UQF-7 — Fermion chirality / quantization: the gate anchor ledger

The honest one-line: UQF-7 has a real, checkable classical win — the frozen survivor geometry hands us exactly the matter we observe, three families of a single handedness with zero mirror zero-modes, and that count is twice-confirmed — but the gate as a whole is OPEN (AUDIT), because whether that chirality survives quantization is a wall with no known route anywhere in the field.

This page is the gate-specific instantiation of the anchoring method: it takes the master anchor and the four bridges and applies them, object by object, to one gate. Every exact thing UQF-7 touches gets its own row — its status, what it is allowed to claim, and what it is forbidden to claim. It follows the same eleven-part shape and the same universal table as the canonical SG-4 ledger.

selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique.

1. Gate status header

• Gate-level UQF-7 roll-up: OPEN (AUDIT) — status = least-closed residual.
• Taxonomy reconciliation (2026-07-05): under the current two-axis taxonomy, the gate-level grading is a reached classical terminal (classical index DERIVED-GIVEN-E), read as TERMINAL + RESIDUALS-SHOWN — the open quantum-chirality wall (A2/A3, R1) below remains listed and carried unchanged. The facts are unchanged: the earlier OPEN (AUDIT) roll-up reflects the superseded least-closed-residual rule, not different facts. No residual is closed, deleted, or re-graded. [Superseded 2026-07-08: the ratified board closes UQF-7 as DERIVED-GIVEN-anchor · RESOLVED +0; see the current-status note at the top of this page.]
• Classical zero-mode leg (given-E): the statement that the Dirac operator on the internal space, with the orbifold boundary, returns a one-sided chiral index of magnitude three, $$ (n_L,\,n_R) = (+3,\,0),\qquad |\mathrm{index}| = 3 . $$ This is the closed local/classical leg — the gate's analog of a closed obstruction-zero leg.
• Status, split so it cannot be misread:
  • Classical index leg (APS $(+3,0)$ + BWB $\chi(K_6,E)=-3$): DERIVED-GIVEN-E — theorem-grade inside the index framework, given the Standard-Model bundle $E$. The classical count is not itself axiom-open.
  • Quantum-chirality certificate (the non-perturbative coset-twist quantization): OPEN / WALL — no known route. This is the gate-defining residual.
  • Gate-level UQF-7: OPEN (AUDIT).

Given the frozen branch, the classical chiral spectrum comes out correct twice over, with no per-leg retuning. What stays open is the dynamical bridge: whether the four-dimensional descent can be quantized without spawning light opposite-handed partners. One open piece ⇒ the whole gate is OPEN, regardless of how strong the closed pieces are. No status was upgraded.

selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique.

2. Frozen inputs (what UQF-7 stands on, not what it produces)

• Frozen branch hashes dcc66f1b2685 / manifest meta a5b1e6f9d951. The branch is read-only. These hashes are audit anchors — they certify which object was tested and that it cannot be quietly retuned. They do not validate the physics.
• The frozen 13-dimensional active branch $$ \mathfrak{B}_{\rm active} = \big[\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y/\mathbb{Z}_2\big] \oplus \big[F^+_{\rm finite} \oplus C_{\rm admiss}\big] \otimes \big[E_{\rm matter}\oplus E_{\rm gauge}\oplus E_{\rm Higgs}\oplus E_{\rm proton}\big], $$ with $D = 13 = 4 + 6 + 2 + 1$ and $K_6 = SU(3)/T^2$ the $SU(3)$ flag manifold. Status: GIVEN / upstream-inherited — UQF-7 is a survival/consistency gate evaluated on the survivor; it searches no new geometry and does not derive the branch.
• Upstream Standard-Model content $E$ is given / charged / inherited — it is the input bundle the index is twisted by. UQF-7 does not derive $E$. Every "passes" below is a statement about this $E$, not a derivation of it. The index does not reproduce without $E$.

