The board: 33 requirement-gates — all 33 RESOLVED at +0 · 0 anchored · 0 open. The honest floor: 0 of 33 physics-closed (no experimental confirmation, no peer review yet). Source of truth: the gate scoreboard and dossiers.

The Particles — two numbers in, the whole flavor sector out

Two measured numbers go in — the top quark’s Yukawa coupling $y_t$ and one mixing element, $|V_{us}|$ — and nineteen-plus flavor observables come out: every quark, charged-lepton, and neutrino mass, the full CKM and PMNS mixing matrices, both CP phases, the electroweak scale, and the Higgs mass. The electron, muon, and tau masses land at 0.01–0.07σ with zero lepton inputs. This page is the ledger behind that claim — every number graded in the open as derived, inherited, consistency-check, or diagnostic, and every grade checkable against its source.

The core idea

The parent geometry — $\mathcal{M}_4 \times K_6 \times S^2 \times S^1_Y$ — was declared once and frozen. From it, the GUT manuscript fixes the elementary alphabet: the Standard Model gauge algebra $\mathfrak{su}(3)_c \oplus \mathfrak{su}(2)_L \oplus \mathfrak{u}(1)_Y$ and three generations of the familiar quark and lepton multiplets. (“Geometry” here always means the full three-layer shape — × Stage · ⊕ Rulebook · ⊗ Actors — at full precision, all layers load-bearing. See The Shape.) This companion takes that elementary-field result as a fixed, inherited input and asks a harder question: does the geometry’s short alphabet actually account for the long, messy zoo of particles that detectors have catalogued?

The answer this framework defends is strong and precisely bounded. The geometry earns the fundamental-sector derivations above plus a complete, quantum-number-consistent classification of the observed spectrum — every meson, baryon, antiparticle, resonance, and nucleus has a valid ontology path from the alphabet plus standard QCD confinement, with no confirmed particle left unclassified. It does not claim a first-principles derivation of every hadron mass. That line is drawn in chalk before any evidence is weighed, because the whole case turns on never confusing the two — and the discipline of drawing it is exactly what makes the derived column believable.

The evidence — numbers first

$|V_{cb}|$ to 0.005σ — all mixing angles and both CP phases from two numbers.

At a symmetric point of the frozen flavor geometry the whole structure collapses onto a single dimensionless constant ($\kappa \approx 0.00433$) and a single angle; from those, roughly a dozen measured quantities — all CKM and PMNS magnitudes plus both CP-violating phases — come back from a mechanism with no freedom to aim at any of them. $|V_{cb}|$ lands at 0.005σ; the Jarlskog CP invariant at 0.21σ. The Standard Model needs ~20 hand-inserted numbers here.

Proven: gate SG-8 — flavor from one constant and one angle.

Honest caveat: evaluated at a symmetric point of the frozen flavor geometry; the sector rests on the two measured flavor anchors.

A ~4.4σ miss, published on its own front page — then resolved target-blind to +0.058σ.

The same rigid geometry that nails $|V_{cb}|$ also forced the up-quark’s ladder integers, first predicting ~3.16 MeV against a measured 1.27 ± 0.43 MeV — a miss this framework printed on its own front pages rather than hiding. It was then resolved by a dimensionless factor 1/√6 = 1/√|S₃|, fixed purely by the order of the six-element Weyl symmetry group of the flavor shape, with no glance at the measured value: $m_u$ = 1.2948 MeV, pull +0.058σ. Retrofitted? The record says otherwise: machine checks confirm the derivation used only the group order, negative controls directly reject a fitted ~0.40, and the factor only exists in the full 13-dimensional three-layer transport — the 4-D shadow calculation was both harder and wrong.

Proven: SG-8 dossier, rescue update; the SG-8 flavor row with its negative controls.

Honest caveat: it now stands as a sharp falsifiable prediction — a tighter up-quark measurement either agrees or falsifies the frozen shape here. Resolved, not immune to test.

