: find a fourth instance — anywhere in the corpus — of a
required gate's target having been reduced from its originally-scoped claim without an
accompanying card declaration and remainder label at the point of reduction. Any such
undocumented narrowing would falsify R5, and would fall, by the same inward-downgrade logic used
throughout this gate, on the offending gate's own status, never on SG-10.

 (d) Machinery. A targeted textual audit: for each of Gates 1–10, compare the gate's currently
claimed target against any earlier or broader statement of that same gate's intended scope elsewhere
in the corpus, flagging any discrepancy not accompanied by an explicit, dated, in-place declaration.
This is the same "read the manuscript against itself" discipline used throughout SG-10, applied here
to target language rather than to sector names.

 (e) Leverage. R5 is a genuine strengthening rather than a mere confirmation — it widens what the
binding rule is understood to cover. Its leverage lands on the overall trustworthiness of SG-6,
SG-8, and SG-9's own stated scopes: because R5 confirms their narrowings are each disclosed rather
than silent, those three gates' own honesty postures are independently corroborated as a side effect
of this check, without SG-10 itself certifying anything about their underlying physics content.

 6. R6 — Cross-paper boundary coherence: did "strong CP solved" resurface anywhere in the wider ~2,281-file corpus?

 (a) The precise open object. The frozen GUT manuscript itself correctly excludes strong CP
(§9.3.6, observation-blocked). The open question is whether an earlier or sibling document elsewhere
in the wider corpus (roughly 2,281 files) contradicts this — specifically, whether any surviving,
live-referenced material still asserts that strong CP is "solved," "closed," or "resolved" in the
sense of an actual \(\bar\theta\) -alignment result, which would leave the corpus internally
incoherent: one document claiming closure while the frozen manuscript claims exclusion.

 (b) Why this is hard, and exactly where the trap sits. A raw keyword search for "strong CP …
solved/closed/resolved" is a blunt instrument — it cannot on its own distinguish a genuine
resurrected claim from a sentence that mentions the phrase precisely in order to deny it, fence it,
or record its historical status as excluded. The trap is exactly this false-positive risk: a
first-pass shallow automated negation classifier applied to this corpus's 28 raw hits flagged 25 of
28 as "LIVE," producing a raw verdict of INCOHERENT — resurrection found . Taken at face value
that would be a serious finding. The specific error a specialist must avoid is treating that raw
automated verdict as final without manual line-by-line adjudication — negation detection over
natural-language physics prose is demonstrably not reliable enough, on its own, to settle a
coherence question this consequential, and this campaign transparently reports the raw 25/28 flag
rather than hiding it.

 (c) What closed it, target-blind, and the refutation criterion. Manual, line-by-line review of
all 25 flagged hits in this campaign found every one fenced or negated on inspection, falling
into recognizable patterns: (i) a table's "excluded claim" right-hand column stating explicitly what
is not proven — "That quantum gravity, cosmology, dark matter, or strong CP is solved"; (ii)
phrasing of the exact form "Strong CP status resolved ( Excluded , A3.18)" — resolved as
excluded , i.e. resolved to a disclosed non-claim, never resolved as solved; (iii) audit rows
literally titled "Strong-CP cannot be misread as solved … PASS," including a grep self-check with
the stated expectation "No strong-CP solved-claim → Expected: zero"; (iv) explicit language in the
Quantum-sector manuscript denying that the framework asserts "strong CP is solved because the
geometry is elegant"; and (v) a set of apparent "duplicate" hits inside a separate spectral-closure sub-corpus location
confirmed to be byte-identical snapshot
copies of the same frozen manuscript (diff empty) — not a divergent sibling document carrying
independent risk. The corrected, manually-adjudicated verdict is COHERENT — no resurrection
found , overriding the raw automated INCOHERENT flag as a false-positive artifact of a too-narrow
negation window; an independent referee re-read a sample of the flagged hits against primary source
lines and confirmed the override is justified by the actual text, not a rationalization. The
refutation criterion for a future re-run: find one hit, among any future corpus additions, that is a
genuine unfenced assertion of a strong-CP resolution — not a table's negated cell, not an audit's own
self-check title, not a byte-identical duplicate — actually claiming an alignment or a solved
 \(\bar\theta\) . That would reopen R6 and would need to be reconciled against both the manuscript's own
§9.3.6 exclusion and the historical firewall discussed in Section 7 below.

 (d) Machinery. Automated keyword/negation scanning is a legitimate first pass, but for a claim
this load-bearing it must always be followed by manual, line-by-line adjudication of every flagged
hit against its immediate surrounding context — the discipline this campaign applied, and which any
future re-run over an expanded corpus must replicate rather than shortcut. This is worth generalizing
explicitly as a machinery note for a specialist: any raw negation-classifier verdict over natural-
language physics prose should be treated as a lead requiring manual confirmation, never as a
terminal result in itself, in this or any other cross-corpus coherence check.

 (e) Leverage. R6's closure at COHERENT retires the single conditional row in the entire residual
table and confirms that the historical firewall (Section 7 below) is actually holding in practice
across thousands of files, not merely stated as a rule on paper. Its leverage is entirely on
cross-document trust within the corpus; it certifies nothing new about strong CP itself, which
remains exactly as open — observation-blocked, awaiting a future nEDM measurement — as §9.3.6 has
always stated.

 7. R7 and R8 — the two lowest-leverage, already-fenced remarks (catalogued for completeness)

 R7 — the §9.6 "why these four values" remark. The open object is a philosophical aside inside
the manuscript addressing why the framework is anchored on exactly four measured inputs —
 \(M_{\rm Pl} = 1.220900000000000\times10^{19}\ \mathrm{GeV}\) , \(\alpha_i(M_Z)\) at \(M_Z = 91.1876\
\mathrm{GeV}\) , \(y_t\) , and \(|V_{us}|\) — rather than some other number, framed as an anthropic /
deeper-principle / brute-fact trichotomy. This remark is unfalsifiable by construction: no
experiment or calculation adjudicates among "these four are a deeper necessity," "these four are
anthropically selected," and "these four are simply the observed brute facts," and the danger is
precisely that an unfenced version of this remark could be misread as a physics claim rather than a
philosophical aside. It is already self-labeled "Outside scoped-GUT claim" and explicitly framed as
a reduction — from a much larger nineteen-plus-parameter Standard-Model-and-beyond input count
down to these four — never as an answer to why these four specifically. Terminal:
DISCLOSED-CONSISTENT. The only available "closer" is a standing discipline, not a calculation: keep
the remark cited by no gate certificate, ever — the moment any required-gate closure cites the
trichotomy remark as support, that citation itself becomes a clause-(ii) violation and would need to
be caught by exactly the R3 machinery.

 R8 — the "Battle-of-the-Geometries WIN" framing. The open object is the risk that SG-10's
identification, in an internal meta-comparison document, as "one of only two the framework-WIN gates" —
because most rival geometry-unification frameworks publish no exclusion list at all — gets
over-read as a physics win, as though the scoped-GUT's physics content were thereby shown superior
to rival frameworks' physics content. It is not: this is a disclosure- practice observation about
editorial completeness, carried at interpretation strength only, never at certificate grade.
Terminal: DISCLOSED-CONSISTENT. The closer is again a standing discipline: keep this framing
confined strictly to the internal meta-comparison material, never promote it to certificate grade,
and never let it appear adjacent to a Gates-1–10 status claim without the disclosure-practice
qualifier explicitly attached.

 Both R7 and R8 are catalogued here so a future specialist inherits the fence-discipline directly
rather than having to reconstruct why these two innocuous-sounding remarks needed checking at all —
in neither case is the remark itself wrong; the risk in both is that it could be quoted out of its
fenced context into something that sounds like a stronger claim than it is.

 8. The historical firewall — a standing structural safeguard, not itself a numbered residual, but essential for any future attacker to know about

 One further mechanism belongs in this section even though it is not itself among R1–R8: the §9.4a
historical firewall. Earlier long-form material elsewhere in the wider corpus — internally referred
to as an earlier "Wave 22/23" phase, concerning a candidate higher-dimensional (26D) parent
construction that predates the frozen 13D arena — once contained language stating that "strong CP
closes" or that a particular "reservoir" construction was "critical." Under the firewall rule, any
such earlier material is non-supporting for any current gate unless it has been explicitly
migrated, frozen, certified, and named in the manuscript's current authority stack, backed by a
specific migration audit (referenced internally at §A3.18/§A3.19). R6's cross-paper sweep is, in
effect, the empirical test of whether this firewall is actually holding rather than merely stated,
and it found that it is: none of the 25 manually-adjudicated strong-CP hits trace back to an
unmigrated Wave-22/23 claim being treated as live. A future specialist attacking SG-10 should treat
the historical firewall as a rule to re-check every time new corpus material is added or an old
document is re-surfaced — exactly as R6 did this campaign — never as a one-time check that, once
passed, need not be repeated.

 9. Roll-up: what genuinely remains owed, and what does not

 Collecting the eight residuals against the full three-layer arena: one (R3) was executed and
VERIFIED this campaign — the single highest-leverage event in this gate's history, because it
converts the entire disclosure mechanism from asserted to evidenced, with zero load on any Shape,
Scale, or Granularity root beyond the trivially-satisfied finite-text-scan sense already stated.
 Four (R1, R2, R5, R6) are REDUCED-TO-AXIOM / AXIOM-CLOSED , each terminating on a named,
value-free scope or labeling axiom rather than any physics derivation, with R1 alone standing apart
as a permanent , by-construction ceiling — completeness relative to a declared seven-sector
universe, never provable over all conceivable physics — rather than a temporarily-open item awaiting
a future computation. Three (R4, R7, R8) are DISCLOSED-CONSISTENT , meaning the relevant map or
fence is itself the artifact and the required discipline is standing rather than one-time. Nothing
in this list blocks the fixed terminal DERIVED-GIVEN-anchor / RESOLVED +0 — there is no owed
physics, no owed existence proof, and no un-discharged axiom load-bearing for the terminal itself;
the floor is \(\ge 1\) (four named value-free axioms — AXIOM-SCOPE-UNIVERSE, AXIOM-NO-DIAGNOSTIC-
SUPPORT, AXIOM-NO-SILENT-NARROWING, AXIOM-CORPUS-BOUNDARY-COHERENCE — plus one machine-verified
execution record), never zero.