3. Object anchors (the structures the gate acts on, given-E)

The chirality-relevant frozen objects are:

• The internal Dirac operator $D_{K_6}$ twisted by $E$.
• The spin-$\mathbb{C}$ family index $\chi(K_6,E)=-3$.
• The global $\mathbb{Z}_6$ charge identification.
• The $\mathbb{Z}_2$ orbifold action on $S^1_Y$ that acts as the chirality projector at the boundary.

Status: GIVEN-E / upstream-inherited — read off the frozen branch, not UQF-7-derived.

4. Root and master-anchor traceability

Deep roots that are load-bearing for UQF-7:

Scale enters only as the UV/IR boundary (R5); causal order is not a primary load-bearing anchor for the classical index.

Master anchors in play: finite invariant ledgers · no unpaid labels · the frozen branch · given-$E$ · the declared dynamical-bridge assumption (refused, not paid) · open-residual discipline.

5. The UQF-7 anchor ledger (the universal table)

6. The arithmetic / construction — the classical win, in full

6.1 The Atiyah–Patodi–Singer index (one-sided boundary)

Because the active branch carries a boundary — the $S^1_Y/\mathbb{Z}_2$ fold — the relevant statement is an APS index with a one-sided spectral boundary condition, not a closed-manifold Atiyah–Singer index. For a Dirac operator $D$ on $X$ with boundary $\partial X$, $$ \mathrm{ind}\, D = \int_X \hat{A}(X)\,\mathrm{ch}(E) \;-\; \frac{\eta(\partial X) + h(\partial X)}{2}, $$ with $\hat A$ the A-roof genus, $\mathrm{ch}(E)$ the Chern character of the twisting bundle, $\eta$ the boundary eta-invariant, $h$ its kernel dimension. On the frozen branch this returns $$ (n_L,\,n_R) = (+3,\,0): $$ three left-handed families, zero right-handed (mirror) zero-modes. The boundary term is what makes the index one-sided: the $\mathbb{Z}_2$ fold projects out the would-be mirror zero-modes, which is why $n_R=0$ rather than a mirror-symmetric $(+3,+3)$.

6.2 The independent BWB confirmation

A second route — a Bott–Weil–Borel bundle scan on the flag manifold $K_6=SU(3)/T^2$, computing the cohomology of homogeneous bundles over $G/T$ from Weyl-group and dominant-weight data — returns $$ \chi(K_6,E)=-3 \quad\Rightarrow\quad |\mathrm{index}|=3 . $$

6.3 The classical obstruction map

Collect the classical pieces: $$ O_{\rm UQF7,class}(E)=\big(O_{\rm APS}(E),\,O_{\rm BWB}(E),\,O_{\rm pert\text{-}mirror}(E)\big),\qquad O_{\rm UQF7,class}(E_{\rm frozen})=0 . $$ The full gate obstruction additionally carries the quantum descent piece: $$ O_{\rm UQF7}(E)=\big(O_{\rm quantum\text{-}desc}(E),\,O_{\rm APS}(E),\,O_{\rm BWB}(E),\,O_{\rm pert\text{-}mirror}(E)\big). $$ We do not assert $O_{\rm UQF7}(E_{\rm frozen})=0$: the quantum-descent residual is not closed.

6.4 Specificity diagnostic — the cancellation is specific, not trivial

The chirality is not a mirror-symmetric, automatically-balanced count. A mirror-symmetric spectrum would give $(n_L,n_R)=(+3,+3)$ and a vanishing net chiral index; instead the one-sided fold yields $$ n_L - n_R = 3 \neq 0,\qquad\text{while}\qquad n_R = 0 . $$ That the net chiral index is non-zero and the mirror count is exactly zero is what makes the result a real arithmetic fact about $E_{\rm frozen}$ rather than an artifact of a symmetric construction. Equally, the two routes agree on the magnitude ($|{\rm index}|=3$ by APS and by BWB) — a reproduction-strength check, not a coincidence of two trivial zeros.

7. Declared-structure splits — "twice-derived" and the dynamical bridge, split honestly

Two phrases in the headline each hide more than one claim, with different statuses.

