A discrete programme that builds the Standard-Model skeleton from two fixed inputs — and ships every load-bearing step as machine-checked code you can run yourself.
A 5:29 film on TFPT's machine-checked discrete compiler, its separate open physical-TOE gates, the August structural wave, documented falsifications, and candidate predictions with live kill switches.
What if the laws of nature are not a list of fitted constants but the output of a tiny compiler? Topological Fixed-Point Theory begins with two declared axioms. The boundary constant c₃ equals one over eight pi and a five slot carrier. From them, it builds D₅ plus A₃, joins the two through a cyclic μ₄ glue and reaches E₈. Then it reads off the discrete standard model structure, the gauge group, three families, hypercharges, and the flavor operators together with dimensionless fixed point readouts. The claim is not that every physical detail is solved, it is narrower and testable. A small machine constructs a large rigid skeleton then names every bridge it still needs.
The flagship line is alpha inverse, 137.0359992168. The verifier finds it as the unique positive stationary root of the boundary U(1) Ward identity. It is not fitted to the measured value, mutate the permitted terms and the root does not survive. E₈ is the checksum behind the discrete construction, 240 roots lock the D₅ and A₃ sectors into one even, unimodular rank eight lattice. In the current corpus, 1009 machine-checked verification modules test this architecture, its numerical identities, its reductions and its failures. Every load-bearing claim has a script and a claim identifier. The status ledger, not the rhetoric, decides whether a line is exact, conditional, open or a kill test.
That discipline forces two status cards to sit side by side. The first is the compiler rest. It has three named interfaces. v_geo, the one dimensionful calibration that pure numbers cannot supply. G_net, the seam-to-E₈ net identification, conditionally closed on its MMST route, but open as an unconditional parent claim. And F_transfer, the typed interfaces that carry selected compiler structures into masses, QCD, baryogenesis and cosmology. Beside it sits a stricter card, the physical theory of everything rest. Its master contract is the AND of eight gates. None is fully closed. They demand the seam continuum, a complete three plus one dimensional local quantum theory, a chiral measure and uniform mirror gap, controlled infrared physics, internally fixed couplings and neutrino dynamics, emergent gravity and the physical state. So the honest sentence is precise. TFPT closes a discrete compiler. It does not yet certify a strict physical theory of everything.
The August wave did not erase that frontier. It compressed it. First, the seam boundary theory was reduced to one external charged scaling limit theorem. Five supporting lemmas were proved in-house. The cross product step, a uniform growth bound, the first telescoping estimate, the integer D₅ plus A₃ pairings and the order-four outer action. The remaining analytic target is isolated in a 20 plus page memorandum and a send-ready specialist package. Second, the DET16 mirror mechanism is exact on the full 2¹⁶ cluster. A rank one projector, a gap exactly equal to one and all 45 Spin(10) commutators vanishing. A cited stability theorem now supplies a volume uniform finite chain leg. The full dynamical four-dimensional claim remains conditional. Third, the first 3+1-dimensional lattice scaffold now lets gauge content, a chiral wall mirror gapping and the seam clock coexist. The Hamiltonian-class dynamics has a Lieb–Robinson bound, a norm-convergent time evolution, a gauge-invariant quasilocal algebra and ground and thermal states. Phase uniqueness, the limiting gap and infrared universality remain open. Finally, the finite axiom core premises now derive in-house. The remainder is zero modulo the same external MMST identification. P2 remains typed as an axiom and the genuine four-dimensional functional is still a gate. The gain is not a victory slogan, it is convergence. Many vague gaps have become one external theorem, one physical unit and a short list of explicit four-dimensional obligations.
A serious compiler must also record what does not compile. The number-preserving Casimir projector does not isolate the mirror state, its multiplicities explode instead. Eight preregistered Schur-texture constructions all fail because the even seam data forces the wrong degeneracy and the naive extension of the alpha grammar to the strong and weak couplings fails in all 64 tested conventions while the U(1) control survives. These routes are not quietly deleted, they become permanent constraints. The future mechanism must evade the exact reason each one died. That is how the project protects itself from numerology. A failed pattern is evidence, not decoration.
The newest neutrino chain shows how the live frontier is meant to work. As a candidate, it gives a normal-ordering mass sum near 0.0599 electron volts, a leptonic CP phase near 287.7 degrees and a pentagon-class misalignment with phase 288 degrees and angle two pi over 35. At finite level, all three mixing angles land within 0.56 sigma. But the mechanism that turns the seam operator into the flavor operator is still open. There is no seesaw closure. The labels stay candidate and numerical, not exact physics. DESI can press on the mass floor. DUNE can separate 287.7 degrees from the older 240 degree branch. JUNO can test the reactor-angle structure. So is reality compiled? We still do not know. What exists now is more disciplined than an answer by proclamation. A machine-checked compiler with a sharpened map of what remains. Every closed line has a proof object. Every gap has a name. Every prediction has a kill switch.