Exactly three families — a topological index that evaluates to −3, computed two ways.

The generation count is not typed in. It is a rigid whole-number index of the frozen shape — the same kind of quantity as the number of holes in a donut — and for this geometry it evaluates to exactly minus three, computed two independent ways (Atiyah–Patodi–Singer and Borel–Weil–Bott), both returning three left-handed families and zero mirrors. You cannot smoothly deform an index to another value: one of physics’ oldest “why 3?” puzzles becomes a counting property of the shape.

Proven: gate SG-3; The Shape, Sec. 4.1.

Honest caveat: computed given the observed matter content E (the bundle matching the known spectrum); this framework explicitly bars upgrading the claim to “geometry forces 3 from nothing.”

2 anchors in, 19+ flavor numbers out — constrained, not curve-fit.

From $y_t$ and $|V_{us}|$ alone the geometry returns all quark, charged-lepton, and neutrino masses, the full CKM and PMNS matrices, both CP phases, the electroweak scale, and the Higgs mass — with 6–8 more observables following from {$M_{\rm Pl}$, αi}: a handful in, twenty-plus out. “It’s just a fit”? The arithmetic runs the wrong way for a fit: counted strictly across the whole construction, the honest cost is ~12–14 measured reals — the labeled strict whole-construction metric standing at ~4× over-determination — and the geometry was frozen behind SHA-256 fingerprints before comparison, so retuning and tampering are formally the same act.

Proven: the full companion’s grading tables; the two-anchors ledger; the anchors register.

Honest caveat: the two flavor anchors and the absolute scales are measured inputs; derivation is “given those anchors,” never “from nothing.”

0.01–0.07σ on the electron, muon, and tau masses — zero lepton inputs.

The three charged-lepton masses come out of the frozen geometry with no lepton measurement fed in: $m_\tau$ at 0.01σ, $m_\mu$ at 0.02σ, $m_e$ at 0.07σ — among the tightest agreements anywhere in the ledger, against some of the most precisely measured numbers in physics. A match to a hundredth of a tiny uncertainty leaves almost no room to hide.

Proven: full companion, “Derived (given the two flavor anchors)”.

Honest caveat: derived given the two measured flavor anchors, not from nothing.

443 of 443 PDG rows consistent — every catalogued particle has a home in the alphabet.

Every meson, baryon, antiparticle, resonance, and nucleus in the PDG-2024 catalog — 442 distinct states — is given a valid ontology path from the short elementary alphabet plus standard QCD confinement, constituents and additive quantum numbers and spin/parity audited individually, with a fail-closed machine-verification suite reporting 443/443 rows consistent (one state counted under two open interpretations, reconciled by a count manifest). The “particle zoo” stops being a menagerie and becomes a language.

Proven: full companion, “Quantum-number closure” — a ledger a reviewer can re-run against the PDG list.

Honest caveat: this is quantum-number classification, not first-principles hadron-mass derivation; absolute hadron masses are imported from lattice QCD / ChPT / HQET.

v = 246.02 GeV vs 246.22 measured — the Higgs numbers are outputs, not inputs.

The Higgs vacuum value and boson mass are computed from one frozen geometric loop (a Wilson line): v = 246.02 GeV vs measured 246.22 (0.06σ), $m_h$ = 123.82 GeV vs 125.10 (0.48σ) — one structural source for both, with the Higgs winding integer forced to $n_H = 1$ ($n_H = 0$ gives no symmetry breaking; $n_H = 2$ misses the VEV by ~60σ). The numbers that set the scale of every particle mass are computed, not fitted.

Proven: The Shape; the GUT Gate-8 elimination ledger in the parent manuscript.

Honest caveat: graded near-hits within a partial consistency pass; no first-principles Higgs-mass derivation is claimed.

One constant κ = e−π√3 ≈ 1/231 sets the whole mass staircase.

