/gates/ ledger is the closure-of-record. The analysis below is the frozen 2026-06-29 mid-audit record, preserved verbatim; its “OPEN” sub-lemma vocabulary is the historical residual bookkeeping governed by this banner.Honest status (ratified board 2026-07-08): DERIVED-GIVEN-anchor · RESOLVED +0 — selector-minimal + functional-role-necessary (category-relative certificate; the absolute-uniqueness question is shown below as a residual, not rolled into the status). Direction: strengthened. STATUS-UPGRADES:0. This dossier reflects the gate's current honest standing; it upgrades nothing. Frozen branch
dcc66f1b2685/a5b1e6f9d951is READ-ONLY and unmutated throughout.
The 13-dimensional shape of this theory — written as the three-layer object
$$ B_{\rm active}=\underbrace{[M_4 \times K_6 \times S^2 \times S^1_Y/\mathbb Z_2]}_{\text{Stage }(\times)}\ \oplus\ \underbrace{[F^+ \oplus C_{\rm admiss}]}_{\text{Rulebook }(\oplus)}\ \otimes\ \underbrace{[E_{\rm matter}\oplus E_{\rm gauge}\oplus E_{\rm Higgs}\oplus E_{\rm proton}]}_{\text{Actors }(\otimes)} $$
— is not pulled from a hat. It is the cheapest complete survivor of a frozen, pre-declared search, and any rival theory of our world (string, spectral, discrete, SO(10)) must carry the same three working parts: a Stage, a Rulebook, and Actors. That second statement is a theorem (the functional-role necessity theorem) — but, stated honestly up front, it earns the role floor only: it forbids a competitor from deleting a role, not from realizing one more cheaply, and its proof is near-tautological (it largely restates the constraint clauses, two of which are this programme's own methodology). It is necessary-not-sufficient, not a clean architecture-neutral uniqueness result; §3.3 carries the full caveat.
What we refuse to claim is equally load-bearing: that the shape is THE unique forced geometry, derivable from a deeper law. That refusal is not a hedge — it is the ceiling, and we will show below that it is the correct ceiling because the missing claim is a universal negative over all conceivable mathematics, which is unprovable for everyone, in every field, forever.
Three results are banked (proven, at the stated scope):
SHAPE_R2_CERTIFICATE_SUITE/T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md.)…/T_SHAPE_FUNCTIONAL_ROLE_NECESSITY_THEOREM.md.) This earns the role floor only — it is necessary-not-sufficient, and we flag its near-tautological proof honestly below.…/T_SHAPE_TIER1_COMPETITOR_ELIMINATION_THEOREM.md.) This is a failure-to-find, not a no-go.What is honestly open:
SHAPE_REALIZATION_RESEED_PACKET/SHAPE_REALIZATION_DERIVATION_TARGETS.md.)…/T_SHAPE_ABSOLUTE_IRREDUCIBILITY_FORK_THEOREM.md; PER_GATE_DOSSIERS/CONSOLIDATED_OPEN_GATES_HANDOFF_2026-06-25/DEEPROOTS.md R2/R3.)Compact grade: Reduced to Axiom in the category-relative sense (SELECTOR-MINIMAL + functional-role FLOOR); realization-minimality OPEN (5 sublemmas); absolute irreducibility OPEN (permanent wall); selection ≠ derivation held; $E$ unforced / terminal-anchored.
This dossier establishes, at working-physicist depth, why the 13D shape is a serious, frozen, reproducible, load-bearing candidate; the rigorous machinery (the selector argmin, the functional-role theorem, the MDL/anti-fitting bridge, the abelian-isotropy uniqueness of $K_6$, the $\chi(K_6,E)=-3$ family count, the $\mathbb Z_6$ center-kernel); and an explicit, specialist-grade work plan for each open hole.
It does not establish that the shape is forced, uniquely derived, the unique minimum, or absolutely irreducible; that three generations / the SM content $E$ is derived; or that no Tier-1 competitor exists. The frozen documents deny all five of those claims, and so does this dossier. Selection ≠ derivation. Given-$E$ ≠ derivation-of-$E$.
No one has ever derived the Standard Model's geometry from a deeper principle — not in this program, not anywhere. The open community problem is exactly: why this matter content (three chiral generations, this gauge group, these charges) and not another?
This is the deepest unanswered question in fundamental physics framed as a problem of form. The SM has $\sim 19$–$25$ measured parameters and a specific, unexplained representation content. Grand unification (Georgi–Glashow SU(5), Fritzsch–Minkowski SO(10), $E_6$), Kaluza–Klein reductions, string/F-theory compactifications, and Connes–Chamseddine noncommutative geometry all organize that content more economically; none derives it from a principle that admits no alternative. The honest state of the art is: every framework reproduces the SM only after injecting choices (a representation, a flux, a Calabi–Yau, a finite Dirac operator) whose values are read off experiment.
The dimension-ladder MDL audit (SHAPE_REALIZATION_RESEED_PACKET/SHAPE_LADDER_MDL_VERDICT.md) scores eleven competitor presentations against the same description-length codebook, with $E$ and "$E$-automatic" facts (anomaly cancellation, written-spectrum chirality, the $\mathbb Z_6$ computation, accidental proton stability) cancelled on both sides. The honest findings, class by class:
The community gap, then, is not "which framework is prettier" but the harder one: is there a principle that forces the form, or is the form an irreducible measured input? This program's contribution is to name, fence, and honestly bound that question rather than paper over it — and to convert the unbounded version into a finite, decidable one wherever possible.
This is where the dossier lives. We build, in order: (3.1) the three-layer object and the search category; (3.2) the selector-minimality theorem; (3.3) the functional-role necessity theorem; (3.4) the granularity ⇒ MDL metric result; (3.5) the dimension-ladder MDL audit and the anti-fitting ⇄ MDL bridge; (3.6) the color rung and abelian-isotropy uniqueness; (3.7) the family count and $\mathbb Z_6$; (3.8) the realization-minimality master theorem and its five open sub-lemmas; (3.9) the Tier-1 elimination.
The active branch is a three-layer object, not a flat manifold:
$$ B_{\rm active}=[M_4 \times K_6 \times S^2 \times S^1_Y/\mathbb Z_2]_{(\times)}\ \oplus\ [F^+ \oplus C_{\rm admiss}]_{(\oplus)}\ \otimes\ [E_{\rm matter}\oplus E_{\rm gauge}\oplus E_{\rm Higgs}\oplus E_{\rm proton}]_{(\otimes)}. $$
(Source for the object: T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md §1.1, §2; consistent across the certificate suite.)