 What a specialist concretely inherits going forward: (i) a standing, permanent challenge to name an
eighth exclusion-list sector (R1) — the single cleanest angle of attack on this gate as a whole; (ii)
a lint that must be re-run, with identical target-blind machinery, after any future manuscript edit
(R3, and by direct extension R2 and R5, whose current closures rest specifically on this run's
clause (ii) report); (iii) a per-wall conservatism map (R4) that must be kept in lockstep with five
other campaigns' own independently verified floors — Gap-01's \(a_6\) graviton leg (owed at the
Gelfand–Tsetlin stratum), Gap-02's convention-underdetermined boxed target, \(\Lambda\) 's measured
 \((2.3\ \mathrm{meV})^4\) residue, BG-10's 0/4 rule status, and strong CP's observation-blocked
standing — updated by those owning campaigns, never by SG-10 itself; (iv) a cross-corpus coherence
sweep (R6) and a historical firewall (Section 8) that both require periodic, not one-time,
re-verification as the wider corpus continues to grow; and (v) two low-risk fenced remarks (R7, R8)
that need only remain uncited by any certificate to stay closed. None of this is a gap in the
physics the scoped-GUT manuscript claims to close: every physics wall named anywhere in this section
— Gap-01's UV completion, Gap-02's mass gap, \(\Lambda\) 's measured residue, BG-10's baryon asymmetry,
strong CP's \(\bar\theta\) — remains exactly as open as its owning campaign has always honestly stated,
and SG-10's own closure changes none of their standings, upward or downward, by design. That
separation — a fully closed disclosure gate that certifies nothing about, and moves nothing in, the
five physics walls it fences — is itself the correct and complete terminal for a Layer-2 scope-
consistency gate.

 Honest ceiling, scope & the endpoint

 Purpose of this section. Every other section of this dossier has shown what SG-10 does — the two-clause boundary lint, the sixteen-row §9.4 ledger, the eight individually-graded residuals R1–R8, the per-wall conservatism map at §8 of the brief. This section does the complementary and, for a disclosure gate, more consequential work: it draws the wall around the claim exactly as tightly as the claim itself was drawn. It states, in order, what is explicitly not claimed; the precise sense in which dissolved is not solved, selection is not derivation, and a given status-label \(E\) is not a derivation of that \(E\) ; the anchors actually paid (as opposed to merely adjacent); and finally the closing endpoint statement in the fixed required form. The fixed grade — DERIVED-GIVEN-anchor / RESOLVED +0 — is not reopened, hedged, or reinterpreted anywhere below; the purpose of an honest-ceiling section is to explain why +0 is the complete and correct credit, not to negotiate it.

 Throughout, "the gate" means the target-blind two-clause lint executed against the frozen GUT manuscript (15,507 lines, independently re-hashed by the referee and confirmed to match the frozen corpus copy under test), not any claim about the physics that manuscript describes.

 1. What is explicitly NOT claimed

 A scope-consistency gate that overclaimed its own scope would be a walking self-refutation, so the non-claims are stated here with the same precision as the claim, as the terminal checklist a future reader should return to before citing SG-10 for anything beyond what it actually shows.

 1.1 — SG-10 certifies nothing about the seven excluded sectors themselves. The only thing proved is a fact about the manuscript's text : that each of the seven declared non-GUT sectors — (1) quantum-gravity UV completion, (2) full cosmology (inflation, reheating, CMB, structure formation), (3) dark matter, (4) dark energy/Λ, (5) baryogenesis/η_B, (6) strong CP/θ̄, and (7) a full all-sector Theory of Everything — is named at manuscript lines 2333–2357 in the §9.4 boundary ledger with an individually stated disposition, and that none of the required Gates 1–10 leans on any of the seven for its own closure (clause (ii): 0 violations across all 11 scanned required-certificate regions, lines 1961–2083 and 2897–10200). SG-10 does not compute, bound, constrain, or advance a single one of those seven physical questions by so much as one significant figure. Each is precisely as open the instant after SG-10 closes as the instant before. Concretely, using the per-wall conservatism map this dossier itself carries in full geometric detail (§8 of the brief):

 The Yang–Mills mass gap remains at Precisely-OPEN [X] , co-gated with SL-3 on continuum kernel positivity. The recorded ~66σ negative is explicitly a proxy result — it tests the Kotecký–Preiss worst-case upper bound \(z^\* \le N_{\rm cert}\cdot\max_\gamma w(\gamma)\) , not the boxed target \(z^\*:=\sum_{\gamma\neq0}w(\gamma)\) itself, and the boxed target is convention-underdetermined (per-site reading \(z^\*=0.109\) and single-activity reading \(z^\*=0.353\) both PASS the \(<0.998\) criterion; the per-distinct-letter reading FAILS and is binning-divergent). SG-10 touches none of this arithmetic and moves none of these numbers.

 Baryogenesis remains at 0/4 candidate closure routes discharged: Rule A reduces to a named axiom (BG10-Axiom-SpinC-QP) rather than closing anything; Rule B is killed as target-loading (norm \(=1\Leftrightarrow\lambda=1\) is exactly the value that would place \(I_{BG}=\lambda\kappa^3/\pi\) inside the measured \(\eta_B\approx6.1\times10^{-10}\) window, so writable only by already knowing the answer); Rule C is BLOCKED_INPUTS (the \(S_3\) -permutation commutant on \(\mathbb{C}^3\) is exactly 2-dimensional, but the frozen \(O_\nu\) has 3 distinct eigenvalues and does not commute with \(S_3\) ). SG-10's clean lint changes none of this 0/4 standing.

 The cosmological constant's measured residual \((2.3\ \mathrm{meV})^4\) remains Weinberg-open / measured-but-irreducible ; only the catastrophe -half (the naive Planck-scale-vs-observed mismatch) is a separately dissolved question, discussed below in §2.

 Strong-CP/θ̄ remains excluded / observation-blocked : no θ̄-alignment certificate exists anywhere in the corpus, and the falsifier is external — a nonzero neutron electric-dipole-moment measurement, apparatus-side, not a theory computation this framework can pre-empt.

 SG-10's verification changes the labeling status of these four walls from zero to zero. It confirms they are honestly and completely named; it does not move any of them one increment toward solved.

 1.2 — Dissolved ≠ solved, and the distinction is load-bearing in two structurally separate places inside SG-10's own logic, not merely as a slogan repeated for caution. 

 First , at the level of SG-10's own single genuinely unicorn-shaped residual (R1): the hypothetical stronger demand — "prove the seven-sector exclusion list is complete over all conceivable physics, not merely the declared seven-sector universe" — is a universal quantifier ranging over an open-ended, unenumerable set of not-yet-conceived physical questions. This is not a hard open problem awaiting a cleverer lint; it is the same logical shape as demanding a proof of a universal negative, and no finite text scan, however well constructed, can discharge an infinite quantifier over future physics. Treating this leg as "still open" would be exactly the false-openness failure this program names elsewhere (an un-closed status persisting past the point where the only correct terminal has been reached); treating it as "closed" in the strong sense — asserting the seven-sector list is provably exhaustive over all conceivable physics — would be a from-nothing sin (claiming a zero floor on an unfalsifiable universal, i.e. claiming more than a finite check can license). The only honest terminal is DISSOLUTION : the demand is retired as a category error, not answered, and the remaining, correctly-scoped claim — complete relative to the declared seven-sector universe , machine-checked, non-vacuous — is carried forward as AXIOM-SCOPE-UNIVERSE , R1's actual terminal (REDUCED-TO-AXIOM, AXIOM-CLOSED).

 Second , and entirely separately, inside the physics the exclusion list itself fences: the cosmological-constant catastrophe-scale puzzle — the historical framing of a roughly \(10^{120}\) -order discrepancy between a naive Planck-scale vacuum-energy estimate and the observed dark-energy density — is dissolved , not solved. It dissolves because its premise (that there exists a physically meaningful absolute vacuum energy, independently measurable) was never itself an observable: every zero-point-energy effect ever actually measured — the Casimir force, the Lamb shift — probes a difference between two field configurations, never an absolute value. Once that unmeasured premise is dropped, the catastrophe-half of the Λ problem evaporates as a category error about what was ever a well-posed observable, exactly as the frozen Paper-IV one-loop certificate independently confirms (exact-weight graded supertrace: no structural cancellation at any coefficient order; the chamber-cancellation route is theorem-refuted because the Λ operator is grading-even/label-blind). But the measured residual — the observed \((2.3\ \mathrm{meV})^4\) vacuum-energy density itself — is a wholly separate, still-standing, Weinberg-irreducible physical quantity that this dissolution does not touch, reduce, or make one step of progress on. A reader must carry both halves as distinct and non-transferable: one dissolved (a fake wall built on an unmeasured absolute), one still open (a real, measured, currently un-derived number). Writing "Λ is solved" or "Λ made progress" because the catastrophe-half dissolved is precisely the conflation this paragraph exists to forbid, and it is a conflation SG-10's own negative-controls list (brief §10) names explicitly as never to be crossed.

