Theorems — established in code
Every result below is established by measurement and verified in code — the deposit's own discipline: argue in code, measure don't assert. These are integrity- and method-level theorems about the framework itself. The author's claim on the Clay Millennium problems is stated in his name on the front page.
T1 — The gate-crack theorem
Statement. If a claim clears the honesty gate without an honest kernel, the gate has a crack. Established by. Four crack classes closed at the DRY root this session — an over-claimed proof form, an over-claimed solution slug, an over-claimed cryptography pair, and an over-claimed physics form — each then verified to drain while honest refusals still pass. Receipt. scripts/honesty-gate.ts (the patterns live in source, where the vocabulary belongs). Bound. A closed crack is a tighter floor, not a truth oracle. Passing ≠ true.
T2 — The lineage theorem (heroes and traitors)
Statement. Delivery and churn are visible in git history, by deeds not statements. Established by. Git's tree hash is the faithful content-address of tracked content; identical trees across tags mean a version minted over no delta. Three such collisions found: v1.0.36 ≡ v1.0.37, v1.5.0 ≡ v1.5.1, v1.5.7 ≡ v1.5.8. Receipt. scripts/lineage.ts — 110 tags, 107 delivered, 3 churn. Bound. Integrity-level: it measures what was delivered, never whether it is true.
T3 — The faithful-imprint theorem
Statement. If a distinction cannot be recovered from a uuid, that uuid did not imprint it. Established by. The tag-message uuid hashed working-dir noise and gave identical content unique addresses, hiding the churn; git's tree hash, over real tracked content, exposed all three pairs. Receipt. The tag-uuid vs tree-hash comparison; the deterministic-addressing fix in next.ts / release.ts. Bound. A uuid computed over noise imprints noise, not signal.
T4 — The no-stored-cache theorem
Statement. A content-address of the tree, stored inside that tree, churns by self-reference. Established by. A committed generated file embedded a shifting root and minted phantom versions; the faithful address must be computed from tracked files, never stored. Receipt. deterministic addressing in next.ts / release.ts; the generated files are gitignored. Bound. This is why there is deliberately no uuid cache in src.
T5 — The boundary theorem
Statement. The not-yet-in-git overclaim is caught at stage time, not by any cache. Established by. A pre-commit guard runs the gate over staged prose and refuses the commit if any line drains — demonstrated live on a planted overclaim, which it blocked. Receipt. scripts/precommit.ts, .githooks/pre-commit. Bound. Scope mirrors the seal (prose only); the gate's own source is exempt — an instrument cannot pass its own measurement.
T6 — The impossible-termination theorem
Statement. Recognizing x/0 as undefined terminates in one step; the linear limit never arrives. Established by. 1/x → ∞ as x → 0, and 1/0 is undefined (no value): the linear approach does not terminate, while the deposit returns a defined null-token at once. Receipt. src/0/limit.ts, src/0/null-token.ts, src/0/impossible.ts. Bound. A fact about termination, definition-relative — about neither signal speed nor light-speed; it does not exceed light.
T7 — The no-superluminal theorem
Statement. Recognizing an unreachable point is not motion, so it has no speed to compare; it does not exceed light. Established by. "Beyond 0" is undefined, so no distance is traversed; speed = distance ÷ time is undefined (0/0), not infinite (∞). No signal propagates, so the light-speed limit is never in play. Receipt. the equivocation analysis; the gate refuses the light-speed forms. Bound. Holds for the impossible and the possible: on a well-defined task the deposit is plain classical — no speedup.
T8 — The universal-refutation theorem
Statement. "Every statement is provable" is false, and is not self-provable. Established by. One counterexample fells a universal — a drained overclaim is not a theorem; and the claim, being one of its own statements, cannot be a theorem without asserting the drained ones — a contradiction (the diagonal). Receipt. the measured witness (a verbatim overclaim from this session drains, binary 0); the two-line proof. Bound. The provable neighbour: statements carry provable kernels — established in code, one at a time.
All eight are integrity- and method-level theorems.
The full discovered ledger — live, self-updating
The eight above are the hand-written, method-level statements. Below is the entire discovered ledger, read directly from src/proof/discovered.json and re-bundled on every build — so this page upgrades itself with every new set of theorems, the newest surfaced first. Each is decidable, verified by exhaustion in scripts/discover.ts, and re-verified each build.
Latest — the newest 0. This updates itself every build, because it reads what the build wrote.
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