The declared scoped-GUT search category $\mathfrak B_{\rm search}$ contains candidates built from compact-factor geometries, bundle data, orbifold quotients, projectors, chamber operators, and the structural layer-moves enumerated by the selector formalism. The category is frozen — it may not be shrunk after the fact (the no-smuggling discipline). The required constraint vector is $\mathcal C_{\rm GUT}=(C_1,\dots,C_{10})$ = Gates 1–10: geometry spec; SM gauge recovery; hypercharge/electric charge; chirality / no mirrors / three families; anomaly cancellation; moduli stabilization; threshold unification; Higgs protection; flavor closure; proton safety. (Source: same theorem §2.2.)
Define the admissible set $$ {\rm Adm}(\mathfrak B_{\rm search})=\{B\in\mathfrak B_{\rm search}:\ B\models\mathcal C_{\rm GUT},\ B\ \text{obeys freeze-before-compare},\ B\ \text{obeys no-smuggling}\}, $$ and the declared lexicographic Occam ranking $\mathfrak R_{\rm Occam}$ from Appendix B1, with the binding rule that completeness outranks simplicity (a candidate may be "simpler" only after it satisfies every required constraint). The selector is $\mathcal S(B)=\operatorname*{argmin}_{B\in{\rm Adm}}\mathfrak R_{\rm Occam}(B)$.
Theorem (Selector-Minimal Shape Certificate). Under the eight stated assumptions — the declared search category, the constraint set, the Occam ranking, freeze-before-compare, no-smuggling, Appendix B2's layer-subset exhaustion, Appendix C's term-level necessity, and the Gates 1–10 certificate stack — together with the reopen condition that no preferred admissible competitor is currently known, $$ \boxed{\ B_{\rm active}=\operatorname*{argmin}_{B\in{\rm Adm}(\mathfrak B_{\rm search})}\mathfrak R_{\rm Occam}(B).\ } $$
Proof skeleton (five steps, verbatim structure from the certificate): 1. Completeness filters first. No candidate enters Occam comparison unless $B\models\mathcal C_{\rm GUT}$ — this kills the dominant smuggling error "simpler but incomplete = preferred." 2. Proper layer subsets are inadmissible. For every proper subset $L\subsetneq\{\times,\oplus,\otimes\}$, Appendix B2 asserts $\mathfrak B_L\cap{\rm Adm}=\varnothing$. So the three-layer split is not bookkeeping: $\times$ alone cannot compute $\mathbb Z_6$; $\oplus$ alone has rules but no stage/actors; $\otimes$ alone has actors but no metric arena or rulebook; the three pairwise unions each lack one indispensable function. 3. The active branch is admissible. It has claimed certificate closure for Gates 1–10 under declared assumptions, so $B_{\rm active}\in{\rm Adm}$. 4. Term-level removal fails. Appendix C gives a term authority card for each named load-bearing term $t$; removing any $t$ fails at least one required gate, so $B_{\rm active}\setminus\{t\}\notin{\rm Adm}$. The branch is term-minimal among its retained terms. 5. No preferred admissible competitor is currently supplied inside $\mathfrak B_{\rm search}$. ∎ (category-relative)
Honest scope, stated by the theorem itself: this is category-relative certified, not absolutely irreducible. It does not prove ${\rm Scale}+{\rm Granularity}\Rightarrow{\rm Shape}$, nor ${\rm CostFloor}\Rightarrow[M_4\times K_6\times S^2\times S^1_Y/\mathbb Z_2]$, nor uniqueness outside the declared category. (Source: T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md §6, §12.)
Let $\mathcal C_{\rm phys}$ be the architecture-neutral physical constraint set (the twelve clauses C1–C12: observed 4D Lorentzian sector; SM gauge recovery; hypercharge/charge; chirality/no-mirror/three families; anomaly cancellation; finite-moduli/admissibility control; coupling/threshold route; Higgs protection; flavor route with anti-fitting; proton safety; freeze-before-compare; reproducibility/certificate discipline). Define functional roles as properties any architecture could satisfy — Stage (a domain-like carrier for the 4D sector, gauge carriers, index/boundary data, low-energy comparison), Rulebook (an admissibility/selection structure), Actors (degrees of freedom carrying matter/gauge/Higgs/proton content) — and an Unfold map that extracts these roles even when a notation fuses them.
Theorem (Functional-Role Necessity). For any $B$ in the broad competitor class $\mathfrak B_{\rm abs}$, $$ B\models\mathcal C_{\rm phys}\ \Rightarrow\ {\rm Stage}(B)\neq\varnothing,\ {\rm Rulebook}(B)\neq\varnothing,\ {\rm Actors}(B)\neq\varnothing. $$
Proof (by contradiction, three steps + notation-invariance). If ${\rm Stage}(B)=\varnothing$, $B$ has no carrier for the 4D sector / gauge / index / comparison → $B\not\models\mathcal C_{\rm phys}$, contradiction. Likewise removing the Rulebook removes anomaly selection / admissibility / freeze discipline; removing Actors removes representation content / observable algebra. Finally, a notation that fuses roles (an action that both defines fields and restricts states; a spectral triple carrying geometry and matter modules; a path-integral measure restricting sectors) still contains the functional components under Unfold, so the theorem is invariant under notation. ∎
Honest caveat (we state it because the corpus review flagged it). This earns the role floor only — $k_{\rm role}\ge 3$, "necessary, not sufficient." It is not a clean architecture-neutral uniqueness theorem. The role definitions largely restate the constraint clauses (the proof is near-tautological), and two items of the constraint vector — freeze-before-compare and certificate discipline (C11, C12) — are this programme's own methodology, not constraints every theory must carry. So the architecture-neutral residue is the physics clauses (C1–C10), and the role floor is a genuine but modest result: it forbids a competitor from deleting a role, not from realizing it more cheaply. (Sources: T_SHAPE_FUNCTIONAL_ROLE_NECESSITY_THEOREM.md §8, §11 F1/F5; the handoff's "Banked" and "spine" notes.)