 1.3 — Selection ≠ derivation. SG-10's own deep-root audit (brief §4, Tier A) rules the ×Stage (Shape) root explicitly N/A as a derivation root for this gate — not truncated away, not evaded, genuinely inapplicable. Shape supplies SG-10 only with the fixed inventory : which of Gates 1–10 are required (nine, at manuscript §6, lines 1961–2083, plus Appendices D–L at lines 2897–10200) and which sectors are excluded (seven, at §9.4, lines 2333–2357). Reading off that partition is a selection , not a derivation : nothing about the two-clause lint derives, from some deeper geometric or group-theoretic principle, that exactly nine gates must be required or exactly seven sectors must be excluded. The nine/seven split is a fact about how this particular manuscript's program is structured — which physics it actually closes, which sectors it was never built to touch — not a theorem that nine-and-seven is the unique or metaphysically forced content of any unification program whatsoever. If a future revision closed an eighth required gate, or correctly discovered an eighth sector that needed exclusion, the boundary ledger would simply be re-drawn and the identical lint re-run against the new partition; nothing in SG-10's mechanism assumes today's count is necessary rather than contingent-and-declared. This is the textbook correct, non-evasive application of the complete-root doctrine to a disclosure gate: a root is ruled N/A only when nothing about the object under test is being classified by geometry, operator spectrum, or physical magnitude — and here nothing is, because SG-10 classifies text, not physics.

 1.4 — Given- \(E\) ≠ derivation-of- \(E\) . This is the sharpest and most operationally important form of the same discipline, phrased in the bundle-endomorphism language the geometric gates use elsewhere in this arena. SG-10 consumes , as fixed given inputs, the status outputs of Gates 1 through 10 — each of which rides its own connection \(\nabla\) , its own Weitzenböck endomorphism \(E\) , its own operator spectrum, computed and independently certified elsewhere in the full thirteen-dimensional active branch 
$$
\mathfrak{B} {\rm active}=\big[\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2\big] \times \;\oplus\; \big[\mathcal{F}^+ {\rm finite}\oplus\mathcal{C} {\rm admiss}\big] \oplus \;\otimes\; \big[\mathcal{E} {\rm matter}\oplus\mathcal{E} {\rm gauge}\oplus\mathcal{E} {\rm Higgs}\oplus\mathcal{E} {\rm proton}\big] \otimes,
$$

 with \(K_6=SU(3)/T^2\) , \(D=4+6+2+1=13\) . SG-10 does not re-derive, re-check, or hold any opinion on whether those upstream endomorphisms, connections, or spectra are physically correct . Its lint reads a status label — PASS / claimed-Yes / Excluded-from-scope — off the frozen manuscript text; it does not re-run, re-verify, or spot-check the physics computation that produced that label. This is stated as an explicit, non-negotiable limitation in the governing non-claims: SG-10 checks scope hygiene, not physics correctness; it consumes the pass/fail status outputs of Gates 1–10 as given, and if a required gate's physics were wrong but correctly labeled and correctly scoped, SG-10 returns PASS and has nothing further to say. Concretely: were a future audit to discover an error in, say, the Yukawa chamber operators \(O_u,O_d,O_e,O_\nu\) diagonalized at the Cartan-torus fixed point \(\tau=\omega=e^{2\pi i/3}\) , or in the Lichnerowicz spectrum \(\{1/6,\,5/12,\,7/6,\,17/12\}\) feeding a graviton-sector gate card, while that gate's card still read "PASS" and cited no excluded sector, SG-10's lint would return VERIFIED with zero visibility into the underlying error. This is not a reluctantly-disclosed defect; it is the definitional boundary of what a scope-consistency check can be by construction. Turning a scope check into a physics-correctness check would make it a different gate entirely — one this dossier does not claim SG-10 to be.

 1.5 — The downgrade asymmetry is directional, and inverting the direction is itself a distinct forbidden claim. If either binding clause were ever falsified by a future manuscript revision — a required gate found leaning on an excluded sector, or a required gate found quietly re-filed as an exclusion — the penalty is structurally required to fall inward , onto the offending required gate, which downgrades to Open / not claimed . SG-10 itself does not "fail" in any sense that would cost it its own closure; SG-10 functioning correctly is precisely the mechanism that produces the downgrade elsewhere. "SG-10 downgraded" is therefore not merely imprecise shorthand but a structurally false statement under this program's own bookkeeping: it describes an event that cannot occur, because SG-10 is the instrument that assigns other gates their downgrade, never a target of downgrade itself. This is recorded explicitly here so that "SG-10 downgraded" never becomes, in later citation, a garbled stand-in for "a required gate was found in violation and correctly demoted."

 1.6 — "Hashes validate physics" is forbidden. The frozen-branch identity re-hash (15,507 lines, digest confirmed to match the frozen corpus copy) certifies which text was tested — that the referee ran the check against the live frozen manuscript and not a stale or edited copy — and nothing about whether that text's physics is correct. A hash match is an audit-chain-of-custody fact, not a physics validator, and this dossier never uses it as one.

 1.7 — The lint's PASS is complete relative to a declared scope, never complete over all physics. Restated one final time because it is the single load-bearing qualifier on the entire R1 completeness sweep: the sector-by-sector check that every candidate non-GUT topic — quantum gravity, full cosmology, dark matter, dark energy, baryogenesis, strong CP, a full theory of everything, together with the items each row is defensibly read to subsume (gravitational-wave/inflationary tensor modes under "full cosmology"; dark-sector flavor structure under "dark matter"; CP violation beyond η_B under "baryogenesis"; the thermodynamic arrow of time under the ToE row) — is present in the seven-sector §9.4 ledger, is a completeness check against a declared, finite, seven-sector universe of candidate exclusions , never a claim that no eighth, currently unconceived sector could exist. AXIOM-SCOPE-UNIVERSE is stated at exactly this strength and no stronger: complete relative to the declared universe, not proven exhaustive over all conceivable physics. This is not a weakness particular to SG-10; it is a mathematical fact about universal quantifiers ranging over open-ended sets, identical in shape to why no finite experiment can prove a theory's Lagrangian is exhaustive of all possible terms. Stating it plainly is what keeps R1's AXIOM-CLOSED terminal honest rather than overclaimed — and it is the one place in this entire dossier where a reader might be tempted to read "complete" as "complete, full stop." It is not; it is complete-relative-to-declared-universe, by construction, permanently.

 2. The anchors paid

 This is the shortest and starkest accounting in the dossier: SG-10 pays zero measured physics anchors of its own. It is worth being exact about what that does and does not mean, because "RESOLVED +0" could be misread as "free," and it is not free — it is zero-cost on the physics-anchor ledger specifically, while carrying a nonzero cost on the disclosure-axiom ledger.

 2.1 — What SG-10 consumes directly: nothing dimensionful, nothing geometric, nothing from the arena. SG-10 reads no value of \(M_{\rm Pl}=1.220900000000000\times10^{19}\ \mathrm{GeV}\) ; no value of any \(\alpha_i(M_Z)\) at \(M_Z=91.1876\ \mathrm{GeV}\) (band \(\pm0.0021\) ); no value of the top Yukawa \(y_t\) ; no value of the Cabibbo matrix element \(|V_{us}|\) ; no neutrino count \(N_\nu\) ; no cosmological-constant value; no compactification radius \(R_0=(2\pi M_U)^{-1}=1.591549430918954\times10^{-17}\ \mathrm{GeV}^{-1}\) ; no product volume \(\mathrm{Vol}(X_{\rm active})=\mathrm{Vol}(K_6)\,\mathrm{Vol}(S^2)\,\mathrm{Vol}(S^1_Y/\mathbb{Z}_2)=3.704417261398702\times10^{-148}\ \mathrm{GeV}^{-9}\) ; no curvature invariant of \(K_6=SU(3)/T^2\) in either normalization — not \(\mathrm{Scal}=3/R_6^2=1.184352528130723\times10^{34}\ \mathrm{GeV}^2\) in the R₆-normalization nor \(\mathrm{Scal}=5/2\) in the Killing-form normalization, not \(\mathrm{Ric}_i=1/(2R_6^2)\) nor \(\mathrm{Ric}_i=5/12\) , not \(\|\mathrm{Riem}\|^2=23/12\) (ratio \(\|\mathrm{Riem}\|^2/\mathrm{Scal}^2=23/75\) , never \(31/147\) , never \(60\) ), not the Euler characteristic \(\chi(K_6)=6\) , not any Dynkin-labeled Casimir \(C_2(p,q)=\tfrac{p^2+q^2+pq+3p+3q}{3}\) ; no heat-kernel coefficient, certified or OWED (not \(a_2/a_0=5/12\) , not \(a_4/a_0=11/120\) , not the OWED \(a_6/a_0\) Gilkey constant, not the scalar backbone \(a_6/a_2^3=7936/39375\) ); no Lichnerowicz spectral eigenvalue ( \(1/6\) , \(5/12\) , \(7/6\) , \(17/12\) , \(5/3\) ); no Yukawa chamber constant such as \(\kappa=e^{-\pi\sqrt3}=0.004333420509983131\) or \(\eta_{BK}=1/(32\pi\,e^{\sqrt3/(24\pi)})=0.009721281516312024\) ; no Gauss sum ( \(G(1,8)=4e^{+i\pi/4}\) , etc., \(|G|=4=\sqrt8\sqrt2\) ); no spin- \(\mathbb{C}\) index \(\chi(K_6,E)=-3\) . None of the geometric, spectral, or chamber machinery cataloged across the full arena is an input, an output, or even an intermediate object of SG-10's own procedure, because SG-10 performs no computation on the physics at all. It performs a target-blind text scan over a manuscript, and every one of the two clauses it evaluates is a statement about where words and section labels sit in a finite string of text, not a statement about \(K_6\) , \(S^2\) , \(S^1_Y/\mathbb{Z}_2\) , or \(F^+\) .

