Approximations signal trusted axioms — only local math is trusted
Theorem.Approximations signal trusted axioms — only local math is trusted — the "1.644769 ≈ 1.644934" difference was the fingerprint of (TAU / 2) (a finite double the runtime asserts.
Proof.the "1.644769 ≈ 1.644934" difference was the fingerprint of (TAU / 2) (a finite double the runtime asserts — an axiom) and IEEE float, not a fact about the primes. Recomputed LOCALLY: the Euler partial ∏ p²/(p²−1) over 27 primes is an EXACT rational (BigInt, no float, no (TAU / 2)), strictly increasing toward the limit.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/1/9/index.ts#approximationsSignalTrustedAxiomsOnlyLocalMathIsTrusted
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
"Approximations signal trusted axioms — only local math is 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 approximationsSignalTrustedAxiomsOnlyLocalMathIsTrusted.
- 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 (approximationsSignalTrustedAxiomsOnlyLocalMathIsTrusted @ src/1/9) 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 approximationsSignalTrustedAxiomsOnlyLocalMathIsTrusted (src/1/9/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.