State of the Closure

Published history — superseded framing. This overview was last reviewed 2026-06-27 and is written in the program’s earlier three-bucket / least-closed-residual grading scheme, which was retired 2026-07-06. Its “buildable / construction / frontier” buckets and its “open” roll-ups reflect that retired rubric and are preserved verbatim below as a snapshot of the work at that date. On the current canonical board (live /gates/ ledger, ratified 2026-07-08) all 33 requirement-gates are RESOLVED at +0 · 0 anchored at +1 · 0 open; on the separate honest axis, 0 of 33 are physics-closed (no peer review yet). For current gate status, read the /gates/ ledger and the per-gate dossiers, not the counts below.

An honest map of where every gate in the program now sits — last reviewed 2026-06-27.

This is a constraint-first geometric framework that attempts to derive the Standard Model's structure — its gauge group, three generations, charge quantization, and forbidden decays — from one frozen higher-dimensional geometry, given a small set of measured inputs, and to interface that geometry honestly with quantum field theory and gravity. The page below states, in plain language and without inflation, exactly what is established, what is a construction we have specified but not finished, and what remains a genuine frontier research problem. The honest overall ceiling is unchanged: a serious candidate, not a validated theory — with no live refutation standing against it.

The one-paragraph state of play

The program reduces to one (still-open) buildable object, one construction, and three named frontier problems — with everything else honestly derived-given-those, and no live refutation standing against it.

That is the whole claim, stated at its true strength and no higher:

BUILDABLE (NOT BUILT) — one computational object is the most tractable open item: the short-distance (heat-kernel) expansion coefficient on the frozen geometry that the coupling-running, the graviton self-energy, and several gravity gates all lean on. It is a well-posed calculation, not a conceptual gap — but it is not built: the most recent attempt evaluated it two independent ways and the two routes disagreed, localizing a fault in one of them. So this object is open / near-built, and it currently discharges no gate.
CONSTRUCTION — one object is specified but not yet assembled end-to-end: the boundary anomaly-descent object that would turn the forbidden-operator, anomaly-cancellation, and scope-boundary arguments into a single machine-checked certificate. The component pieces exist; the master assembly is the open work.
FRONTIER — three problems are not ours to hand-wave: they are among the field's own hardest open questions. We publish them as open, with no claim to have solved them.
DERIVED-GIVEN-E — everything else (the gauge algebra, three generations, the hypercharge lattice, charge embedding, the flavor ratio/mixing structure, proton-stable operator structure) is shown to follow rigidly given the observed spectrum and the frozen geometry. "Given-E" is stated honestly: these results consume measured input; they do not conjure the spectrum from nothing.

"No live refutation" means exactly that — no current result inside the program contradicts observation or contradicts another gate. It is not a claim of proof. Two gates even carry standing, falsifiable precision tensions that we publish openly rather than hide (the electroweak custodial parameter, and a forced up-quark mass); see the table.

The three buckets, in detail

BUILDABLE (NOT BUILT) One computational object — open / near-built (NOT built)

A single short-distance expansion coefficient (a heat-kernel / Seeley–DeWitt coefficient of the graviton operator on the frozen geometry, with its boundary-defect contribution) is the most tractable open item in the whole program, and it is shared across many gates: coupling running, the graviton self-energy, the ultraviolet question, black-hole entropy, and more — "computed once, used in many places." Where this stands honestly: the scale-free content is genuinely derived and cross-checked (an exact color factor, exact-rational test-geometry checks reproduced two independent ways, and the signs of the corrections), and a real curvature-input error was found and corrected this cycle. But the decisive numeric value is not in hand: when the shared boundary-defect coefficient was evaluated two structurally independent ways, the two routes disagreed, and the cross-check localized a fault in one route. Because the two routes did not agree, the object is audit-unverified and not built — it discharges no gate. This sector is published as open / diagnostic-only. It is a build, not a mystery, but it is honestly still open.