The whole story in four lines — everyday language first, jargon only in parentheses.
Two small inputs set the rules of a discrete compiler. (axioms)
The compiler assembles a rigid mathematical shell that only closes one way. (E₈ audit hull)
From that shell it reads off the Standard-Model skeleton — forces, three families, hypercharge — and a board of concrete predictions.
Every load-bearing step is machine-checked; what is still open or failed is published, not buried.
The Standard Model takes roughly twenty parameters as input and fits the flavor sector by hand. It does not say why there are three families, why the hypercharges take the values they do, or why the strong-CP phase is essentially zero. TFPT asks whether these share one boundary origin — and answers with a status-graded derivation, not a fit.
Read this as a checkable research artifact, not a landing page. Each result is typed, machine-verified, or explicitly open — 1009 Python modules, an independent Wolfram mirror, and a Lean carrier proof. A single versioned ledger is the source of truth.
Falsifiable by design:predictions frozen pre-data — sin²θ₁₂ = 0.3067 (JUNO), r ≈ 0.004 (CMB-S4)·null model: conditional P ≤ 10⁻³⁰·⁷, plus an assumption-minimal ≈ 4.40σ counting floor (1 in 94,500, no subjective probability)
Read top to bottom: declared inputs → exact kernel → numerical fixed points → conditional physics → open interfaces. Each layer states its marker and how it fails.
A fourth chiral generation (N_fam ≠ 3) or a different carrier rank breaks the compiler at the source.
Any failure of the E₈ glue identities or the Lean-checked carrier rigidity.
A unique-root failure for α, or JUNO landing clearly off 0.3067 at high significance.
A robust r ≳ 0.01 kills the R² branch; a transfer that misses its target demotes that bridge — the kernel is untouched.
Declared honestly, not hidden — v_geo is the one genuine [O] unit; G_net and F_transfer are [C], written up as numbered research contracts.
Until mid-2026 the seam was an axiomatized boundary. A chain of machine-checked steps now realizes it geometrically: the seam axioms force one concrete algebraic curve, and the seam's kernel structure is recovered on it exactly. The bedrock premise itself stays open — these are exact slices that narrow it.
ℤ₄-Möbius rigidity pins the four marks to μ₄, and the conformal seam axioms force the μ₃-cover — the genus-3 curve y³ = x⁴ − 1, up to the conjugate sheet. The seam is no longer a template: it has one concrete shape.
A census of cyclic covers: the seam admits only N ∈ {3, 5} as primitive orders, and the compiler's own 3-adic constants (27, 81) pin N = 3 — conditional on the compiler anchor, typed as such.
The chiral seam kernel equals the antiperiodic (NS) mode sum on the 16-site circle exactly — the periodic (Ramond) sum fails as a must-fail control — and the mark-bond midpoints land literally on μ₄ = {1, i, −1, −i}.
Lifted to the cover, the seam is one 48-site NS circle; the lifted clock has exact order 12 with L⁴ = deck — the relation r⁴ = ω becomes lattice combinatorics. The deck classes carry the ℤ₃-twist Casimir data exactly, the interacting orbifold slice stands at the abelian vertex level (twist weight 1/36 from three exact routes, crossing symmetry-protected), and the twist sector is reflection positive under the parafermionic Klein pairing (η = (1,1) unique, N-stable).
[O]Not claimed closed: the seam-realization bedrock (GATE.QGEO / QGEO.SYM.01) is still open. The parafermionic RP twist of the ℤ₃ orbifold (v639) is since resolved at the lattice OS level (v645: mirror × charge conjugation, η = (1,1) unique); the named residues — the continuum orbifold statement and the N_fam = 3 anchor — are tracked in the ledger, not hidden.
The open gatesTwo independent 2026-08 results read the same E₈ hull in new ways: one as a literal error-correcting code, one as the finished geometry whose arithmetic shadow is the primes — with a first measured contact to the Weil operator. Exact where stated, typed where they are readings.
A lattice/coding theorem about the compiler's own hull — no physics claim rides on the reading. Only 2 of 30 code placements carry the equivariant structure; the naive placement fails it — published, not buried.
Classical Jacobi/Hecke facts, realized verbatim by the compiler's own objects; the speculative framings stay typed hypotheses.
