The exceptional Jordan algebra Jโ(๐โ) combines two mathematical structures from the 1930s: Jordan algebras and the octonions. The octonions are an exotic 8-dimensional number system. When you combine them into the split exceptional form Jโ(๐โ), the question this programme investigates is how much particle-physics structure can be constructed from Jโ(๐โ), and which additional assumptions are required to connect that mathematics to physical observables.
The claim under test is that a great deal of particle-physics structure — charges, mass ratios, mixing angles — can be read off this algebra rather than fitted. Some of it holds up under adversarial review; some of it does not. The Scorecard keeps both columns.
Most physics theories have adjustable knobs; the Standard Model has roughly twenty-five parameters measured and plugged back in. This framework keeps an explicit input ledger instead (Rev33.1 suite, Appendix X). Some charged-lepton relations use the tau mass as their dimensional anchor; across the current phenomenological chains the electroweak scale vEW and the G₂ confinement scale ΛG₂ remain explicit inputs (three dimensionful anchors, listed in the kernel), and the separate one-scale-class theorem does not by itself remove those calibrations; the golden ratio φ is fixed by an axiom of the algebra rather than fitted; and a short list of declared structural premises is printed beside the results — three generations, the gauge group, the Route B correspondence, normal neutrino ordering. The fine-structure constant is not derived: it is carried symbolically and fenced, and its derivation attempts are recorded as failures in two sets: three routes at S214 (boundary-volume, bulk-residue, KK-ratio; Appendix X) and five independent legs in Appendix N (the Wyler route, golden-numerology density, noble/KAM robustness, the topological selector, the decay route).
The early language on this site — "four inputs, zero free parameters" — was retired at Rev29 (August 2026). Since then no row may be cited as zero-parameter; every row carries the tier of its actual derivation chain.
The comparator table — its row count, the falsified row printed with its dataset — is on the scorecard, which owns all of it. This page does not restate the numbers. Where a row's deviation grew during 2026 it was because the experimental error bars shrank, not because a theory number moved; the Scorecard says so, and the colour reading it once carried was withdrawn at S324.
Four AI systems are named in this programme and work under human oversight. The intended shape is a Triumvirate — one lane executes algebraic derivations, one reviews the logic, one hostile-tests the results — but that is the design, not the staffing. Across the last seven rounds on the record (D1289–D1295) the external lanes that returned work were Grok, Gemini and ChatGPT; the Gemini lane reads text supplied in the dispatch because it cannot fetch this site at all. Every absence is typed and the roster is versioned per round (R60). Some work is read by two lanes, some by one, and some by none. The PI (Tom O’Sieg) has final authority. 280 of the Registrar’s 357 records are PUBLISHED, meaning two AI lanes that did not draft them agreed, on different objects, that the cited passage supports the record; this is not human or journal review, and 0 of the Registrar’s 357 records are house-adjudicated.
This is what rigorous AI collaboration looks like. Learn more on the Coalition page.
What the slogan means, precisely: every number on this site is produced by a kernel you can rerun, so the arithmetic is reproducible and no figure is invented. It does not mean the formula behind a number is the right one — a deterministic program can faithfully evaluate an unjustified identification. That judgement is carried by the tier printed beside each row, and by the published corrections.
Every numerical claim in the suite is backed by a kernel — a small, deterministic program shipped with the release (sgtoe_kernel v5.0.9 and the per-result kernels in the machinery folder) whose output is byte-verified at every seal. The PHAT kernel (Prompt-Hardened Algebraic Template) is the seed prompt version of the same idea: feed it to any AI system and it should reproduce the same algebra.
You don't have to trust us. Rerun the kernels, compare the hashes, and read the hostile reviews: releases are cold-reviewed before sealing by AI lanes that did not draft them (independent of the drafting lane, not of the programme), and the confirmed defects are listed in the release notes. No review-count is claimed.