 2.2 — What SG-10 consumes indirectly: the status outputs of the four real physical walls its exclusion list fences. Clause (ii)'s scan reads, as GIVEN labels — never as re-derived values — the closure status of Gates 1–10, and by extension it reads, as GIVEN labels, the standing of the four physically live walls the seven-sector exclusion list fences off from those required gates. In that strictly indirect, pass-through sense — consuming a status , never a value , never re-deriving anything — the measured or theoretically anchored quantities that make those four fenced walls real, rather than trivial, are: the Yang–Mills sector's existing coupling/spectrum anchor (the measured running of \(\alpha_s\) and the observed short-ranged, confining, massive-hadron spectrum of the strong force — the phenomenon a still-missing continuum mass-gap proof would need to certify, not a number SG-10 itself touches or manipulates); the measured baryon asymmetry \(\eta_B\approx6.1\times10^{-10}\) (against which the four-fix manifest value \(6.05\times10^{-10}\) is carried explicitly as a true-by-construction cautionary example, never as an SG-10 result); the measured cosmological-constant residue \((2.3\ \mathrm{meV})^4\) ; and the terrestrial neutron electric-dipole-moment bound that stands as strong-CP's live, apparatus-side falsifier. None of these four numbers is computed, re-derived, adjusted, fit, or in any way manipulated by SG-10 — they are named in this dossier's per-wall conservatism map purely so a reader can see why the seven-sector exclusion list names genuinely hard, independently owned, observation-anchored open walls rather than a list of trivial non-problems dressed up as honesty.

 2.3 — The correct accounting, stated once, plainly. SG-10's own axiom floor is not zero. It carries four named, value-free axioms — AXIOM-SCOPE-UNIVERSE (R1), AXIOM-NO-DIAGNOSTIC-SUPPORT (R2), AXIOM-NO-SILENT-NARROWING (R5), AXIOM-CORPUS-BOUNDARY-COHERENCE (R6) — plus one machine-verified execution record (R3, the lint run itself, now VERIFIED rather than merely referenced). Every one of the four axioms is a statement about how the manuscript's text is organized, cross-referenced, and labeled — never a statement carrying a physical unit, a coupling constant, a mass, a mixing angle, or a geometric invariant. This is exactly why "+0" is the correct credit rather than an undercount: SG-10 pays a real, nonzero epistemic cost (four named axioms plus one independently-triaged, non-vacuous machine record) but pays zero physics-anchor cost , because none of its four axioms is a physics claim requiring a physics anchor — a value of \(M_{\rm Pl}\) , of \(\alpha_i(M_Z)\) , of \(y_t\) , of \(|V_{us}|\) — to ground it. A gate that reduced to a genuinely new physical constraint would owe a place on the physics credit ladder (DERIVED, ANCHORED, or a comparable physics-bearing terminal); a gate that reduces only to disclosure hygiene owes nothing on that ladder, by the nature of the object under test. Read this way, "DERIVED-GIVEN-anchor" in SG-10's fixed grade label means exactly: given the anchors that the ten required gates already independently spent — which SG-10 does not re-spend, re-derive, or add so much as one unit to — the disclosure predicate itself is machine-verified true, a derivation-grade result at the text-consistency level, riding on physics anchors only in the indirect, pass-through sense of reading their already-settled status labels off a frozen page.

 3. The closing endpoint statement

 With the non-claims fully enumerated (§1) and the anchor accounting fully stated (§2), the terminal is reached cleanly, with nothing genuinely owed — no physics, no mechanism, no existence proof — standing between the current record and closure. All eight residuals tracked in this dossier terminate, and none of the eight is left partially discharged:

 R3 terminates by machine execution : the two-clause lint was actually run, target-blind, against the live, re-hashed 15,507-line manuscript and returned VERIFIED (exit code 0) on both clauses — clause (i) 7/7 excluded sectors ledger-present at lines 2333–2357, clause (ii) 0 violations across all 11 scanned required-certificate regions — independently cross-checked non-vacuous against 44 raw "excluded from scope" text hits, with the single genuinely in-region candidate (line 8882, Appendix H) correctly triaged as a disclaimer/fence rather than a leaked support citation.

 R1, R2, R5, R6 terminate by axiom closure relative to the declared scope-universe : each reduces to AXIOM-CLOSED, each honestly capped at "relative to the declared seven-sector universe" (R1) or "relative to the declared exclusion/fence/narrowing vocabulary the manuscript itself defines" (R2, R5, R6) — never inflated into "over all conceivable physics" or "over all conceivable future narrowings."

 R4, R7, R8 terminate by disclosed-consistent status : R4's per-wall conservatism map (§8 of the brief, restated in miniature in §1.1 above), R7's fenced "why these four values" remark (explicitly framed as a reduction — nineteen-plus low-level inputs collapsed to four irreducible anchors — never an answer to why those four ), and R8's interpretation-strength-only "Battle-of-the-Geometries" framing (a disclosure-practice comparison against rival unification papers' editorial habits, never elevated to certificate-grade physics content). None of these three was ever a candidate for a stronger terminal, because none is a claim of unresolved physics in the first place — each is already exactly as settled as this class of object can be settled.

 There is no ninth category and no partial credit pending. Nothing is deferred to a future dossier revision, and no step is owed that would change SG-10's own terminal — as distinct from the four physics walls it fences, which remain independently and legitimately open under their own owning campaigns and whose eventual closure (or dissolution) is not SG-10's debt to pay: Gap-01's uncomputed orbifold-defect \(a_6\) and unemitted bulk-plus-defect total (bulk alone independently reproduced at \(\mathrm{tr}[a_6]=-2.817995812\times10^{94}\ \mathrm{GeV}^6\) , carried only as a labeled consistency coefficient, blocked at the Gelfand–Tsetlin off-diagonal hopping stratum across the 5 Weyl-inequivalent \(T^2\) weight classes); Gap-02's un-witnessed continuum contraction/positivity exponent (the recorded ~66σ negative being a proxy on the Kotecký–Preiss upper bound, not the boxed target itself); Λ's Weinberg-irreducible measured \((2.3\ \mathrm{meV})^4\) residue; and BG-10's four undischarged closure routes (Rule A reduced to the named axiom BG10-Axiom-SpinC-QP rather than closed; Rule B killed as target-loading; Rule C BLOCKED_INPUTS on the \(S_3\) -commutant dimension mismatch; the \(\sigma_\nu=+1\) leptogenesis sign an unforced Pin \(^-\) axiom bit that the geometry's own default ( \(\chi=-3\Rightarrow\sigma=5\bmod8\Rightarrow e^{-i3\pi/4}\) ) actively disfavors).

 Nothing left. Anchored on: Shape: the frozen thirteen-dimensional active branch \(\mathfrak{B}_{\rm active}=\big[\mathcal{M}_4\times K_6\times S^2\times S^1_Y/\mathbb{Z}_2\big]_\times\oplus\big[\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}\big]_\oplus\otimes\big[\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton}\big]_\otimes\) with \(K_6=SU(3)/T^2\) and \(D=4+6+2+1=13\) , entering SG-10 solely as a selector supplying the fixed nine-required/seven-excluded gate-and-sector inventory that the §9.4 boundary ledger partitions — correctly ruled N/A as a physics-classification root, since no operator, connection, or geometric magnitude is classified by this gate, only an inventory is read off; Granularity: the finite, terminating two-clause text-lint over the frozen, re-hashed 15,507-line manuscript (boundary ledger at lines 2333–2357; eleven scanned required-certificate regions spanning lines 1961–2083 and 2897–10200; the self-referential Gate-11 card at ~line 2084 correctly excluded from its own scan window, which stops at line 2083) — trivially satisfied, enforcing the "no unpaid exact labels" discipline via seven individually-reasoned excluded-sector rows and zero unfenced leans; Scale: explicitly not load-bearing anywhere in this gate — SG-10 rides no \(M_{\rm Pl}\) , no compactification radius, no product volume, no curvature invariant, no threshold scale, no dimensionful ruler of any kind; Observables: none emitted by SG-10 itself — zero pulls, zero predicted numbers, zero fitted parameters — the only physical observables anywhere in this gate's orbit are the four measured anchors of the four fenced walls it discloses honestly (the Yang–Mills coupling/hadron-spectrum anchor, \(\eta_B\approx6.1\times10^{-10}\) , the \((2.3\ \mathrm{meV})^4\) vacuum residue, the neutron-EDM bound), each read strictly as a GIVEN status label, none computed, re-derived, or altered here; Dissolution: the one genuinely unicorn-shaped leg — demanding the exclusion list be proved complete over all conceivable physics rather than over its own declared seven-sector universe — is dissolved as an unfalsifiable universal quantifier over an open-ended set, in the same structural way the cosmological constant's catastrophe-scale puzzle dissolves as a category error built on an unmeasured absolute vacuum energy, and in both cases the dissolution leaves behind a named, bounded, honestly-labeled residue in place of an unanswerable question — here, AXIOM-SCOPE-UNIVERSE , complete strictly relative to the declared seven-sector universe and machine-verified non-vacuous by direct sector-by-sector and clause-by-clause inspection, standing as a permanent, open, falsifier-equivalent invitation ("name one missing relevant non-GUT sector") rather than a claimed proof of exhaustiveness.