A window-portable operator identification inside a preregistered research contract (PRIME.WEIL.OPERATOR.01) — typed, killable, and explicitly not a Riemann-hypothesis claim.
The strongest credibility move is naming the gaps before a reviewer finds them.
What we do not claim. SEAM.EQUIV is not closed as an unconditional theorem. One input bit stays an input (ten blind derivation attempts failed — that’s the point). The first interacting toy fails our own kill test (v529) — published, not buried. Empirical HFQPO searches returned nulls; they are search targets, not claims. No external lab has reproduced the suite yet — we want that to change.
Method
Sandbox firewall, kill criteria before execution, one ledger, generated mirrors — and the process discipline itself measured and certified by the suite (v649). The numbers are censuses, not slogans.
A two-input theory with many small integers is, a priori, at numerology risk. TFPT answers with a layered, machine-checked discipline — making coincidence an expensive explanation of the discrete core, and never letting exact compiler closure pass for closed physics.
TFPT hits all 13 frozen observables; 200k random pseudo-theories reach ≤ 5/13.
Assumption-minimal counting floor: of 94,500 declared F_U(1) variants exactly one α path lands in the CODATA window (1 in 94,500), with no subjective probability (v436).
Only 3 of 8 E₈ Casimir degrees feed a readout — and the 5/8 overhead is forced two-family structure (6·spine ⊔ det-ladder, v431), not diffuse slack.
≈ 102 bits that a random theory of equal complexity reproduces the scorecard — conditional on the declared grammar (v100).
The same small integers (2, 3, 5, 16, 240, 248) recur across every sector because they come from one source: a single machine, fed by two inputs, builds E₈ and reads off the Standard-Model skeleton, the constants, and the scale grammar — dozens of real numbers, none fitted in the closed branch.
Everything starts from the c₃ = 1/(8π) (P1) and the five-slot g_car = 5 (P2). No SM gauge group, no families, no α is inserted by hand — they are consequences.
The carrier gives the D₅ half-spinor, the family geometry ℙ¹∖μ₄ gives A₃, and the closes E₈ = (D₅ ⊕ A₃) + μ₄ as a lattice theorem. E₈ is the ; the SM is a after projection.
The E₈ closure feeds back and fixes the inputs: g_car = 5 is forced three ways and the 8 in c₃ equals rank E₈ = h(D₅) = φ(30). The discrete core is — only π stays irreducible.
Every claim carries a — [E] identity, [E] lattice theorem, [E] formalised, [E] numerical fixed point, [C] conditional, [O] open — and resolves to a single machine-checked ledger. The ledger wins on any disagreement.
D₅ = so(10) (spinor 16) and A₃ = su(4) (the four-puncture family geometry) share the same discriminant group ℤ₄. Their glue norms add to the E₈ root norm:
In words: E₈ is the lattice D₅ together with A₃, glued by the μ₄ simple current.
A closed lattice-theoretic construction — not a blind positing of 248. The E₈ numbers are carrier traces, not inputs.
The fine-structure constant is the unique positive root of a parameter-free cubic built only from c₃ and the abelian coefficient 41 = 10 b₁ — existence and uniqueness are proved:
In words: A parameter-free cubic in α, built only from c₃ and the abelian coefficient 41, set to zero.
In words: Its unique positive root gives the inverse fine-structure constant, about 137.0359992168.
CODATA-2022 recommends 137.035 999 177(21); the deviation is 2.9 × 10⁻¹⁰, about 1.9σ of its uncertainty — a fixed point, not a fit.
Reading rule. The two axioms at the top are the foundation; each lower band depends on the bands above. Exact identities and lattice theorems fail with a single counterexample; numerical fixed points fail against a declared comparison; conditional and open items fail only as named hypotheses. The single source of truth for which claim sits where is the machine-checked status ledger — if the text and the ledger ever disagree, the ledger wins.
The Standard Model takes ~20 parameters as input. Here only two numbers enter: the seam constant c₃ = 1/(8π) on the boundary and a five-slot carrier g_car = 5. No gauge group, no families, no α is put in by hand — everything below is a consequence.
In words: The seam constant c₃ equals one over eight pi; the carrier rank g_car equals five.
240 roots, det 1 — the unimodular audit hull; the SM is a readout after projection
Three doors — pick the one that matches how you want to pressure-test the claim.
Take the guided tour, or watch five and a half minutes of plain language — the claim stack without the jargon tax.
Open the tourRun a check in the browser, read the status ledger, and see exactly how the programme can fail.
Open verificationOne command to the suite green line. External replications: still zero — that is the invitation.
Replication pageThe reading guide, the architecture paper, and the adversarial Red Team — then the full set.