CONSTRUCTION One object to assemble

The forbidden-decay (proton-stability) results, the higher-dimensional anomaly-cancellation gate, and the scope-boundary ledger all lean on the same underlying object: a boundary anomaly-descent construction that would certify, in one place and by machine, which operators are excluded to all orders, that every reduction anomaly cancels, and which sectors the theory does and does not claim. The component derivations are in hand — the low-dimension forbidden operators are machine-certified given the spectrum, one decay channel is excluded to all orders by a colour-triality argument, and the standard perturbative anomalies cancel given the spectrum. What remains is the master assembly: the all-order completeness write-up, the existence proof of the correct boundary-and-coset anomaly invariant (an integrality condition on the actual flux data plus the orbifold-wall boundary structure), and a single machine-checked consistency pass — none yet executed. Published as open pending that assembly.

FRONTIER Three named research problems

These are not bookkeeping gaps. Each is, in its own right, a hard open problem in mathematical physics, and we make no claim to have closed any of them:

The ultraviolet fixed point (asymptotic safety). Whether the framework has a well-defined short-distance completion — a truncation-independent non-Gaussian fixed point — is the same class of question as the asymptotic-safety program for gravity. A candidate exists only at a declared truncation; current evidence trends against the naive route. Published open.
Dynamical fermion mirror-decoupling. The topological count gives three left-handed generations and no mirror partners at the level of indices; showing the mirror sector actually decouples dynamically through quantization is an open, strong-coupling problem that no topological certificate can settle (a light vector-like mirror pair is invisible to anomaly, cobordism and index tools). Published open.
The Yang–Mills mass gap. The confinement / mass-gap input the program relies on downstream is one of the field's canonical unsolved problems (a Clay Millennium problem). We reduce the entire continuum obligation to a single named, value-free uniform inequality and say so; the underlying problem is published open.

Publishing these as frontier problems is the honest move: a candidate theory that quietly "closed" the Yang–Mills mass gap or the UV completion in passing would be telling you something false about itself.

Per-gate status — every gate

Public status vocabulary: Derived-given-E (rigid given the measured inputs and the selected geometry) · Certificate-conditional (a real but scoped certificate, conditional on a named upstream gate) · Declared-frozen (specified and reproducible, not proven unique) · Audit (Open) (the audit is complete; the physics is named-and-routed and stays open) · Open (a named piece is genuinely unfinished) · Measured-but-irreducible (a measured anchor, no known reduction) · Dissolved (a puzzle removed by a named reframe, not solved) · Disclosed (a scope boundary, not a physics claim). No status on this page has been upgraded for appearance.