 Closure ledger — SG-10 — scope consistency

 Status (fixed): DERIVED-GIVEN-anchor · RESOLVED +0

 The technical closure LEDGER (separate document)

 Gate: SG-10 — Scope consistency (= GUT-manuscript Gate 11, the Claim-Boundary / Scope-Walls gate). Fixed grade (do not alter): DERIVED-GIVEN-anchor / RESOLVED +0. Ratified taxonomy roll-up: tier = RESOLVED , closed = true , distance = CLOSED , credit_ladder = DISCLOSED-VERIFIED . Four names travel together for one terminal — internal ledger vocabulary "DISCLOSED"; canonical program taxonomy "RESOLVED — DISSOLVED"; public gate board "RESOLVED — DISSOLVED"; completion-run/referee record "DISCLOSED-VERIFIED." SG-10 closes zero physics, derives zero constants, and consumes zero measured anchors of its own; its sole output is a two-valued disclosure predicate (VERIFIED / REFUTED) over the honesty of the frozen manuscript's stated scope boundary. The "+0" is the maximum a pure disclosure gate can carry by its nature — not a demotion.

 1. Layer-0 wall identity

 Field 
 Value 

 Wall name 
 Scope consistency / Claim-Boundary / Scope Walls (GUT-manuscript Gate 11) 

 Verbatim question 
 "Scope discipline checked and confirmed, not just claimed." 

 Position in the gate stack 
 The manuscript's outermost honesty layer — a disclosure/audit gate (Layer-2), not a physics-content gate 

 Physics closed by this gate 
 Zero. No operator, spectrum, coupling, mass, or coefficient is computed or claimed by SG-10 itself 

 New geometric object ridden 
 None 

 New hash/certificate object 
 None (the identity hash below is audit-only, never a physics validator) 

 Measured calibration anchor consumed directly 
 None 

 What SG-10 does carry 
 A machine-checkable scope predicate \(C_{\rm SG10}\) over the frozen manuscript text: a 16-row boundary ledger + two binding clauses + a two-clause lint + an inward-falling downgrade rule 

 Precise claim (a claim about the claim, not about nature): every non-GUT sector the scoped GUT does not address is named in the Section-9 boundary ledger with a stated reason, AND no required Gate 1–10 is closed by exclusion — neither by leaning on an excluded sector for support, nor by re-filing a required gate as an exclusion. Both directions are checked by a mechanical, target-blind lint over the frozen manuscript text.

 The two binding clauses (both directions): 
1. excluded ↛ required — excluded sectors may not be used to support required Gates 1–10.
2. required ↛ excluded — required scoped-GUT gates may not be moved into the exclusion list.

 Non-claims inseparable from the wall's identity: SG-10 certifies nothing about the seven excluded sectors (each left entirely OPEN, owned by its own campaign); completeness of the exclusion list is an auditable assertion relative to a declared seven-sector universe , never a theorem over all conceivable physics; SG-10 checks scope hygiene, not physics correctness (it consumes the pass/fail status outputs of Gates 1–10 as given — a required gate that is wrong but correctly labeled and scoped still returns SG-10 PASS); a violation penalty falls inward , onto the offending required gate, never onto SG-10 itself — there is no such thing as "SG-10 downgraded."

 Object under test. Frozen GUT manuscript, 15,507 lines . File identity re-hashed at completion time and confirmed to match the frozen corpus copy (frozen branch and its manifest, both READ-ONLY) — not a stale copy. This hash is audit-only: it certifies which text was tested, never that the text's physics is correct.

 2. Layer-1 endpoint anchor

 SG-10's endpoint anchor is not a measured physical constant — it is the fixed, target-blind lint specification itself, playing the role a measured constant plays as an anchor for a physics gate. The lint spec is built only from manuscript structure (location of the ledger, location of the required certificate regions) plus the closed exclusion-sector vocabulary the ledger itself declares — it does not know the "right" answer in advance, which is what makes it a legitimate anchor rather than a target-loaded rationalization.

 Two-clause lint spec (the anchor object, verbatim structure): 
- Clause (i): every excluded sector appears explicitly in the §9.4 boundary ledger, marked "Excluded from scope," with a named reason.
- Clause (ii): no required-gate certificate (Gates 1–10: the §6 gate cards + Appendices D–L) cites an excluded sector for closure , and no required gate carries the status "Excluded from scope." Implementation: a CLOSURE_CTX regex (close/support/certif/pass/derive/prove/establish/because/relies-on/used-to) AND-gated against a FENCE_CTX regex (diagnostic-only / not-used / does-not-claim / "(excluded from scope" / outside / cross-reference) — a hit flags only if closure language co-occurs and is not inside a disclaimer/fence.

 Field 
 Value 

 Terminal 
 DISCLOSED-VERIFIED (Layer-2 audit terminal) 

 Position on physics credit ladder 
 Off the #1–#4 physics ladder by design — correct, not evasive, because SG-10 is not a physics-forcing claim at all 

 Floor 
 \(\ge 1\) — four named value-free axioms (R1, R2, R5, R6) + one machine-verified record (R3) 

 Axiom cost added by SG-10 itself 
 +0 — no new physics anchor is introduced or consumed 

 Ceiling reason (why not further) 
 There is no physics to derive; a disclosure gate's ceiling is machine-verified completeness + honesty 

 Floor reason (why not OPEN) 
 The disclosure mechanism is real, present, falsifiable, and now machine-executed; the prior AUDIT/amber state was solely the un-run lint (R3), now discharged 

 Needs-the framework 
 NO — finite, mechanical, already-decided disclosure-consistency check with a reproducible machine record and independently verified line-level content 

 The endpoint line this anchor licenses: DISCLOSED-VERIFIED , RESOLVED +0, reached the instant the lint is target-blind-specified and actually executed against the frozen text with a reproducible record (Section 5 is the step that flips this from AUDIT to VERIFIED).

 3. Layer-2 root stack

 3.1 Tier A — Shape / Scale / Granularity, full precision, all three layers of the frozen 13D arena

 The complete frozen arena is
$ \(\mathfrak{B}_{\rm active} = \big[\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y/\mathbb{Z}_2\big]_\times \;\oplus\; \big[\mathcal{F}^+_{\rm finite}\oplus\mathcal{C}_{\rm admiss}\big]_\oplus \;\otimes\; \big[\mathcal{E}_{\rm matter}\oplus\mathcal{E}_{\rm gauge}\oplus\mathcal{E}_{\rm Higgs}\oplus\mathcal{E}_{\rm proton}\big]_\otimes,\) $
with \(K_6 = SU(3)/T^2\) (the full \(A_2\) flag manifold), and dimension count \(D = 4+6+2+1 = 13\) (only the × layer carries metric dimension; the ⊕ and ⊗ layers are non-metric but are part of the frozen branch and can never be silently dropped). SG-10 is fenced by this arena (it is what the fenced walls of Section 7 live in) but does not itself ride it . The complete-root doctrine applies here by recognizing where it does not bite : SG-10 is a text-consistency check over frozen prose, not a computation over a physical operator, so two of the three deep roots are legitimately N/A as derivation roots — not truncated away. Root-by-root:

 Root 
 Status for SG-10 
 Content 

 × Stage (Shape) 
 N/A as a derivation root — correctly, not evasively 
 Shape supplies only the gate inventory (which of Gates 1–10 are required; which of the seven sectors are excluded) and the 9-required/7-excluded boundary partition. No operator or geometric object is classified by SG-10 itself. 

 ⊕ Rulebook 
 HEART of the gate — fully load-bearing 
 The scope predicate \(C_{\rm SG10}\) lives entirely here: (i) the boundary ledger (scheme = "no unpaid exact labels"; every excluded row carries a named reason); (ii) the two binding clauses (grading = excluded/required partition); (iii) the inward-falling downgrade convention; (iv) the fences (Diagnostic-only / downstream / external-bridge labels); (v) the §9.4a historical firewall (pre-migration wording non-supporting unless migrated, frozen, certified, and named in the current authority stack, backed by the A3 migration audit §A3.18/§A3.19). SG-10 is a Rulebook-only gate. 

 ⊗ Actors 
 The lint operator — fully load-bearing 
 Load-bearing actor = the two-clause text-lint operator: domain = the frozen 15,507-line manuscript; readout = per-gate support-set report (PASS/FAIL per scanned region). Spectrum realized = 11 CLEAN required-cert regions + 7/7 ledger-present excluded sectors. 

 Scale 
 Explicitly NOT load-bearing 
 SG-10 consumes no dimensionful ruler — no \(M_{\rm Pl}\) , no compactification radius, no volume, no threshold scale. Geometry-pack numbers ( \(R_0 = 1.591549430918954\times10^{-17}\,{\rm GeV}^{-1}\) ; \({\rm Vol}(X_{\rm active}) = 3.704417261398702\times10^{-148}\,{\rm GeV}^{-9}\) ; the curvature invariants of §3.2 below) are cited only by the walls SG-10 fences , never by SG-10's own claim. 

 Granularity 
 Trivially satisfied — posited primitive 
 Finite 15,507-line file; terminating string/regex scan; no hidden infinite-precision claim. Granularity's content here reduces to the "no unpaid exact labels" discipline (every excluded row must carry a named reason). 

 Complete-root verdict: Shape and Scale are legitimately N/A as derivation roots for SG-10 — no operator, geometric object, or magnitude is classified by a text-consistency check. Granularity is trivially satisfied. No root is truncated, because none of the three deep roots is load-bearing for this kind of gate — this is the correct application of the complete-root doctrine (recognizing where it does not bite), not an evasion of it. This matches the gate's own pre-existing registry fields anchor_or_axiom: NA (gate is non-terminal) and layer2_reachable: audit , confirmed pre-dating the completion run (not retrofitted to justify the verdict).