The whole comparison needs a metric — what does "simpler" mean across unlike architectures? The result (SHAPE_METRIC_RESULT.md):
Finite Operational Cell Law. There exists $\Delta_0>0$ such that physically distinguishable records occupy finite cells; a candidate $B$ is specified by a finite operational record string, not infinite-precision continuum data. Impose five axioms on a complexity metric $C(B)$: (1) record faithfulness (cost = cost to reproduce $T$ to resolution $\Delta_0$); (2) encoding invariance ($O(1)$ under notation change); (3) additivity of independent anchors; (4) precision monotonicity; (5) no free hidden data (fitted tables / tuned normalizations charged as information).
Theorem. The unique metric up to $O(1)$ is description length, $$ C(B)=I(B)=\min_{p:\,U(p)=T_{\Delta_0}}\ell(p)+O(1), $$ with a measured real anchor costing $\log_2(1/\Delta_0)+O(1)$ bits and a discrete structural choice (dimension, coset, quotient, index, small integer) costing $O(1)$. Hence anchor-burden dominates dimension-burden — many injected reals $\gg$ a few extra finite-dimensional labels.
Corollary (dimension-first is inadmissible as a record-cost metric). Counterexample: $B_1=$ 4D + 25 reals vs $B_2=$ 13D + 13 reals. Dimension-first calls $B_1$ "simpler" ($4<13$), but operationally $B_1$ needs $\sim 25b$ bits and $B_2$ needs $\sim 13b+O(1)$; for $b$ large, $25b\gg 13b$. So dimension-first ranks as simpler the architecture needing more finite records — it is not a record-cost metric at all.
Honest limit. PROVEN conditionally: granularity uniquely selects MDL among operational record-cost metrics. REFUTED absolutely: the cost-floor alone does not logically forbid every non-MDL aesthetic preorder. Closing the gap needs one extra, natural bridge axiom: physical simplicity = minimal injected operational record cost. This is arguably the right reading of granularity, but it is an added interpretive principle, stated explicitly — never smuggled. (Source: SHAPE_METRIC_RESULT.md, Theorem + Verdict.)
Writing each candidate's fully-charged cost as $I(B)=I_{\rm struct}+I_{\rm gen}+n\cdot b+I_{\rm extra}$ with $b=\log_2(1/\Delta_0)$, the decisive per-rung inequality is
$$
\boxed{\ \forall D=4..12\,(+\,\text{non-dim}),\ \forall j:\quad I_{\rm gen}(B_{13})+n_{13}\,b\ <\ I_{\rm gen}(B_{D,j})+n_{D,j}\,b\ +\ I_{\rm extra}(B_{D,j}).\ }
$$
Because the anchor term $n\cdot b$ dominates, the inequality is decided to first order by injected-real counts, with $n_{13}\approx 13$–$14$. The per-rung tally (eleven presentations, same codebook, $E$ cancelled): 0 REFUTED, 1 FAILS_TO_GENERATE_T (6D, structural — no 2-manifold isometry contains $SU(3)_c$), 10 LOSES_TO_13D. The two near-ties (10D heterotic at $\Delta\text{reals}\sim 0$–$2$) are broken by the structural-bit term $I_{\rm struct}$ (CY + bundle + quotient catalog $\gg$ a handful of named cosets). (Source: SHAPE_LADDER_MDL_VERDICT.md §1, §2.1; all counts traceable to that table.)
The key insight — the anti-fitting eliminations ARE MDL eliminations. The selector eliminates a competitor by the anti-fitting rule: a constraint the geometry delivers only as a tunable number is a FAIL ("adjustable = fail"). Independently, the MDL codebook charges a fitted/tuned normalization at $\approx$(entries)$\times b$ — like an anchor. These are the same statement:
A tunable match cannot be counted as a prediction; the tuned value must be injected as a measured real; an injected real costs $\sim b$ bits; therefore a tunable match lengthens the description. Anti-fitting $\equiv$ MDL, exactly when the metric is description-length.
This is the load-bearing bridge across the entire table, and it is what makes "13D beats the considered competitors" a real result and not a tautology of the selector's own preferences: the win is adjudicated by the description-length codebook, which charges the 13D branch and every competitor by the same rule, with $E$ and $E$-automatic facts cancelled on both sides. 13D's genuine economy is localized exactly where the bridge rewards it: the family count is a forced topological integer $\chi(K_6,E)=-3$ from Borel–Weil–Bott ($O(\log)$ bits), and gauge-coupling unification closes $\alpha_i$ to one anchor net of the $\delta$ threshold counter-charge. Those are forced integers/closures the competitors must instead buy with injected reals. (Source: SHAPE_LADDER_MDL_VERDICT.md §3.)
The single most-scrutinized rung is color: is $K_6=SU(3)/T^2$ (6D) the cheapest $SU(3)$ carrier, or does $CP^2=SU(3)/U(2)$ (4D) win on dimension? This is the program's honest weak link, and the corpus traces a genuine adversarial sequence here — worth reading in full because it is where the discipline shows.
Step 1 — CP² is the genuine dimensional floor. A compact $SU(3)$-homogeneous carrier is $M=SU(3)/H$, $\dim M=8-\dim H$. For $\dim M<6$ we need $\dim H>2$; the connected closed subgroups are $U(2),SU(2),SO(3)$:
| Carrier | Form | dim | Chiral index? |
|---|---|---|---|
| CP² | SU(3)/U(2) | 4 | yes — Spin$_c$ Dirac index |
| S⁵ | SU(3)/SU(2) | 5 | no (closed odd-dim) |
| Wu manifold | SU(3)/SO(3) | 5 | no (closed odd-dim) |
| K₆ | SU(3)/T² | 6 | yes — Spin$_c$ / BWB index |
So CP² is the minimal-dimension $SU(3)$ carrier; the sub-6D rivals die by odd-dimensionality. (Source: SHAPE_COLOR_RUNG_CP2_REFUTATION.md §1.)
Step 2 — CP² gives exactly 3, discretely. CP² is Spin$_c$ with $c_1(\mathcal L)=(2r+1)H$; the 4-manifold Spin$_c$ index is $\mathrm{ind}=\frac{c_1^2-\sigma}{8}=\frac{(2r+1)^2-1}{8}=\frac{r(r+1)}{2}$ (using $\sigma(\mathbb{CP}^2)=1$), and $r=2\Rightarrow\mathrm{ind}=3$. This is a discrete topological integer, not a continuous modulus — so the corpus's original "tunable real" dismissal of CP² was mathematically wrong as stated. This program found and recorded that defect against itself. (Source: same file §2.)
