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 short film: the whole Standard Model, gravity and 27 predictions out of almost nothing — why E₈ is the proof layer, how the two inputs fix themselves, the beauty of one connected object, and how we keep it honest rather than numerology.
A program begins as a few lines of source code — and unfolds into something huge and detailed. Here's an honest question, not a claim: could reality work the same way? Could the rules of our universe be the output of something tiny — compiled, not chosen? Let's look at where that idea leads — and how it could fail.
Start at the end — with what this one idea actually produces. Almost the whole Standard Model — our rulebook for every known particle and force: the forces, why matter comes in three families, the single Higgs, the masses, how they mix. Gravity — Einstein's equation, with its constants fixed instead of assumed. Pieces of cosmology — the early universe, how much ordinary matter there is, dark energy. The strength of light — the famous one over one-thirty-seven — is just one line among many. And twenty-seven concrete, testable predictions. That's the output. The real question: from how much input?
Here's the surprising part: almost nothing goes in. Two numbers. A tempo — set by the edge of space. And a width: how many slots the building block has — five. And those two aren't even truly free. Strip it down, and what's left is one small whole-number pattern — and π. A huge, detailed result from a tiny source. That gap — between almost nothing and all of this — is the whole story.
How can two numbers carry that much? Because they don't just get plugged in — they have to pass a test. The parts they build must fit into one rigid mathematical object: E₈. E₈ isn't a force of nature. It's a proof layer — the referee that certifies the pieces fit only one way. Two hundred and forty points, one perfect pattern. If anything were off, nothing would lock. Most possible universes simply don't compile.
Now turn it around. If the proof closes for only one tempo and one width… then the proof decides them. The inputs are forced by the structure they build. The thing works out its own starting point. The loop closes on itself. That's the fixed point the theory is named after. Not a model you tune until it fits — a structure that has to be what it is.
Once you see it, the elegance is hard to miss. The same small numbers — two, three, five — run through every part, because it's all one object. And it isn't frozen. A simple clock gives the whole thing a single resting state. So the constants aren't dialled in by hand — they're where it settles. Almost no free choices, one connected picture.
Now the fair objection: small whole numbers that fit reality — isn't that just numerology, like seeing faces in clouds? We took it seriously. Nobody drew this picture top-down. It assembled itself — out of hundreds of small, independent checks, each verified by computer, that slowly clicked into one whole. E₈ proves the pieces can fit. These checks prove we're not fooling ourselves — every load-bearing claim machine-verified twice, with a team tasked to break it. We froze predictions before the data, then ran two hundred thousand random look-alikes. They get at most five right; this gets all thirteen. By luck? Below one in 10³⁰ — effectively zero.
And it hasn't stopped. Five new results — each machine-checked, each honestly labelled. One. The calculating engine of the deepest route used to be declared. Now it is derived — its key number, sixty-four, is computed three independent ways instead of put in. One global integral stays open. Two. The bridge from timeless Euclidean math back to real, physical time now stands — at the free level: the reflection structure exists, and the little clock returns as a genuine time operator. Three. The seam has a temperature — exactly the black-hole value its founding constant demands. Geometry, anomaly, and now temperature — all from c₃ = 1/(8π). The seam is a miniature horizon. Four. Ten blind tests prove the one remaining input bit cannot be derived — it is a genuine choice. But it is now physically defined — in principle readable by an interferometer. One axiom becomes one measurement. And five — reported just as loudly: the first interacting toy model fails one of our own kill tests. A real threat — and the first constructive filter for the one construction site left.
So what's still open? The interacting seam. One global integral. One unit no pure number can give. Every gap labelled — and still killable: neutrino mass, proton decay, dark energy. One clean miss, and it's wrong.
So — is reality compiled? We still don't know. That's the honest answer. But the version you can test keeps getting sharper — more derived, less declared; every gap marked, every test named. Maybe the constants were never arbitrary. Maybe they simply had to add up.
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 — 523 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.
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.
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.