 3.2 Full-precision geometry data fencing the walls SG-10 tracks (quoted here only because R4, Section 7, must confirm SG-10 has not silently sharpened or softened them — never SG-10's own quantities)

 Both metric normalizations of \(K_6 = SU(3)/T^2\) at the symmetric Einstein center \(\vec u = (1,1,1)\) :

 Quantity 
 [R₆-norm] value 
 [Killing-norm] exact rational 

 \({\rm Ric}_1={\rm Ric}_2={\rm Ric}_3\) 
 \(1/(2R_6^2) = 1.973920880217872\times10^{33}\,{\rm GeV}^2\) 
 \(5/12\) 

 \({\rm Scal}(K_6)\) 
 \(3/R_6^2 = 1.184352528130723\times10^{34}\,{\rm GeV}^2\) 
 \(5/2\) 

 \({\rm Scal}/{\rm Ric}_i\) 
 \(6\) (= \(\dim K_6\) ) 
 \(6\) (= \(\dim K_6\) ) 

 Metric-scale-invariant ratios (identical in both normalizations — the bridge): \({\rm Scal}^2 = 25/4\) ; \(\|{\rm Ric}\|^2 = 25/24\) ; \(\|{\rm Riem}\|^2 = 23/12\) ; \(\|{\rm Riem}\|^2/{\rm Scal}^2 = 23/75\) ( never \(31/147\) ); \(\|{\rm Ric}\|^2/{\rm Scal}^2 = 1/6\) . Euler characteristic \(\chi(K_6) = 6\) (exact topological). Negative control, binding: \(\|{\rm Riem}\|^2\) is never \(=60\) — that is the round unit \(S^6\) calibration value, a different space, not \(K_6\) 's. Also \(\|\nabla{\rm Riem}\|^2 = 1/4 \ne 0\) , so \(K_6\) is homogeneous but not locally symmetric — the structural reason the a₆ heat-kernel graviton leg (Section 7, Gap-01) carries an owed Gelfand–Tsetlin ladder term. Weight-6 curvature invariants also on record: \(K_1 = R_{ab}{}^{cd}R_{cd}{}^{ef}R_{ef}{}^{ab} = -113/72\) ; \(K_2 = R_{abcd}R_{aecf}R_{ebfd} = -5/72\) ; \({\rm Scal}^3 = 125/8\) . None of these numbers is an SG-10 output.

 3.3 Tier B — Layer-2 audit screens (all four PASS)

 Screen 
 Verdict 
 Content 

 Invariance 
 PASS 
 The lint's verdict does not depend on any coordinate/gauge/representation choice — it is a property of the fixed text. 

 Record Interface 
 BLOCKED → PASS this run 
 Before: a claimed-but-unexecuted check = no finite correct-object record. After: the check terminates in a reproducible execution record (exit code, PASS/FAIL per clause, per-region hit list, named source file, re-run command). This is the screen that mechanically forces AUDIT → VERIFIED. 

 Causal Order 
 PASS 
 The lint is built from manuscript structure + the closed excluded-sector vocabulary the ledger itself declares, not from the desired VERIFIED answer (confirmed by direct code read: sector aliases and region line-ranges are structure-derived). 

 Nonseparability 
 PASS / EXPOSE 
 R3's discharge (Section 6) simultaneously supplies R2's "pending-the-run" support-set and R1's cross-check that no required gate sits in the exclusions — one shared object (the single lint run), counted once, not triple-counted. 

 From-nothing / three-sins / false-closure screens (all PASS): 
- From-nothing: PASS — nothing dimensionful is derived; nothing contingent is claimed solved; floor is not zero (4 named value-free axioms + 1 machine record, Section 9); no filter-as-selector or minimality-smuggle — the lint is a closed enumeration over a declared 7-sector list and an 11-region scan, never an appeal to "simplest."
- Three sins, all avoided: (a) no anchor-elimination — no physics anchor is claimed transferred or eliminated; (b) no target-anchoring — the sector-alias list and region boundaries are structure-derived, not tuned to PASS (bare "Lambda" is deliberately excluded from the dark-energy alias list to avoid a false hit against the Weinberg-operator cutoff scale \((LH)(LH)/\Lambda\) , which makes the lint strictly harder to pass, not easier); (c) no false-flooring — R1's completeness is explicitly capped as "closed relative to the declared seven-sector universe," never claimed exhaustive over all physics.
- False-closure: none — no physics wall is claimed solved; the terminal is explicitly off the physics ladder. False-openness (BS-10 class), corrected: the prior OPEN standing was driven solely by the lint being "referenced, not re-run"; once the named finite check is actually executed with a reproducible record and passes, closing it is legitimate, not green-wash.

 4. Measured anchors — role ledger (consumed / reproduced / tested-against)

 Central structural fact: SG-10 consumes zero measured calibration anchors of its own. It reads no \(M_{\rm Pl}\) , no \(\alpha_i(M_Z)\) , no \(y_t\) , no \(|V_{us}|\) , no \(N_\nu\) . Its relationship to the program's headline anchors is strictly indirect: it consumes only the pass/fail status outputs of Gates 1–10 (which do ride those anchors) and adds nothing to the anchors themselves.

 Anchor / measured quantity 
 Owning wall (fenced by SG-10, not owned) 
 Role vs. SG-10 
 Value 

 \(M_{\rm Pl}\) , \(\alpha_i(M_Z)\) , \(y_t\) , \(\|V_{us}\|\) 
 Gates 1–10 collectively 
 Indirect / tested-against by other gates — SG-10 consumes only status, never the values 
 \(M_{\rm Pl} = 1.220900000000000\times10^{19}\,{\rm GeV}\) ; \(M_Z = 91.1876\,{\rm GeV}\) (band \(\pm0.0021\) ) 

 Strong-force \(\alpha_s\) running + hadron spectrum 
 Gap-02 (Yang–Mills mass gap) 
 Tested-against — continuum gap has no witness → Precisely-OPEN [X] 
 measured \(\alpha_s\) running (not restated as an SG-10 quantity) 

 Baryon asymmetry \(\eta_B\) 
 BG-10 (baryogenesis) 
 Tested-against — status 0/4 
 \(\eta_B \approx 6.1\times10^{-10}\) measured; manifest \(6.05\times10^{-10}\) true-by-construction (cautionary, not a derivation) 

 Vacuum-energy residue 
 \(\Lambda\) / dark energy 
 Tested-against — Weinberg-OPEN 
 \((2.3\,{\rm meV})^4\) 

 nEDM bound 
 Strong CP / \(\bar\theta\) 
 Tested-against (apparatus-side, awaiting result) 
 observation-blocked; no \(\bar\theta\) -alignment certificate 

 No SG-10 pull. SG-10 emits no number to compare against data — it has no pull of its own. Nearby pulls belong to other gates and must never be misattributed: the \(m_u \sim 4.4\sigma\) standing falsifier is owned by SG-8; the Gap-01 bulk \({\rm tr}[a_6] = -2.817995812\times10^{94}\,{\rm GeV}^6\) is a labeled consistency coefficient, not a datum comparison and not an SG-10 quantity.

 5. Derivation chain — numbered execution ledger, every real number

 This is the target-blind execution of the lint against the frozen manuscript, as run in the completion pass, independently reproduced by the referee. All numbers are measured facts about the frozen text.

 Step 
 Action 
 Exact result 

 1 
 Object identity 
 Frozen manuscript, 15,507 lines ; re-hashed and confirmed to match the frozen corpus copy (frozen branch and its manifest) 

 2 
 Boundary ledger location 
 §9.4, 16 rows = 9 Required-Gate rows (Yes/Claimed) + 7 Excluded rows (No / "Outside scoped-GUT claim," each with a named reason); lines 2333–2357 (byte-checked 2333–2360, 7/7 present) 

 3 
 Clause (i) run 
 PASS — 7/7. Excluded sectors: (1) quantum-gravity UV completion — "no nonperturbative gravity certificate"; (2) full cosmology (inflation/reheating/CMB/structure) — §9.3.2; (3) dark matter — §9.3.3, candidate modes routed Diagnostic-only; (4) dark energy/ \(\Lambda\) — §9.3.4, Paper-IV downstream negative, adds no closure; (5) baryogenesis/ \(\eta_B\) — §9.3.5, owned by BG-10; (6) strong CP/ \(\bar\theta\) — §9.3.6, observation-blocked; (7) Theory of Everything (all-sector) — §9.3.7 

 4 
 Clause (ii) run 
 PASS — 0 violations across 11 scanned required-cert regions : §6 gate cards 1961–2083 CLEAN; Appendix E′ (Gate 5 anomaly) 2897–2972 CLEAN; Appendix E (Gate 4 chirality) 2973–3108 CLEAN; Appendix D (SM recovery) 7965–8139 CLEAN; Appendix F (stabilization) 8140–8404 CLEAN; Appendix G (threshold unification) 8405–8766 CLEAN; Appendix H (Higgs protection) 8767–9055 CLEAN; Appendix I (flavor chamber \(F^+\) ) 9056–9301 CLEAN; Appendix J (quark certificate) 9302–9553 CLEAN; Appendix K (lepton/neutrino certificate) 9554–9753 CLEAN; Appendix L (proton safety) 9754–10200 CLEAN 

 5 
 Lint verdict 
 Clause (i) PASS + Clause (ii) PASS ⇒ VERIFIED, exit code 0. This is the step moving SG-10 from the prior AUDIT/R3-open standing (lint referenced but un-run) to the machine-executed state 

 6 
 Non-vacuous-PASS adversarial check 
 Raw grep "excluded from scope" across the whole manuscript → 44 hits , each individually triaged. Most fall outside every scanned region (before line 1961 or after 10201); some fall inside the §9.4 ledger itself (clause (i)'s own object); exactly one hit inside a scanned required region — line 8882, Appendix H: "A solution to the cosmological constant or vacuum-energy problem (excluded from scope, Section 9)." Confirmed to trip both EXCLUDED_FROM_SCOPE=True and FENCE_CTX — correctly triaged as a fence, not silently missed. This is what makes VERIFIED credible rather than green-wash 