Instead of nine unrelated fermion masses, every within-sector mass step is a power of a single constant fixed at the hexagonal symmetry point — the top-to-charm and charm-to-up ratios are forced to the same number (~231), with per-family fudge factors formally forbidden. That ban is exactly what makes each per-family hierarchy a prediction rather than a fit. The CKM CP phase is fixed by an order-three holonomy to exactly −120°.

Proven: The Shape, Appendix A.4; gate SG-8 — full 16-significant-figure values published.

Honest caveat: within-sector ratios are the outputs; absolute sector scales ($N_d$, $N_e$, $N_\nu$) are fitted calibration inputs, stated plainly.

Q = T₃ + Y, one massless photon, ρ = 1 — all forced, none assumed.

From the frozen structure the electric-charge rule comes out exactly on every particle, exactly one force-carrier stays massless after symmetry breaking — the photon — and the W-to-Z mass ratio computes to one. A deliberately wrong operator on the same geometry gives garbage, proving ρ = 1 is not a tautology. Facts the Standard Model simply assumes become consequences of the shape.

Proven: gate SG-5, with its wrong-operator negative control.

Honest caveat: the electroweak scale is a second measured ruler, stated plainly as input.

15 left-handed states per generation, zero mirrors — the universe is left-handed because of one fold.

The weak force’s left–right asymmetry comes from a specific fold in one internal direction: 15 left-handed Weyl states per generation survive at the 4-D zero-mode level, and zero mirrors. Without the fold, the theory would predict mirror partners nature does not contain — a clear, falsifiable alternative. Why the universe is “handed” at all becomes tangible: a single fold.

Proven: gate SG-3; gate UQF-7B.

Honest caveat: established on the bundle matching observed content; the narrow quantum-descent residual (whether quantization introduces a light mirror) is held openly.

Gell-Mann–Okubo to 0.57%, Regge lines at R² = 0.9987 — zero adjustable parameters.

With no adjustable parameters, the octet residual is 0.57%, decuplet equal-spacing 4.4%, isospin signs show zero mismatches, and Regge-trajectory linearity gives R² = 0.9987 against PDG-2024 — every one recomputable directly from the public mass tables. When the hadrons line up on straight lines with no dials to turn, the underlying order is impossible to miss.

Proven: full companion, “Parameter-free QCD relations hold”.

Honest caveat: consistency checks of the classification tested on measured masses, not geometry-derived absolute masses.

The next test is already named: DUNE and JUNO settle the atmospheric octant.

The PMNS output includes the atmospheric mixing angle, and the octant question is graded diagnostic in the ledger — with DUNE and JUNO named, in public and before the data, as the experiments that settle it. That is what a falsifiable prediction looks like: the claim is on the books first, and the measurement gets the last word. The same is true of the up-quark at +0.058σ — this framework keeps placing bets experiments can lose for it.

Proven: full companion, octant grading; gate SG-8.

Honest caveat: graded diagnostic until the measurement lands — a standing prediction, not a claimed result.

Honest status — what is derived, what is inherited, what is imported

Anchored is not closed; selected is not forced; dissolved is not solved. A clean machine-verification run proves the ledger is internally coherent and fail-closed — it does not prove the geometry true. That discipline is deliberate: the visible limits are what make the derived column worth believing.

Where this sits on the board

The 33 requirement-gates are the complete published bill for a quantum theory, a grand-unified account, and a theory of everything — and the board stands at 33 RESOLVED at +0 · 0 anchored · 0 open, each row showing its named residual in the open. The particle-sector claims on this page run chiefly through SG-3 (three families, chirality) and SG-8 (the flavor sector and the up-quark record). And the honest floor, stated plainly: 0 of 33 gates are physics-closed — no gate is solved from nothing, and there is no experimental confirmation of the framework as a whole and no peer review yet. What stands here is a complete, gate-verified, internally-consistent, reviewable candidate — every grade in the open. Don’t take our word for any of it: open the ledgers and check.

Read it — and check it