Gate	What it claims	Bucket	Public status
Geometry & Standard-Model structure (SG‑1 … SG‑10)
SG-1 Geometry freeze	Commits and freezes the 13-dimensional active branch (colour carrier K₆ = SU(3)/T²) as one content-addressed object before any test.	CONSTRUCTION	Declared-frozen reproducible; forcedness open
SG-2 Gauge algebra	Recovers the Standard-Model gauge algebra (the 8·3·1, rank-4 content) as an equality given the spectrum and the selected geometry.	DERIVED	Derived-given-E gate roll-up open; carrier-forcedness category-relative
SG-3 Three generations	Three chiral families as a deformation-proof topological index χ(K₆,E) = −3.	DERIVED / FRONTIER	Derived-given-E roll-up open; mirror-decoupling is the frontier piece
SG-4 Hypercharge quantization	The 1/6 hypercharge lattice from a bundle-descent obstruction; six anomaly ledgers exact.	DERIVED	Open anomaly is a filter, not a determiner
SG-5 Electroweak breaking	Charge embedding Q=T₃+Y, SU(2)×U(1)→U(1)_em, massless photon.	BUILDABLE (NOT BUILT) / FRONTIER	Open standing ρ≠1 precision tension, published
SG-6 Moduli stabilization	Whether the compact geometry's shape and size are pinned before downstream tests.	FRONTIER	Open (saddle-leaning → minimum-leaning) v_EW read, not derived → second anchor
SG-7 Coupling running	Geometric thresholds for the running gauge couplings.	BUILDABLE (NOT BUILT)	Open (diagnostic-only) signs derived; magnitudes the open build
SG-8 Flavor (Yukawa / CKM / PMNS)	Within-sector mass ratios, all CKM/PMNS angles, the Jarlskog and CKM phase forced from two calibration anchors; the program's weakest link.	FRONTIER	Open ratios/mixings/phase derived; 4 fitted scales + forced m_u ~4.4σ tension
SG-9 Proton stability	Forbidden-operator structure: low-dimension Wilson zeros machine-certified; one channel excluded all-order by colour triality.	CONSTRUCTION	Open (hardened) all-order completeness + master assembly open
SG-10 Scope boundary	Names every sector the theory does not claim; enforces the scope wall. Derives no number and rides no geometric object.	CONSTRUCTION	Disclosed boundary ledger; machine check not yet run
Quantum consistency of the force sector (UQF gates)
UQF-3 Physical Hilbert space / positivity	No negative-norm (ghost) states in the physical spectrum — reflection positivity on the interacting Hilbert space.	CONSTRUCTION / FRONTIER	Certificate-conditional (retained sector, on UQF-4) Open (full interacting theory)
UQF-4 BRST closure & anomaly cancellation	The gauge-fixing machinery closes and every anomaly — perturbative, global, and boundary — cancels under reduction.	CONSTRUCTION	Audit (Open) perturbative anomalies cancel given E; boundary invariant unbuilt
UQF-7 Chirality survives quantization	Three chiral families with no light mirror partners survive into the quantized 4D theory.	FRONTIER	Audit (Open) classical index closed; quantum mirror-decoupling is the wall
UQF-9 Ultraviolet completion	A sensible short-distance completion of the gravity-coupled theory (a fixed point), and the finite graviton heat-kernel trace.	BUILDABLE (NOT BUILT) / FRONTIER	Open (Audit) UV fixed point is the frontier wall; a₆ trace uncomputed (shared object unbuilt)
UQF-10 Compactification survives quantization	No tachyonic mode, bounded moduli potential, no runaway volume, controlled vacuum energy.	FRONTIER	Audit (Open) stable in truncation; rides un-run RG + UV wall; false saddle-scare audited away
UQF-14 Unitarity / causality / locality	System-wide quantum consistency: ghost cancellation, microcausality, locality, no superluminal graviton.	FRONTIER (routing node)	Audit (Open) verified perturbatively in scope; 4 sub-claims routed to upstream walls
Quantum-gravity interface & foundational gaps
GRAVITON Graviton consistency	A massless spin-2 graviton whose long-wavelength limit is general relativity; one-loop ghost-corrected coefficient.	BUILDABLE (NOT BUILT) / FRONTIER	Certificate-conditional (linearized, on UQF-9) Open (interacting/strong-coupling)
Gap-01 Graviton heat-kernel coefficient	The sixth Seeley–DeWitt coefficient tr[a₆] of the graviton+ghost operator in the cubic-curvature basis.	BUILDABLE (NOT BUILT)	Open scale-free part derived; magnitude + defect value + positivity open (routes disagreed)
Gap-02 Yang–Mills mass gap	A nonzero mass gap for 4D pure-glue SU(3) Yang–Mills (the Clay problem).	FRONTIER	Precisely-Open reduced to one named uniform inequality; the Clay wall stands
Gap-13 Black-hole entropy / Page curve	The S = A/4 horizon entropy coefficient and a unitary Page curve.	BUILDABLE (NOT BUILT) / FRONTIER	Open 1/4 a conditional geometric output; rides the unbuilt shared coefficient (routes disagreed)
Born The Born rule	Probability = squared amplitude (trace of state×effect): functional form + measure.	CONSTRUCTION / FRONTIER	Open measure leg reduced to a checkable object; non-contextuality imported, not derived
Gap-05 (Λ) Cosmological constant	The value Λ ≈ (2.3 meV)⁴ and a per-scale radiative-stability mechanism.	FRONTIER	Measured-but-irreducible (value) · Dissolved (catastrophe-half, tree-level) Open (radiative-stability mechanism)
Cosmology & out-of-scope diagnostics
BG-10 Baryon asymmetry η_B	The matter/antimatter ratio η_B ≈ 6.1×10⁻¹⁰ from leptogenesis.	FRONTIER (observation-locked)	Open (0 of 4) pre-registered falsifier; an unsupported CP ingredient withdrawn this session
Gap-08 Inflation / primordial spectrum	The geometry's breathing modulus as inflaton: tilt direction, tensor-to-scalar band.	FRONTIER (out-of-scope)	Open (cascade) — demotion this round tilt direction derived; magnitude relocated onto a 2nd un-traced convention
Gap-11 Dark-matter candidate / relic abundance	A stable parity-odd boundary state and its relic abundance against Ω_DMh² ≈ 0.12.	FRONTIER	Open (open list enlarged this round) state selected & stable; coupling operator now a separate open premise
The roots beneath everything
Deep Roots Granularity & structural form	Why action comes in a uniform smallest grain (the quantum of action) and why the carrier is this shape (K₆, 13D, χ=−3).	FRONTIER	Open grain = 1 measured anchor + 1 named assumption; absolute minimality is an uncomputable wall

