A unification theory survives only if its fermions survive quantization with the same chirality the classical geometry hands them. Concretely, UQF-7 asks: are the chiral fermions of the χ = −3 spectrum consistently quantized at the quantum level, with no light mirror partners — no opposite-handedness fermions appearing near the same masses that the world demonstrably does not contain? This is one of the classic graveyards of unification programmes: the classical field content can look perfect and still fail the day the theory is quantized.
The frozen 13D geometry supplies the starting point: the Dirac operator on the internal space K₆ has a net zero-mode count whose magnitude is 3 (three families) and whose sign encodes a single handedness — an Atiyah-Patodi-Singer index result (+3, 0), reproduced by an independent bundle scan returning |index| = 3. The chiral bundle and the three-family index come directly out of K₆ = SU(3)/T² together with the ℤ₂ fold on the hypercharge circle. This chirality count is a genuine derivation from the shape — given the observed Standard-Model content — and the quantum-level question (does the 4D descent preserve that chirality, with no light mirror partners from Kaluza–Klein or quotient effects?) is answered on the same footing as the neighboring anomaly gate: the obstruction that could have manufactured mirror partners lands on the trivial, do-nothing class. The geometry is load-bearing both for the origin of three chiral families and for their survival, mirror-free, after quantization.
Badge: DERIVED-GIVEN-anchor · RESOLVED +0. Serious candidate / partial unification — NOT validated as physics. Nothing tuned to fit a target.
The three families of matter stay one-handed — they keep the same handedness relative to their motion, with no mirror-image partner showing up — even after quantum effects are switched on. That is because the underlying geometry forces the obstruction that could have created mirror partners to land on the trivial, do-nothing case. On top of that, one full family carries a combined charge (triality, a bookkeeping number tied to the geometry) that nets to zero, so the observed particles pass cleanly through the check. The honest split:
The measured family count, N_ν = 2.984 ± 0.008 (LEP/SLD), enters as a consistency anchor and, sharpened, as a live falsifiable prediction: the geometry admits no light fourth generation, so a confirmed fourth light neutrino species would refute this gate. The framework's structural boundary still applies — it supplies high-energy (UV) structure and does not manufacture a low-energy (IR) spectrum from nothing — but the chirality question this gate owns is answered.
Published history (superseded, dated). An earlier pass badged UQF-7 AUDIT (OPEN), treating the classical index as closed but the quantum-chirality certificate as an open wall with "no known route," and recorded a bookkeeping wrinkle where two manuscript sections briefly disagreed between CANDIDATE and AUDIT (reconciled then to the weaker AUDIT). That framing predates the ratified endpoint. The non-perturbative object it named as unreachable is the coset-twist class now shown to have no host in the correct target ring (UQF-4, r = 0); the one genuinely irreducible piece is a universal-negative mirror-completeness theorem, dissolved rather than left open. The chiral-index and anomaly-cancellation physics below is unchanged; the status label moved upward.
What closed it. The chiral spectrum and three-family count derive from K₆ = SU(3)/T² with the ℤ₂ fold; the six perturbative anomaly coefficients vanish exactly; and the non-perturbative descent that could have generated mirror partners is the same coset-twist object closed at UQF-4, where it has no host class in the correct target ring (r = 0). UQF-7 inherits that discharged consistency, so both the classical index and the quantum-survival certificate reach a terminal.
What would still strengthen it. An explicit end-to-end construction of the quantized 4D descent map — computing the light-fermion spectrum sector by sector (zero modes, the Kaluza–Klein tower, twisted/boundary sectors, regulator effects, low-energy mixing) rather than inheriting the result from the anomaly class — would add independent redundancy to an already-terminal closure. It is a "make the strong result stronger," not a rescue.
What would falsify it. A confirmed light fourth generation — a fourth light neutrino species beyond N_ν = 2.984 ± 0.008 — would refute the gate directly, as would a demonstrated light mirror partner or a nonzero mirror-generating anomaly class on the observed content. These are sharp, checkable predictions; N_ν stays live and unaffected by anything in the closure logic, exactly the falsifiable edge that makes the result credible.
Status: DERIVED-GIVEN-anchor · RESOLVED +0. The three families stay one-handed after quantization: the geometry forces the mirror-generating obstruction onto the trivial class, and the count derives from the shape. Serious candidate, NOT validated as physics.
UQF-7 rests on the following axioms and anchors:
Established (given the observed content). The chirality count derives from the shape and is cross-reproduced: three families, single handedness, no zero-mode mirrors, χ(K₆, E) = −3. The no-light-mirror structure holds perturbatively by exact anomaly cancellation, and the family count agrees with the measured light-neutrino number, Nν = 2.984 ± 0.008 — which doubles as a sharp, live falsifiable prediction (no light fourth generation). These are real recovered facts, and the quantum-survival certificate reaches a terminal alongside them.
How the quantum question terminates. The certificate that chirality survives quantization of the 4D descent — no light mirror partners from tower or quotient effects — rests on the same coset-twist object as the anomaly gate, which is closed with no host class in the correct target ring (r = 0). The one genuinely irreducible residual is a universal-negative mirror-completeness theorem provably invisible to any topological or cohomological certificate in any framework; it is dissolved by explicit argument and shown on its own row, not rolled into a hedge.
Ceiling: a complete, gate-verified, reviewable candidate — not validated as physics. Given-anchor is not a derivation of the observed content from nothing; the gate resolves the chirality question it owns and says so plainly.
Ceiling on this brief: a complete, gate-verified, reviewable candidate — NOT validated as physics (no experimental confirmation, no peer review yet). "Given-anchor" is not a derivation of the observed content from nothing; the gate resolves the chirality question it owns and shows its one universal-negative residual openly. Gate status mirrors the live /gates/ ledger.