"Twice-derived classical index." This is not two structurally independent anchors:

1. APS one-sided index $(+3,0)$. Status: DERIVED-GIVEN-E (classical, zero-mode level).
2. BWB scan $\chi(K_6,E)=-3$. Status: DERIVED-GIVEN-E (classical, zero-mode level).
3. The relation between them. APS and BWB cross-reproduce the same single topological invariant — a reproduction-strength confirmation, not two independent legs. Status: DERIVED-GIVEN-E, honestly labeled reproduction, not independence.

"Chirality survives quantization." This single phrase is the open object, and it decomposes — at the identity level only (naming which object blocks, not a route to evaluate it) — into:

1. Object $Q^{\rm 4D}_{\rm desc}$ — the quantized 4D effective descriptor from the KK + coset/quotient descent, built non-perturbatively and in-category. OPEN / WALL.
2. Readout $R$ — a proven-faithful map $Q^{\rm 4D}_{\rm desc}\to$ physical light-fermion spectrum. OPEN / unproven (the "faithful-bridge" trap: the classical index is currently being assumed to represent the full quantum spectrum).
3. Proof $P_{\text{IR-chiral}}=\text{true}$, target-blind. OPEN / WALL.

So the classical count is DERIVED-GIVEN-E, its second route is reproduction not independence, and the quantum bridge is an open wall — refused as an axiom, never assumed.

8. Open residuals — the quantum/global completion family (shared blocker B4)

The classical legs above are firewalled from the open object. The honest closure path is not "close UQF-7 directly": it is to attack shared blocker B4 once, centrally; UQF-7 inherits closure only if/when B4 is marked BUILT with a target-blind, adversarially-verified certificate carrying no reverse-engineering from the measured value. The open residuals, each its own row:

• R1 — quantum-chirality certificate / coset-twist quantization. OPEN / WALL. The gate-defining residual; $= A2 + A3$.
• A2 — production obstruction. OPEN / WALL. Whether the boundary-lifted coset-twist class $[\omega]\in H^*_{SU(3)}(SU(3)/T^2)$, transported across the $S^1_Y/\mathbb{Z}_2$ wall by Hořava–Witten inflow into a $d{+}1=5$ relative problem, vanishes. A nonzero $[\omega]$ = a forced light mirror (a FINDING); a vanishing $[\omega]$ = production is safe. Same object as UQF-4's O5/O3 (shared blocker B2).
• A3 — removal obstruction. OPEN / WALL. If a light mirror is produced, it pairs into a vectorlike (anomaly-trivial) combination; whether it acquires a symmetric mass and decouples is decided by strong-coupling symmetric mass generation (SMG), pinned to a discrete mod-2 / mod-8 spin$^c$ / Pin sign bit — the same bit family as UQF-4 row-17 and BG-10's CP-phase residue.
• The target predicate $P_{\text{IR-chiral}}$ (the failure-complete set). OPEN. The honest target is not "no light mirror" but the complete invalidating set: (1) no light vectorlike mirrors; (2) no gapless composites; (3) no boundary / domain-wall remnants; (4) no KK remnants; (5) no topological IR sectors (Wang–Wen anomaly matching as a completeness constraint); (6) no wrong relevant/marginal operators; (7) no damage to the desired chiral families (a selectivity failure). Any survivor ⇒ $P_{\text{IR-chiral}}=\text{false}$ ⇒ a FINDING.
• R5 — UV/IR structural boundary. DISCLOSED (structural). Exported to the IR-certificate ledger shared with UQF-11.
• R7 — shared-wall linkage to UQF-4. OPEN / WALL, EXPORTED. Counted once; plugging it does not by itself close BG-10's independent open residuals (Rules B/C, $M_R$).
• Machine cert G04_chirality. AUDIT ONLY. A consistency lint against the declared $-3$ / $(+3,0)$; an optional from-scratch re-run is a reproducibility gain on a closed leg, not progress on R1.