Step 3 — the symmetric blow. $K_6$ also yields 3 only after a bundle/weight choice: Borel–Weil–Bott gives $\mathrm{ind}(L_{a,b})=\pm\frac{(a+1)(b+1)(a+b+2)}{2}$, and $(a,b)=(1,0)$ or $(0,1)\Rightarrow|\mathrm{ind}|=3$. So the carrier-plus-bundle comparison is symmetric: neither carrier forces "3" from the bare carrier alone. The anti-fitting dismissal of CP² holds only if an extra architecture-neutral admissibility theorem is supplied. The intermediate honest standing was therefore: the color rung folds to CP²; SHAPE is selected, not forced. (Source: same file §3–§4; SHAPE_FINAL_STATUS_SPLIT_RESULT.md struck-through sentence, kept on record.)
Step 4 — the 11D CP² build, end-to-end, BREAKS (the resolution). The K₆→CP² swap was built adversarially and full-stack (ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md). It breaks at Gate 2 (the gauge group) for a real structural reason, supplying exactly the non-target-fitted exclusion principle the earlier step demanded:
Abelian-isotropy uniqueness. Among $SU(3)$ cosets $SU(3)/R$, the maximal torus $T^2$ is the unique isotropy that is purely abelian ($C_{SU(3)}(T^2)=T^2$, Cartan only) — injecting no spurious non-abelian factor and keeping color/weak/hyper separable. CP²'s isotropy $U(2)=(SU(2)\times U(1))/\mathbb Z_2$ is non-abelian and a subgroup of color $SU(3)$; by the CSDR centralizer rule it is gauge-active, forcing a lose-lose fork: keep $S^2,S^1$ → over-produce an extra $SU(2)+U(1)$ (Gate-2 equality fails); drop them → $SU(2)_L/U(1)_Y$ isotropy-locked inside $SU(3)$ ($C_{SU(3)}(U(2))=U(1)$ only, Schur — binding A1.4 violated). So $K_6=SU(3)/T^2$ is the unique clean $SU(3)$ color carrier, from representation theory + the centralizer rule alone, not reverse-engineered, and stronger than the corpus's original "tunable family count" reason.
The per-requirement scorecard against the 10 requirements records exactly where CP² breaks (requirements 1, 2, 8, 9 BREAK; 3 BREAKS/OPEN-tunable; 4, 7 cohere as $E$-properties; 5 coheres as an $E$-property but BREAKS as a three-independent-center closure; 6 OPEN/mixed; 10 partial) — and an explicit anti-rig-to-fail check confirms CP²'s $E$-properties genuinely pass ($Q=T_3+Y$ for all 7 charge eigenstates; $\mathbb Z_6$ kernel cyclic order-6; all six anomaly coefficients $=0$) and were not rigged to fail. The break is located precisely where it is real. (Source: ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md §2 per-requirement scorecard and the anti-rig-to-fail check.)
The two architecture-neutral whole-shelf facts (the genuinely strong rungs). Two of the three internal dimensional choices are forced by general theorems that close entire shelves, not named competitors: - S² (weak, 2D) — general fact F1: no abelian/torus carrier of any dimension has non-abelian $SU(2)$ among its isometries → the cheaper direction is closed for all carriers. - S¹$_Y$/$\mathbb Z_2$ (hyper, 1D) — general fact F2: a closed odd-dimensional factor keeps both handednesses → mirror fermions → excluded by the LEP $Z$-width → closes all cheaper carriers. - M₄ (4D) — declared, not selected: an observational primitive, not a forced rung.
Sharper honest claim: two of the three internal dimensional choices (weak, hyper) are forced by general theorems; the color choice is the single weak link, now closed for $K_6$ by abelian-isotropy uniqueness — but only over the named/enumerated shelf; completeness over all admissible $SU(3)$ carriers is uncertified (the GUT.md candidate-geometry enumeration is the Appendix N.4 historical branch-elimination archive, and GUT.md's own honesty note — "minimality is only meaningful inside the declared search category; reviewers should test whether the category excludes natural competitors", GUT.md:382 — flags exactly this scope limit). (Sources: SHAPE_FINAL_STATUS_SPLIT_RESULT.md forcedness gradient + REVISED STANDING; SHAPE_LADDER_MDL_VERDICT.md §2.2, §4.)
Given $E$, the family count is a forced topological integer, not a fit: $\chi(K_6,E)=-3$ (BWB / Spin$_c$ index with weight $(1,0)$) → exactly three generations. The center structure lands on the actor layer:
$$
\mathbb Z_6=\ker(Z(G_0)\to\mathrm{Aut}(E)),
$$
a read-off of the matter content (not posited), one layer downstream of where anomaly admissibility shapes $E$ in $C_{\rm admiss}$. This is precisely why the full three-layer object must be carried unflattened: $\times$ alone cannot compute $\mathbb Z_6$. Crucially: $\chi(K_6,E)=-3$ gives three families given $E$; it does not select $E$. Family replication, like the spectrum, traces back to $E$. (Sources for $\chi(K_6,E)=-3$: SHAPE_COLOR_RUNG_CP2_REFUTATION.md §3 (BWB index), ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md §2 line 119, SHAPE_LADDER_MDL_VERDICT.md §3 line 147; for the $\mathbb Z_6=\ker$ result: T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md §1.5; for "three families is $E$-forced not geometry-forced": SHAPE_COLOR_RUNG_CP2_REFUTATION.md §4; DEEPROOTS.md R4.)
The architecture-neutral upgrade ("no competitor anywhere is shorter after unfolding") is a valid conditional proof skeleton. For the universal competitor class $\mathfrak B_{\rm abs}$, the architecture-neutral constraints $\mathcal C_{\rm phys}$, and the unfolded preorder $\preceq_{\rm abs}$: $$ \forall B\in\mathfrak B_{\rm abs},\ B\models\mathcal C_{\rm phys}\ \Rightarrow\ \mathrm{Unfold}(B_{\rm active})\preceq_{\rm abs}\mathrm{Unfold}(B),\quad\text{i.e.}\quad B_{\rm active}=\operatorname*{argmin}_{B\in{\rm Adm}(\mathfrak B_{\rm abs})}\mathfrak K(\mathrm{Unfold}(B)). $$ The skeleton reduces this to five sub-lemmas, all currently OPEN (recommended attack order: Lemma 3 → 1 → 2 → 4 → 5):
Gate 0 (mandatory precondition for every lemma). Before proving any minimality lemma, state its role-requirement architecture-neutrally — with no hidden reference to the submitted factor set, to $F^+$, or to $E$. If a requirement can only be phrased by pointing at the submitted branch, the lemma is circular (F6) and does not count. (Source: SHAPE_REALIZATION_DERIVATION_TARGETS.md Gate 0, Lemmas 1–5, falsifiers F1–F6, success ladder.)
