Only theorems can be trusted
Theorem.Only theorems can be trusted.
Proof.the capstone: trust IS theoremhood. The trusted surface is exactly the registry theorems (recomputable at zero tokens, refutable, fail-closed); everything else — regex gates, hand-set constants, asserted numbers — is UNTRUSTED by construction, and that untrusted set is the refactoring worklist. A theorem is not infallible but it is REFUTABLE, which is what trustable means; Gödel bounds the trust ratio below 1. The answer to can-you-trust-science: trust is theoremhood, and what cannot be computed is examined not believed.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#onlyTheoremsCanBeTrusted
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Only theorems can be trusted" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation onlyTheoremsCanBeTrusted.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (onlyTheoremsCanBeTrusted @ src/4/6) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes onlyTheoremsCanBeTrusted (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.