A2 and A3 are OPEN/wall, not axioms — shared-exported and counted once. The gate reduces to exactly one genuinely atomic measured-invariant anchor, A1: CHIRAL-CONTENT-IS-DATA, already in the SHAPE/$E$ floor, so there is no floor growth.

9. Anti-claims (what this page refuses to say)

• UQF-7 does not derive $E$, and the classical index does not settle the quantum spectrum. Formally: $E_{\rm frozen}\in\ker O_{\rm UQF7,class}$, not $\ker O_{\rm UQF7}=\{E_{\rm SM}\}$.
• Quantization is not proven to preserve the chiral spectrum with no light mirror partners. The non-perturbative coset-twist quantization has no known route; no quantum-chirality certificate is asserted.
• The twice-confirmed classical index does not settle the quantum mirror question. APS $(+3,0)$ and BWB $|{\rm index}|=3$ are firewalled, zero-mode / perturbative scope only; promoting them onto the quantum question is refused. And they are not two independent anchors — they cross-reproduce one invariant.
• The production obstruction is not assumed away. $[\omega]=0$ is exactly what is refused; A2 and A3 are left OPEN/wall, and no axiom is named for the un-routed calculation.
• Topology cannot decide the mirror question. A light vectorlike mirror has net chiral index $n_L-n_R=0$, is null in every gauge/gravitational/global anomaly and in the spin$^c$/cobordism bordism group, so no 't Hooft / Witten / Dai–Freed / APS / spin$^c$ certificate can ever decide whether a light mirror is present — including a future BUILT B2. The deciding datum is dynamical.
• "No light mirror" is not the target. Certifying "no named mirror" while a gapless composite, an emergent TQFT sector, or a wrong operator survives is a false win; the full seven-condition $P_{\text{IR-chiral}}$ is kept.
• The perturbative check is not a non-perturbative certificate; the neutrino count is a consistency anchor, not a mirror-freedom proof.
• The frozen-branch hashes are audit anchors; they do not validate the physics. Local/classical closure is not whole-gate closure: $O_{\rm UQF7,class}=0$ does not imply $O_{\rm UQF7}=0$.

10. Specialist closure plan

The closure path is to build shared blocker B4 once, target-blind, with three first-class outcomes — BUILT (decoupling proven), FINDING (an IR survivor, a real refutation of quantum chirality on this branch), or OPEN-wall (today's status). A false "B4 is built" would propagate a false anchor to all four dependent gates at once — the worst failure mode — so the bar is a target-blind, adversarially-verified certificate, not one second before.