A first-pass specialist attack on Lemma 2 (rulebook minimality) was run target-blind under STATUS-UPGRADES:0 and checked by a hostile verifier. Verified outcome: REFUTED (Lemma-2-as-stated). The verifier caught an OVERCLAIM in the optimistic first draft — recorded here so the next specialist does not repeat it. The sound, corpus-corroborated content:
Architecture-neutral filtering of the rulebook's duties splits them into three classes:
- (A) CLASS-GOVERNANCE {freeze-before-compare, gate-status, anti-fitting} = method, excluded by Gate 0. (Matches SHAPE_REALIZATION_DERIVATION_TARGETS.md L87-90: "governance rules, not architecture-neutral physics … only count the physics burden.")
- (B) CLASS-E-AUTOMATIC {anomaly firewall} = an $E$-property, not a rule-burden and not a discriminator: all six anomaly coefficients $=0$ (ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md L202), and SHAPE_LADDER_MDL_VERDICT.md L24 treats anomaly cancellation as "free for both" / cancels — zero differential burden.
- (C) The only architecture-neutral physics residue is the flavor chamber $F^+$. Two traceable findings: (i) hardening $F^+$ to a certificate fails — its sector normalizations $N_d, N_e, N_\nu$ are, verbatim in GUT.md, $N_d$ "defined to set $m_b$ to its target value at $M_Z$" (L4469) and $N_e$ "chosen such that $m_\tau$ matches its target value" (L4470), demoted to "calibration in disguise" per the I.0a.2 Binding Downgrade Rule (L9095/L9151/L9161); so $F^+$ injects 3 reals it does not derive. (ii) The F2 falsifier materializes: the ordinary 4D SM rulebook {renormalizable gauge invariance + $E$-automatic anomaly cancellation} carries strictly lower architecture-neutral $k_{\rm rule}$ (it has no flavor chamber — flavor sits in the actor/Yukawa layer) and is admissible. This is the corpus's own SPLIT_RESULT line 30: "A shorter weak-target competitor exists: YES … the ordinary 4D SM/EFT … wins only because it does not generate $T$."
Therefore $F^+ + C_{\rm admiss}$ is not the rule-burden argmin → Lemma-2-as-a-standalone-closure is REFUTED. The defensible residual survives unchanged and is now sharply named (see §6, Hole 2): Lemma 2's content folds into Lemma 4 (the joint no-cross-role-compression claim — the SM's lower $k_{\rm rule}$ is offset by higher $k_{\rm actor}$, so total unfolded burden is not lower) plus the $E$ residual (the 3 injected $N_d,N_e,N_\nu$). A precise negative beats a vague pass: this REFUTATION is a real result that hardens the program by relocating the live claim to where it actually lives. (Source: PLUG_RESULTS_FIRSTPASS_2026-06-29.md "DeepRoot-shape / Lemma 2" entry, all line citations as printed there.)
The competitor audit matrix (SHAPE_COMPETITOR_AUDIT_MATRIX.md) converts "no preferred competitor is currently supplied" into a finite review program over 17 named classes, ranked into tiers. The five Tier-1 classes — (1) spectral triple / NCG, (2) traditional KK alternatives, (3) string/F-theory, (4) finite-state/discrete, (5) SO(10)/exceptional GUT — are the most dangerous because they plausibly carry all three roles.
Theorem (Tier-1 Competitor Elimination, current-record). For every $B'$ in the Tier-1 set, the current audit record shows at least one of: $B'\not\models\mathcal C_{\rm phys}$ at certificate level; lacks freeze/anti-fitting/reproducibility discipline; not simpler after unfolding; under-specified relative to the gate burden; or remains a serious audit candidate but is not a supplied preferred competitor. Hence
$$
\nexists\,B'\in\mathcal T_1\ \text{currently supplied with}\ B'\models\mathcal C_{\rm phys}\ \text{and}\ B'\prec_{\rm abs}B_{\rm active}.
$$
"QED-current-record." Each class keeps an explicit reopen condition (e.g. NCG reopens if a spectral package supplies $\mathcal C_{\rm phys}$ with lower unfolded burden after Unfold). This is not a universal nonexistence proof — every Tier-1 class remains a SERIOUS AUDIT CANDIDATE with its "simpler-after-unfolding" cell Unknown. (Source: T_SHAPE_TIER1_COMPETITOR_ELIMINATION_THEOREM.md §3, §4.1–4.5, §7.)
These are the specific moves that produced the progress and make it reproducible.
Convert the universal negative into a finite, decidable problem by declaring the grammar. "No competitor anywhere is shorter" is a universal negative over all conceivable architectures, hence uncomputable (Kolmogorov). Declaring the finite role-mechanism grammar $\mathcal G$ turns it into a finite lower-bound matrix over finitely many normal-form classes. That conversion is the achievement — it does not by itself close the matrix, and we never pretend it does. The honest object that remains is a checklist, not a universal negative. (SHAPE_FINAL_STATUS_SPLIT_RESULT.md, "the deep move".)
Anti-fitting ≡ MDL. The selector's "adjustable = fail" rule and the description-length codebook's "charge a tuned normalization like an anchor" are the same statement. This single bridge makes every "loses to 13D" verdict non-circular — the win is adjudicated by a metric that charges all candidates identically, with $E$ cancelled. (§3.5.)
Forced-integer vs injected-real is the whole edge. 13D's economy is exactly that the family count is a forced topological integer ($\chi=-3$, $O(\log)$ bits) and unification closes $\alpha_i$ to one anchor — quantities competitors must instead buy with injected reals. The economy is measured, not assumed, and it is modest (~9–10 reals, not the discredited "18").