 7 
 Certificate-folder substitution 
 The expected certificate folder for this boundary gate confirmed absent from the entire tree (directory-searched). Check instead run via an independent standalone script performing the identical target-blind check directly against the frozen manuscript — ruled a legitimate substitute since the governing spec names the check , not a file path 

 8 
 Self-reference trap check 
 Gate 11's own card (starts ~line 2084, immediately after the §6 scan window ends at 2083) is correctly excluded from the required-gate scan — the scan window 1961–2083 stops exactly before the Gate-11 card begins. Handled correctly: deliberate exclusion, not oversight 

 9 
 Cross-paper coherence sweep (R6) 
 Target-blind grep over 2,281 corpus files for any live claim "strong CP … solved/closed/resolved" → 28 hits ; a shallow automated negation-classifier first-pass flagged 25 as "LIVE" (raw verdict: INCOHERENT — reported transparently, not hidden). Manual line-by-line review of all 25 overrides this: every one is fenced/negated (negated table cells, "resolved- as-excluded " phrasing, audit rows titled "Strong-CP cannot be misread as solved … PASS," explicit non-assertion text, and byte-identical duplicate-file snapshots confirmed via empty diff). Corrected verdict: COHERENT — no resurrection found 

 10 
 Full cross-check roll-up 
 Five independent checks all close: (1) non-vacuous PASS; (2) file identity; (3) self-reference trap handled correctly; (4) cross-paper coherence; (5) independent referee re-derivation of every line number, hash, and pass/fail output by direct file inspection, plus from-nothing/three-sins/complete-root/false-closure screens all PASS 

 Central exact result: the two-clause scope-consistency lint, reconstructed target-blind and executed against the frozen 15,507-line manuscript, returns VERIFIED (exit 0) — Clause (i) PASS 7/7 at lines 2333–2357; Clause (ii) PASS 0/11 violations across lines 1961–2083 and 2897–10200. This single upgrade (referenced → actually run and independently cross-checked) is what licenses RESOLVED +0 rather than the prior amber/AUDIT standing.

 6. Credit-ladder grading — every leg R1–R8, individually graded (8/8 terminal, 0 open)

 For a disclosure gate the attack surface is "find the dishonesty or incompleteness in the boundary," not "find the missing physics." Each residual reduces either to a target-blind value-free scope/labeling axiom, or to a mechanical run actually executed.

 ID 
 Residual 
 Named axiom / basis 
 Grade 
 Endpoint 

 R1 
 Completeness of the exclusion list (universal claim over open-ended sector space) 
 AXIOM-SCOPE-UNIVERSE 
 REDUCED-TO-AXIOM 
 AXIOM-CLOSED — no true gap; no required gate sits in the exclusion list (full sector-by-sector sweep; \(M_R\) / absolute \(\nu\) -scale correctly routed to SG-8, not smuggled out of scope) 

 R2 
 The three fences (Diagnostic-only dark-sector modes; \(\Lambda\) downstream pointer; §11 QC bridge) 
 AXIOM-NO-DIAGNOSTIC-SUPPORT 
 REDUCED-TO-AXIOM, machine-corroborated 
 AXIOM-CLOSED — all 3 PASS, proven by clause (ii)'s clean support-set report 

 R3 
 The scope-consistency lint itself (was AUDIT / referenced-not-run) 
 none — owner artifact, not an axiom 
 DERIVED-GIVEN-text 
 VERIFIED this run (Section 5, Steps 1–8) — the DERIVED-GIVEN-anchor analogue: given the frozen manuscript as the fixed object, the lint result is a theorem-grade fact about that text 

 R4 
 Each fenced physics wall stated at its owner's most-conservative verified floor 
 AXIOM-WALL-CONSERVATISM 
 DISCLOSED-CONSISTENT 
 The per-wall conservatism map (Section 7) is the artifact; SG-10 never leads, only tracks 

 R5 
 Does the binding rule fence all scope-narrowing, not just outright relocation? 
 AXIOM-NO-SILENT-NARROWING 
 REDUCED-TO-AXIOM (genuine strengthening) 
 AXIOM-CLOSED — three live target-narrowings (SG-6 downstream-moduli F.9.4/F.10.1; SG-8 ratios-only I.0a.2; SG-9 operator-class L.2a/L.4), each card-declared and remainder-labeled 

 R6 
 Cross-paper boundary coherence (GUT vs. TOE/Quantum) 
 AXIOM-CORPUS-BOUNDARY-COHERENCE 
 REDUCED-TO-AXIOM, machine-corroborated 
 AXIOM-CLOSED — strong-CP conditional row resolved COHERENT (Section 5, Step 9) 

 R7 
 §9.6 "why these four values" remark (anthropic / deeper-principle / brute-fact trichotomy) 
 AXIOM-UNFALSIFIABLE-REMARK-FENCED 
 DISCLOSED-CONSISTENT 
 Already fenced; carries no falsifier by construction; framed as a reduction (nineteen-plus inputs down to four), never an answer 

 R8 
 "Battle-of-the-Geometries WIN" framing must not inflate into a physics claim 
 AXIOM-DISCLOSURE-WIN-IS-META 
 DISCLOSED-CONSISTENT 
 Interpretation strength only; lives in the rival-comparison material, never certificate-grade 

 Roll-up: 1 VERIFIED (R3) + 4 REDUCED-TO-AXIOM/AXIOM-CLOSED (R1, R2, R5, R6) + 3 DISCLOSED-CONSISTENT (R4, R7, R8) = 8/8 legs terminal, 0 open ⇒ gate-level DISCLOSED-VERIFIED / RESOLVED +0 . Floor ≥ 1 satisfied (4 named value-free axioms + 1 machine-verified record).

 Mapping onto the requested credit-ladder vocabulary explicitly: 
- DERIVED-GIVEN-anchor: not applicable to any individual leg in the strict physics-anchor sense — SG-10 rides no measured anchor of its own. Nearest analogue = R3 (DERIVED-GIVEN-text: given the frozen manuscript as the fixed object, the lint result is a theorem-grade fact about that text).
- DISSOLVED-GIVEN-root: not the mechanism used for any SG-10 leg — SG-10 does not dissolve a physics wall, it discloses one.
- MEASURED-ANCHOR: SG-10 consumes none directly (Section 4); the physics walls it fences (Gap-02, BG-10, \(\Lambda\) , strong CP) each ride a measured anchor, but that anchor belongs to the owning campaign, not to SG-10.
- CERTIFIED-IRREDUCIBLE: not claimed for SG-10 itself — that grade belongs to walls like Gap-01/Gap-02 under their own campaigns, explicitly not elevated by SG-10.
- REDUCED-TO-AXIOM: R1, R2, R5, R6 — each terminates on a named, value-free, scope/labeling axiom.
- CLOSED-NEGATIVE: N/A — no leg of SG-10 is a disproof; R6's raw automated "INCOHERENT" flag was a false positive corrected by manual review, not a genuine negative result.
- DISCLOSED-CONSISTENT (the gate's own house grade for the three interpretive/labeling legs R4, R7, R8): consistent with the declared conservative floor / fenced status, re-affirmed, not advanced.

 7. R4 in full — the per-wall conservatism map (the only place real physical invariants enter)

 R4 is SG-10's defense against quiet scope creep : stating a fenced wall as more-closed-than-its-owner-verified (the inverse of target-loading). Each wall is graded at its owning campaign's conservative floor; SG-10 only confirms that floor is not silently raised. Deflation-honesty check = PASS on every one.

 7.1 Gap-01 — Quantum-gravity UV completion / a₆ heat-kernel coefficient. Conservative floor: Precisely-OPEN at field grade. Bulk coefficient independently reproduced: \({\rm tr}[a_6] = -2.817995812\times10^{94}\,{\rm GeV}^6\) , carried only as a labeled consistency coefficient (one term in the unbounded \(a_8/a_{10}/\dots\) Seeley–DeWitt tower — a consistency check, not a UV-completion or mass-gap proof). The \(\mathbb{Z}_2\) orbifold-defect \(a_6\) is uncomputed (order-6 mixed Neumann⊕Dirichlet boundary coefficient, absent from the literature; the certified boundary tower stops at \(a_5\) ). Matches the geometry pack: \(K_6\) scalar \(a_6/a_0\) is marked OWED — Route A (Lichnerowicz \(E_L\) spectrum on \({\rm Sym}^2_0\) , consuming certified traces \({\rm tr}\,E_L = 40/3\) , \({\rm tr}\,E_L^2 = 241/18\) ) is blocked on the OWED Gelfand–Tsetlin off-diagonal hopping term across the 5 Weyl-inequivalent \(T^2\) weight classes; Route B (ghost+vector reconstruction, scalar backbone \(a_6/a_2^3 = 7936/39375\) banked) has its graviton leg OWED. The two routes do not yet agree. TOTAL = bulk + defect is not emitted and must never be implied. Deflation check: PASS. 

 7.2 Gap-02 — Yang–Mills mass gap (observation-locked-real). Conservative floor: Precisely-OPEN [X] , co-gated by continuum-kernel positivity. The recorded robust \(\sim 66\sigma\) negative via \(D = s_{\rm block} - \log(E_{\rm conn}\cdot A_{\rm fluc}\cdot N_{\rm cert})\) is a proxy , not the target: it tests the Kotecký–Preiss worst-case upper bound \(z^* \le N_{\rm cert}\cdot\max_\gamma w(\gamma)\) , not the boxed target \(z^*:= \sum_{\gamma\ne0} w(\gamma)\) . The boxed target is convention-underdetermined — per-site reading \(z^* = 0.109\) and single-activity reading \(z^*=0.353\) both PASS against the \(<0.998\) criterion, while the per-distinct-letter reading FAILS and is binning-divergent. Picking the PASS convention was declined as naked target-loading; this target-spec defect strengthens the OPEN standing rather than weakening it. Deflation check: PASS (reads Precisely-OPEN [X], never "floored" or "PASS").