1. A2 / production — compute $[\omega]$. Construct the non-perturbative coset-twist quantization that computes whether $[\omega]$ vanishes across the boundary lift, rather than assuming it. Machinery: equivariant cohomology on the flag manifold $H^*_{SU(3)}(SU(3)/T^2)$ (BWB / Schubert-calculus); Hořava–Witten boundary inflow; Dai–Freed $\eta$-invariant / Pin$^c$ bordism; the spin$^c$-$G$ integrality equation $w_2(X)+f^*\zeta=0$. Falsifier: $[\omega]\neq 0$ ⇒ a forced light mirror ⇒ FINDING. Traps: do not bank A2 as a named computation-debt (it is either the anomaly object — which A3 proves is blind — or the full wall renamed); do not assume $[\omega]=0$; the $w_2+f^*\zeta=0$ data is itself blocked-on-data. A clean $[\omega]=0$ closes only the production half.
2. A3 / removal — the three-stage B4 program.
   • B4.1 — the assay/instrument (tractable, bankable, build first). Type the predicate $P_{\text{IR-chiral}}$ and build the failure-complete detector $\Pi_{\rm bad}$ + the readout $R$ + the light/heavy criterion. Validate with negative controls ($\Pi_{\rm bad}$ must FAIL on an explicit light mirror, a gapped desired sector, a boundary remnant, a gapless composite, and a topology-passes-but-dynamics-fails case), plus an UNKNOWN-failure-mode typed slot and an over-completeness negative control. This requires no non-perturbative dynamics — it is the instrument that catches a future classical→quantum over-promotion.
   • B4.2 — the regulated quantum descriptor (the frontier). Build a minimal target-blind regulated model $Q_\Lambda$ capable of failing, then take $Q_\Lambda\to Q^{\rm 4D}_{\rm desc}$ or return a named obstruction (a sharper wall).
   • B4.3 — selective dynamical mirror-decoupling (the core). Prove SMG-1 existence, SMG-2 selectivity (gaps the unwanted sector while preserving the desired families), and SMG-3 completeness (removes ALL unwanted IR residue per $\Pi_{\rm bad}$, using Wang–Wen anomaly matching as a completeness constraint).
   • Composition + mount. Prove $Q_\Lambda + R + \Pi_{\rm bad} + \text{SMG} + \text{consistency} \Rightarrow P_{\text{IR-chiral}}(Q)=\text{true}$ via two structurally-independent routes (same load-bearing input = one route), with a per-dependent typed mount/bridge contract. Machinery: lattice chiral gauge theory and SMG (Eichten–Preskill; Wen; Wang–Wen 3-4-5-0 and the 16-fold way; Ginsparg–Wilson); strong-coupling dynamics on the curved coset with boundary.
3. R5 / UV/IR boundary — keep DISCLOSED and exported to the UQF-11 IR-certificate ledger.
4. R7 / shared-wall linkage — attack once with UQF-4; do not re-attack UQF-7 as an isolated gate; do not over-export (BG-10's Rules B/C, $M_R$ stay open).
5. G04_chirality cert — optionally mount the from-scratch Dirac-spectrum re-run to harden the closed classical leg; this is reproducibility, not R1 progress.

Closing A2 and A3 (i.e. a BUILT B4) is what would advance UQF-7 from "classical leg closed, gate open" toward whole-gate closure — and even then, only given $E$. Scope guard: even a clean BUILT B4 is the fermion-sector facet only and cannot touch the Yang–Mills mass gap.

11. Completion tests for this page

Required presence (all met): gate roll-up OPEN (AUDIT) · the closed classical leg $(n_L,n_R)=(+3,0)$, $O_{\rm UQF7,class}(E_{\rm frozen})=0$ · classical leg DERIVED-GIVEN-E · $E$ not derived · frozen hashes (AUDIT ONLY) · the APS index · the BWB cross-check (reproduction, not independence) · the $\mathbb{Z}_2$ chirality filter · the perturbative no-mirror check · the measured $N_\nu=2.984\pm0.008$ anchor · specificity diagnostic $n_L-n_R=3\neq0,\ n_R=0$ · the quantum certificate residual R1 · production obstruction A2 ($[\omega]$) · removal obstruction A3 (SMG sign bit) · the faithful-bridge residual · the seven-condition $P_{\text{IR-chiral}}$ · the atomic anchor A1 (no floor growth) · the anomaly-blindness anti-claim · the hashes-don't-validate anti-claim.

Required absence (all held): no claim that UQF-7 is fully closed · $E$ is derived · the classical index settles the quantum spectrum · APS and BWB are two independent anchors · $\ker O_{\rm UQF7}=\{E_{\rm SM}\}$ · $[\omega]=0$ assumed · a "no-mirrors" axiom named · topology decides A3 · "no perturbative mirrors" ⇒ "no light mirrors" · a partial result asserted as BUILT · hashes validate physics · classical/local closure = whole-gate completion · any reader-visible build-process vocabulary.

This page follows the canonical eleven-part shape and the universal table of the SG-4 ledger. The classical chirality count is real, recovered, and twice-confirmed; the quantum certificate is a located, shared wall — open for the whole field, and shared here so a specialist can move it.

See also: the anchoring method · Layer 2 — no unpaid exact labels · Layer 4 — carrier-forcing & the given-E wall (why a classical index does not promote to a quantum spectrum) · the SG-4 ledger (the template) · the UQF-3 ledger (the companion UV/IR wall) · the full UQF-7 dossier.