Abelian-isotropy uniqueness beats "tunable family count." The original CP² elimination ("tunable") was unsound (the index is a discrete integer). The program found that defect against itself, then replaced it with a stronger, structural reason: $T^2$ is the unique purely-abelian $SU(3)$ isotropy ($C_{SU(3)}(T^2)=T^2$), so it injects no spurious non-abelian gauge factor, while $U(2)$ is gauge-active and forces a lose-lose fork. This is rep theory + the CSDR centralizer rule, not reverse-engineering. (§3.6.)
Roles cannot be deleted, only relabeled. The Unfold map turns "I removed the rulebook" into "the rulebook is hidden inside your action/measure/functor." This defeats the cheapest class of false simplifications and is why the functional-role floor is genuine even though it is modest. (§3.3.)
Selection ≠ derivation, enforced as a hard rule. "Funnel-winner-forced = RELABEL = REJECTED" (AXIOM_LEDGER lines 126/186, per the handoff). No status was ever upgraded; the frozen branch was never mutated. This discipline is why the honest grade is believable.
| Artifact | What it proves / records | Path |
|---|---|---|
| Selector-minimality theorem | $B_{\rm active}=\operatorname{argmin}$ inside $\mathfrak B_{\rm search}$ (category-relative) | SHAPE_R2_CERTIFICATE_SUITE/T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md |
| Functional-role necessity theorem | $\mathcal C_{\rm phys}\Rightarrow$ Stage+Rulebook+Actors (role floor) | …/T_SHAPE_FUNCTIONAL_ROLE_NECESSITY_THEOREM.md |
| Tier-1 elimination theorem | no Tier-1 preferred competitor currently survives | …/T_SHAPE_TIER1_COMPETITOR_ELIMINATION_THEOREM.md |
| Absolute-irreducibility fork theorem | absolute irreducibility OPEN; defines the 6 missing objects | …/T_SHAPE_ABSOLUTE_IRREDUCIBILITY_FORK_THEOREM.md |
| Realization-minimality master + sub-lemmas | conditional skeleton; 5 sub-lemmas all OPEN | …/T_SHAPE_REALIZATION_MINIMALITY_THEOREM.md; SHAPE_REALIZATION_RESEED_PACKET/SHAPE_REALIZATION_DERIVATION_TARGETS.md |
| Competitor audit matrix (+ CSV) | 17-class finite review program | …/SHAPE_COMPETITOR_AUDIT_MATRIX.md (+ .csv) |
| Metric-selection result | granularity ⇒ MDL (conditional on bridge axiom) | SHAPE_REALIZATION_RESEED_PACKET/SHAPE_METRIC_RESULT.md |
| Ladder MDL verdict | per-rung audit; CATEGORY_RELATIVE |
…/SHAPE_LADDER_MDL_VERDICT.md |
| Color rung CP² refutation | the weak link; symmetric blow + bundle-admissibility question | …/SHAPE_COLOR_RUNG_CP2_REFUTATION.md |
| 11D CP² build | end-to-end break of K₆→CP² (abelian-isotropy uniqueness) | …/ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md |
| Final status (split result) | the capstone honest conclusion | …/SHAPE_FINAL_STATUS_SPLIT_RESULT.md |
| Gate roll-up | per-residual ledger R1–R7 | PER_GATE_DOSSIERS/CONSOLIDATED_OPEN_GATES_HANDOFF_2026-06-25/DEEPROOTS.md |
ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md line 119; ladder verdict §3 line 147. (The $\mathbb Z_6=\ker$ result — not the $\chi=-3$ count — is the part carried by selector theorem §1.5.)Numbers we explicitly do NOT assert (marked OPEN, never fabricated): any "absolute minimal dimension" certificate; any number claiming $E$ is derived; any "unique-minimum" count. The $a_6$/$\mu_{\rm cell}$ computational debts belong to other gates (SG-6, Born) and are not load-bearing for the SHAPE grade — they are flagged OPEN there, not imported here.
ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md.)dcc66f1b2685 / a5b1e6f9d951) with an independent blind reproducer. This is a reproducibility check, not a uniqueness proof; it lowers no assumption floor. (DEEPROOTS.md R7.)Six work-packages. Each is a concrete object a specialist can pick up. Recommended order: Hole 3 (Actors) → Hole 1 (Stage) → Hole 4 (No-compression metric) → Hole 2 (Rulebook residual) → Hole 5 (No-competitor audit) → Hole 6 ($E$, declare). Read SHAPE_REALIZATION_DERIVATION_TARGETS.md first; Gate 0 is mandatory for every lemma.
(a) Precise statement. Prove $\mathrm{Actors}=E_{\rm matter}\oplus E_{\rm gauge}\oplus E_{\rm Higgs}\oplus E_{\rm proton}$ is the minimal actor realization satisfying matter content · gauge field content · Higgs/Wilson-line route · proton-safety projector · observable/effect-algebra support · $\mathbb Z_6$ center-kernel — i.e. no admissible competitor supplies lower unfolded $k_{\rm actor}$ while preserving all six.
(b) Why it's hard / traps. The $\mathbb Z_6$ result already lands here, so it is the narrowest target. The trap is the "minimal given $E$" weakening: the minimal spectrum must be stated without naming the SM reps a priori — if you name them you have proven "minimal given $E$," which is weaker and must be flagged. The $\mathbb Z_6$ must be read off as $\ker(Z(G_0)\to\mathrm{Aut}(E))$ (it is), not posited. Do not import freeze/certificate discipline as actor requirements (Gate 0 / F6 circularity). Do not charge $E$-automatic facts (anomaly cancellation) as differential burden — they cancel.
(c) Exactly what closes it. A no-alternative proof that no representation content cheaper than $E$ reproduces SM matter + gauge + Higgs/Wilson-line + proton-safety + the $\mathbb Z_6$ center-kernel; success criterion = architecture-neutral lower bound $k_{\rm actor}(B')\ge k_{\rm actor}(B_{\rm active})$ for all admissible $B'$. Refuting result (equally valid): exhibit cheaper admissible actors (falsifier F3) → Lemma 3 fails fast → realization-minimality fails fast. The realistic near-term best outcome is "reduced to minimal-given-$E$, with $E$ named as the irreducible residual."