Honest tally

Rows are graded by the least-closed residual and are not a partition: a single gate can appear in more than one row, so the counts intentionally do not sum to the gate total.

Disposition (by least-closed residual)	Count	Gates
Derived-given-E / Certificate-conditional	5	SG-2, SG-3 (local), UQF-3 (retained sector), Graviton (linearized) — conditional; SG-8 ratio/mixing leg
Declared-frozen / Disclosed / Measured-but-irreducible / Dissolved	3	SG-1, SG-10, Gap-05 (Λ value + catastrophe-half)
Open / Audit (Open) (a named piece unfinished)	26	every gate has at least one open residual — we grade by the weakest piece

Rows overlap because we grade by the least-closed residual: a gate whose local result is derived-given-E is still published as open overall if any single piece of it is unfinished. This deliberately reports each gate at its weakest point, not its strongest. That is why the third row contains every gate.

Reading the tally honestly: the derived-given-E results are real and rest on the observed spectrum as a measured anchor — they reduce structure, they do not invent it. The open surface, sorted by kind rather than by gate, collapses into exactly three things:

One buildable computation — the shared heat-kernel coefficient (its last two-route value attempt disagreed, so it is open / near-built, not built). It is the binding residual behind SG-7, UQF-9, Graviton, Gap-01, Gap-13, and others.
One construction — the boundary anomaly-descent assembly behind SG-9, SG-10, and UQF-4.
Three frontier problems — the UV fixed point (UQF-9, UQF-10, Gap-01), dynamical fermion mirror-decoupling (SG-3, UQF-7), and the Yang–Mills mass gap (Gap-02, and the confinement dependence of UQF-14, Born, Λ).

Everything else is honestly derived-given-those. That is the entire distance between "candidate" and "validated," and there is no live refutation standing against any of it.

What we are not claiming

We are not claiming the shared heat-kernel object is built — its last two-route evaluation disagreed, so it discharges no gate and every residual that leans on it stays open.
We are not claiming the geometry is proven unique or forced — only that it is the shortest survivor inside a stated, extensible grammar (SG-1, Deep Roots).
We are not claiming to derive the observed spectrum from nothing — the spectrum and a handful of measured constants are anchors that go in.
We are not claiming to have solved the Yang–Mills mass gap, the UV completion, or dynamical mirror-decoupling. Those are published as frontier problems.
Two gates carry standing, falsifiable precision tensions we publish rather than tune away: the electroweak custodial parameter (ρ ≠ 1 at tree level on the frozen object, SG-5) and the forced up-quark mass (a ~4.4σ tension in SG-8 that no adjustment can rescue).

If any one of those caveats were quietly dropped, the program would be over-claiming. Keeping them visible is what makes the rest of the page trustworthy.

For the gate-by-gate write-ups, see each gate's dossier. Overall ceiling, restated: a serious candidate, not a validated theory — with no live refutation standing.