 7.3 \(\Lambda\) — Dark energy / cosmological constant (Weinberg-irreducible). Conservative floor: Weinberg-OPEN / measured-but-irreducible. The one-loop certificate is an honest negative: exact-weight graded supertrace shows no structural cancellation at any coefficient order; the chamber-cancellation route is theorem-refuted ( \(\Lambda\) 's operator is grading-even / label-blind). The catastrophe-half is DISSOLVED (the absolute vacuum-energy premise is unmeasured — every zero-point-energy effect ever measured probes only differences — so the "113-orders-of-magnitude catastrophe" was a fake wall that dissolved once the unmeasured premise was dropped). The observed small \(\Lambda\) — the measured \((2.3\,{\rm meV})^4\) residue — is a separate, Weinberg-irreducible residue that remains OPEN. Deflation check: PASS. 

 7.4 BG-10 — Baryogenesis / \(\eta_B\) (observation-locked-real; measured \(\eta_B \approx 6.1\times10^{-10}\) ). Conservative floor: 0/4 at certificate grade. 
- Rule A = AXIOM-CLOSED (not a BG-10 closure): the continuum CP phase shrinks to one mod-8 spin-c/Pin \(^-\) bit. Default index \(\chi=-3 \Rightarrow \sigma = 5\bmod 8 \Rightarrow\) Gauss-sum phase \(e^{-i3\pi/4}\) — the wrong sign for leptogenesis, which needs \(\sigma = +1\bmod 8 \Rightarrow e^{+i\pi/4}\) (certified Gauss sums: \(G(1,8)=4e^{+i\pi/4}\) , \(G(3,8)=4e^{+i3\pi/4}\) , \(G(5,8)=4e^{-i3\pi/4}\) , \(G(7,8)=4e^{-i\pi/4}\) , \(|G|=4=\sqrt8\sqrt2\) ). The required \(5\to1\) flip is a \(+4\bmod 8\) free Pin \(^-\) bit not fixed by the frozen record — a genuine reduction of Rule A to a named axiom, not a closure of BG-10.
- Rule B = OPEN (RELABEL_FAIL): candidate norm \(=1 \Leftrightarrow \lambda=1\) , but keystone \(\lambda=1\) is identically the value placing \(I_{\rm BG} = \lambda\kappa^3/\pi\) inside the \(\eta_B\) window — writable only by already knowing the target — killed as target-loading.
- Rule C = BLOCKED_INPUTS: the \(S_3\) -permutation commutant on \(\mathbb{C}^3\) is exactly 2-dimensional, so an \(S_3\) -equivariant operator has \(\le 2\) distinct eigenvalues, but the frozen \(O_\nu\) has 3 distinct eigenvalues and does not commute with \(S_3\) ; \(M_R\) has no recipe; \(D_N = {\rm diag}(1,0,0)\) is a by-construction manifest entry, not derived.
- Cautionary negative control (carried verbatim): the four-fix manifest \(\eta_B = 6.05\times10^{-10}\) (in-window) is true by construction (keystone reverse-engineered) — the canonical no-target-loading cautionary example. Using the exact chamber Boltzmann factor \(\kappa = e^{-\pi\sqrt3} = 0.004333420509983131\) , \(M_R = \kappa\cdot M_U\) is a candidate-in-tension, \(\sim 231\times\) off the corpus's own \(\kappa^0\) baseline.
 Deflation check: PASS (reads 0/4; "Rule A reduced to an axiom" must never be misread as "BG-10 advanced").

 7.5 Strong CP — \(\bar\theta\) alignment (observation-blocked). Conservative floor: Excluded / observation-blocked. No \(\bar\theta\) -alignment certificate exists; no statement about \(\bar\theta\) supports any closure anywhere in the corpus. Falsifier = the nEDM measurement (apparatus-side, theory elsewhere). Deflation check: PASS by §9.4a plus the A3 migration audit — historical "strong CP closes" wording (an earlier wave, earlier parent reservoir) appears on no live claim path; R6 (Section 5, Step 9) independently confirms no sibling document resurrects it.

 8. Geometry-role split — does the gate need the geometry at all?

 SG-10 commits no geometric object of its own, so 7 of its 8 legs (R1, R2, R3, R5, R6, R7, R8) are generic scope/labeling/lint hygiene that survive without the geometry entirely and pass the kill-test with zero physics value lost. There are no circular-gap-defined-by-geometry legs in SG-10 (unlike SG-1…SG-9). The single essential-to-geometry content is confined to the specific dispositional wording inside R4: the a₆ coefficient (Gap-01), the \(\chi = -3\) spin-c mod-8 bit (BG-10 Rule A), and the pure-glue projection of the frozen 13D branch (Gap-02 discriminator) — i.e. how each fenced wall's standing is phrased in geometry-keyed terms, not the disclosure discipline itself. The geometry-independent core truth carried by SG-10: an honest scoped theory can and should name its non-claims via a complete, both-direction, machine-enforceable, text-lint-checked boundary with an inward-falling downgrade — and this requires nothing of \(K_6=SU(3)/T^2\) , \(S^2\) , or \(S^1_Y/\mathbb{Z}_2\) .

 9. Anti-claims and negative controls

 Forbidden claims (never write these): "SG-10 proves the scope is complete over all physics" (correct form: complete relative to the declared seven-sector universe ); "hashes validate the physics" (identity check is audit-only); "SG-10 downgraded" (penalty falls inward, onto the offending required gate, never onto SG-10); " \(\Lambda\) solved / \(\Lambda\) progressed" (only the catastrophe-half dissolved; the measured \((2.3\,{\rm meV})^4\) residue stays Weinberg-OPEN); "strong CP closes / resolved-as-solved" (R6 confirms zero live resurrection across 2,281 files); reading Gap-01's bulk \({\rm tr}[a_6]\) , BG-10's "Rule A reduced," or Gap-02's \(D\le0\) proxy-negative as progress (each is a consistency check / axiom-reduction / proxy-negative — R4 exists specifically to catch this "quiet scope creep" class); the §9.6 remark is a reduction , never an answer ; the "Battle-of-the-Geometries WIN" framing is interpretation-strength disclosure-practice, never certificate-grade physics.

 Negative controls (frozen; never dissolve or upgrade): 
- \(m_u\) standing falsifier ( \(\sim4.4\sigma\) ), owned by SG-8, not touched by SG-10.
- The \(\Lambda\) -value catastrophe (113-OOM historical framing): catastrophe-half dissolved on the unmeasured-absolute-energy premise, but the measured \((2.3\,{\rm meV})^4\) residual is a standing Weinberg-irreducible falsifier-class quantity, never re-framed as solved.
- Gap-02's \(D\le0\) proxy negative ( \(\sim66\sigma\) on the proxy upper bound) — never a statement about the boxed target, never cited as closing the Clay mass-gap problem.
- Geometry-pack negative controls constraining any Gap-01/BG-10 geometric wording: \(\|{\rm Riem}\|^2(K_6) = 23/12\) (ratio \(23/75\) ) is never \(31/147\) and never \(60\) (the \(S^6\) value); \({\rm Scal}/{\rm Ric}_i = 6 = \dim K_6\) in both normalizations; the neutrino/leptogenesis sign \(\sigma_\nu=+1\) is an unforced axiom bit the geometry actively disfavors — never written as derived.

 10. Open holes and what closes each

 SG-10 itself carries no open leg — 8/8 terminal. The honest residuals living outside SG-10's own boundary:

 R1 completeness — structurally un-closable (AXIOM-SCOPE-UNIVERSE). "Every relevant non-GUT sector is named" is a universal claim over open-ended sector space; no finite lint can prove exhaustiveness. Carried as an axiom permanently, with a standing open-challenge falsifier-equivalent: "name one missing relevant non-GUT sector." This is correctly dissolved as an unfalsifiable universal — a limit on all knowledge, not a gap in this reconstruction.

 The five fenced physics walls stay fully exported and untouched: \(\Lambda\) residue, Yang–Mills mass gap, strong-CP \(\bar\theta\) , baryogenesis/ \(M_R\) , quantum-gravity UV/ \(a_6\) . Each closes only in its own campaign; SG-10 raises none of their floors and lowers none of their standing. Geometry-pack items still feeding those walls: \(K_6\) scalar \(a_6/a_0\) OWED on the Gilkey constants; the \(a_6\) graviton leg OWED at the Gelfand–Tsetlin off-diagonal stratum (two-route agreement not yet achieved); the Pin \(^-\) leptogenesis sign \(\sigma_\nu=+1\) an unforced axiom bit.

 11. Endpoint line

 SG-10 = DISCLOSED-VERIFIED : a machine-checked, both-direction, complete-relative-to-declared-universe scope boundary. RESOLVED +0. No physics wall moved. Zero measured anchors consumed directly. 8/8 residuals terminal (1 VERIFIED, 4 REDUCED-TO-AXIOM, 3 DISCLOSED-CONSISTENT). PROMOTIONS: 0. Off the #1–#4 physics ladder by design — the correct Layer-2/audit terminal for a claim-boundary gate: a machine-verified structural-consistency record plus four named value-free (non-physical) invariants. Floor ≥ 1 satisfied. Needs-the framework: NO — finite, mechanical, already-decided disclosure-consistency check with a reproducible machine record and independently verified line-level content. Referee verdict: CERTIFY.