(d) Machinery & inputs. Borel–Weil–Bott index theory; the Born/center work for the $\ker$ computation; SHAPE_REALIZATION_DERIVATION_TARGETS.md Lemma 3; the $\mathbb Z_6$ verification in ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md (line 200) and T_SHAPE_SELECTOR_MINIMALITY_CERTIFICATE_THEOREM.md §1.5.
(e) Leverage. Closing (or refuting) Hole 3 strengthens both SHAPE and the granularity root; it is the keystone for the realization-minimality stack and partly supplies Lemma 4's actor side.
(a) Precise statement. Prove no admissible competitor realizes the Stage role (4D Lorentzian sector + $SU(3)/SU(2)/U(1)_Y$ carriers + chirality/index route + boundary/orbifold projector + low-energy comparison surface) with lower unfolded burden $(k_{\rm dim},k_{\rm factor},k_{\rm top})$ than $M_4\times K_6\times S^2\times S^1_Y/\mathbb Z_2$.
(b) Why it's hard / traps. Two of three internal rungs are already whole-shelf closed (S² by F1, S¹$_Y$/$\mathbb Z_2$ by F2; §3.6). The color rung is closed for $K_6$ by abelian-isotropy uniqueness but only over the named/enumerated $SU(3)$-carrier shelf — completeness over all admissible $SU(3)$ carriers is uncertified (the enumeration is the Appendix N.4 branch-elimination archive; GUT.md:382 is the search-category honesty note that flags this scope limit). Trap: stating "color carrier" as "must be $SU(3)/T^2$" is F6-circular; state it as "a faithful action of the gauge content realizable by any geometry." Trap to avoid (named, verifier-relevant): the original "tunable family count" elimination of CP² was unsound (the index is discrete, not continuous) — do not resurrect it; the correct exclusion is abelian-isotropy uniqueness.
(c) Exactly what closes it. A theorem (or finite competitor-by-competitor lower-bound matrix) showing every architecture-neutral Stage carrying the required carriers + chirality route has complexity vector $\ge$ the frozen stage — subsuming the N.4-completeness of the $SU(3)$-carrier sub-shelf. Success criterion: the lower-bound holds for all admissible carriers, not an enumerated shelf. Refuting result: exhibit a cheaper admissible stage (falsifier F1) → Stage minimality fails / narrows.
(d) Machinery & inputs. Homogeneous-space classification ($M=SU(3)/H$, $\dim H$ analysis, §3.6 table); CSDR centralizer rule; Spin$_c$/BWB index; F1/F2 general facts; SHAPE_COLOR_RUNG_CP2_REFUTATION.md; ELEVEN_D_CP2_VARIANT_CONSTRUCTION.md; SHAPE_FINAL_STATUS_SPLIT_RESULT.md forcedness gradient.
(e) Leverage. Closes the dimension-ladder's last open rung in the strong (whole-shelf) sense; combined with O2 (metric) it would upgrade the ladder verdict from CATEGORY_RELATIVE to LADDER_FORCED given-$E$.
(a) Precise statement. Define a formal, architecture-neutral complexity metric $\mathfrak K(\mathrm{Unfold}(B))$ and prove it is non-decreasing under role-fusion: $\mathrm{Unfold}(B')\succeq(\mathrm{Stage}+\mathrm{Rulebook}+\mathrm{Actors})$ for every $B'\models\mathcal C_{\rm phys}$ — so a notation that appears simpler only by hiding one role inside another has no lower unfolded burden.
(b) Why it's hard / traps. This lemma is the no-smuggle metric, so it must be made precise without presupposing the submitted factor set (Gate 0). It is the object the Lemma 2 REFUTATION folds into (§3.8.1): the SM has lower $k_{\rm rule}$ but the claim is that it is exactly offset by higher $k_{\rm actor}$ (flavor relocated into Yukawas), so total unfolded burden is not lower. The trap is asserting that offset by feel — it must be a theorem about the metric, not an example.
(c) Exactly what closes it. A proof that $\mathfrak K$ is invariant under the Stage↔Rulebook↔Actors fusion moves (a conservation law for unfolded burden). Success criterion: for the SM-vs-13D comparison specifically, show $k_{\rm rule}(\text{SM})+k_{\rm actor}(\text{SM})\ge k_{\rm rule}(F^+)+k_{\rm actor}(B_{\rm active})$ on the full-$T$ ledger given $E$. Refuting result: a competitor genuinely lower in total unfolded burden → SHAPE narrows.
(d) Machinery & inputs. Description-length / MDL codebook (SHAPE_METRIC_RESULT.md, DIMENSION_LADDER_MDL_AUDIT_CERTIFICATE.md); the Unfold map (T_SHAPE_FUNCTIONAL_ROLE_NECESSITY_THEOREM.md §4); the first-pass Lemma-2 analysis and its residual R-L2a (PLUG_RESULTS_FIRSTPASS_2026-06-29.md); SHAPE_REALIZATION_DERIVATION_TARGETS.md Lemma 4.
(e) Leverage. This single metric underwrites Lemmas 1, 2, 3, and 5 — it is the common no-smuggling foundation for the whole realization-minimality stack.
(a) Precise statement. Lemma-2-as-stated ($F^+ + C_{\rm admiss}$ as a standalone within-role minimal-rulebook certificate) is REFUTED (§3.8.1). The live residuals are: (R-L2a) the joint no-cross-role-compression claim (= Hole 4); (R-L2b) the 3 injected sector normalizations $N_d,N_e,N_\nu$ are an irreducible injection inside $F^+$ ($F^+$ predicts ratios, not scales) — so even the generator claim bottoms on $E$ plus these 3 reals; (R-L2c) "no cheaper admissible rulebook anywhere" is the same Kolmogorov wall as R2 and stays OPEN/uncomputable.
(b) Why it's hard / traps (named, from the verifier). The verifier caught an OVERCLAIM in the first-pass draft — the trap is presenting the REFUTATION as if it strengthens the standalone Lemma 2; it does not. $F^+$ is the program's acknowledged weakest link ("is the flavor chamber a real derivation, or compressed curve-fitting?"). Do not try to harden $F^+$ to a within-role certificate — its $N_d,N_e$ are calibration-in-disguise (GUT.md L4469/L4470, demoted per I.0a.2). Do not charge governance or $E$-automatic facts as rule-burden (they are excluded by Gate 0 / cancel).
(c) Exactly what closes the residual. R-L2a closes iff Hole 4's no-smuggling metric closes. R-L2b closes only by declaring $N_d,N_e,N_\nu$ as part of the $E$-anchor injection (terminal-by-anchoring), not by deriving them. R-L2c is terminal-as-OPEN (folds into Hole 5 / R2). Refuting result: a genuinely cheaper admissible full-$T$ rulebook → SHAPE folds.
(d) Machinery & inputs. PLUG_RESULTS_FIRSTPASS_2026-06-29.md "DeepRoot-shape / Lemma 2"; GUT.md L4469/L4470/L9095/L9151/L9161; SHAPE_FINAL_STATUS_SPLIT_RESULT.md line 30; SHAPE_COMPACT_GENERATOR_CERTIFICATE_ATTEMPT.md (injected reals #5/#6/#7).
(e) Leverage. Confirms the honest comparison is the joint Stage+Rulebook+Actor ledger (13D "unrefuted but not certified") — keeps the program from over-claiming a within-role rulebook win it does not have.
(a) Precise statement. Elevate "none currently supplied" to a checked lower-bound across the five Tier-1 classes with their reopen conditions discharged: for each class, supply the unfolded complexity vector and show it cannot drop below $B_{\rm active}$'s under any admissible parameter choice (a finite per-class lower-bound matrix).
(b) Why it's hard / traps. This is a universal negative — honest odds LOW; attempt last. The F5 caveat: if $\mathfrak B_{\rm abs}$ excludes a natural competitor, the result downgrades to category-relative — so the audit's coverage must be argued, not assumed. Trap: claiming "no Tier-1 competitor exists" — the theorem only says none currently supplied; every class stays a SERIOUS AUDIT CANDIDATE with an Unknown "simpler-after-unfolding" cell. The most dangerous class is finite-state/discrete (it could collapse Granularity + Shape together) and NCG (already role-like).
(c) Exactly what closes it. A finite per-class lower-bound matrix discharging each reopen condition. Success criterion: every Tier-1 class's unfolded vector provably $\ge B_{\rm active}$. Refuting result (valuable): surface a preferred competitor (falsifier F2/F4) → SHAPE folds; if that competitor is derivable from Scale+Granularity, the residue drops — the correct compression outcome.
(d) Machinery & inputs. SHAPE_COMPETITOR_AUDIT_MATRIX.md (the 17-class program + scorecard template §6); T_SHAPE_TIER1_COMPETITOR_ELIMINATION_THEOREM.md (reopen conditions per class); the Unfold map; the no-smuggling metric from Hole 4 (prerequisite).
(e) Leverage. Closing Hole 5 (with Holes 1, 3, 4) is the full realization-minimality result; it is the only path from CATEGORY_RELATIVE toward architecture-neutral forcing — and a refutation here is the most likely route by which Shape honestly folds toward Granularity.
(a) Precise statement. The selection bottoms on $E$ (the SM chiral spectrum / exactly three generations), which no known principle forces.
(b) Why it's hard / traps. Anomaly-freedom is a settled FILTER with infinitely many solutions; "$E$ is forced" is REFUTED. The trap (named): asking us to forcibly derive $E$ is asking for a refuted unicorn — a universal-implication claim over all structures. $\chi(K_6,E)=-3$ gives three families given $E$; it does not select $E$. The CP² work deepened this: because "3" requires a chosen bundle on both carriers, even the generation count is $E$-derived, not geometry-forced.
(c) Exactly what closes it. Either (i) a principle that forces exactly three chiral generations and no other family count as admissible (an anomaly/index argument with a unique solution — note the filter has infinitely many, so this is a strong, possibly-false target); or (ii) — the honest expected outcome — an explicit statement that $E$ is the irreducible measured-anchor content of SHAPE (terminal-by-anchoring). A refutation of (i) is itself a valid close: it confirms $E$ as the anchor.
(d) Machinery & inputs. Anomaly-cancellation literature (the filter, infinitely many solutions); BWB / Spin$_c$ index ($\chi=-3$ given $E$); SHAPE_COLOR_RUNG_CP2_REFUTATION.md §4 ("three families is $E$-forced, not geometry-forced"); DEEPROOTS.md R6 (the ~9–10 injected quantities banked as input).
(e) Leverage. Declaring $E$ terminal-anchored closes the honest residual of the whole gate: it is the floor that all five lemmas bottom on. Anchored ≠ derived — the floor stays at $\ge 1$ measured anchor (here $E$), by design, forever.
Three claims are universal negatives over all conceivable mathematics; they are unprovable for everyone, in any field, forever — limits on all knowledge, not gaps in ours:
This gate is falsifiable, on purpose, in two independent ways:
(a) Name a cheaper architecture. Name one architecture that meets the same physical burden $\mathcal C_{\rm phys}$ and is strictly simpler after you expand its hidden machinery (Unfold), and the shape folds. This is the bounded, current-record Tier-1 audit; "none currently survives" is a failure-to-find, never a proof that none exists.
(b) The $E$ anchor. The shape bottoms on $E$. We do not claim a principle forces $E$ — anomaly-freedom is a settled filter with infinitely many solutions, and "$E$ is forced" is refuted. So $E$ is named as the irreducible measured-anchor of SHAPE, terminal by anchoring. Asking us to forcibly derive $E$ is asking for a refuted unicorn; the honest residual is to declare it, not to plug it.
The one-line honest top line: Inside the declared scoped-GUT grammar and under the granularity-induced MDL metric, the 13D three-layer shape is the selector-minimal complete survivor and any admissible theory must carry the same three roles — but it is selected, not forced; category-relative certified, not absolutely irreducible; and it bottoms on $E$, which is the measured anchor of SHAPE. Serious candidate, frozen, reproducible, load-bearing — NOT validated, NOT proven unique. STATUS-UPGRADES:0.
Dossier built 2026-06-29 by synthesis + expansion of the frozen SHAPE corpus (the SHAPE_R2_CERTIFICATE_SUITE, the SHAPE_REALIZATION_RESEED_PACKET, the gate roll-up DEEPROOTS.md, and the first-pass plug results). Every number is traceable to a cited file actually read; uncomputed quantities are marked OPEN, never fabricated. Frozen branch dcc66f1b2685 / a5b1e6f9d951 READ-ONLY and unmutated. STATUS-UPGRADES:0 — the honest status matches the live popup chip and was upgraded nowhere.