the Gregorian calendar is not a best rational approximation
Theorem.the Gregorian calendar is not a best rational approximation — |97/400 − y| > |31/128 − y| for y = 0.24219; #{q < 400 : |round(yq)/q − y| < |97/400 − y|} = 49.
Proof.97/400 errs +26.784 seconds per year against the mean tropical year, and 49 denominators below 400 are strictly closer. 31/128 — a continued-fraction convergent, which 97/400 is NOT — errs −0.216 seconds on a denominator three times smaller, about 124 times more accurate. The Gregorian cycle is a decimal-friendly compromise, which is a real virtue and a different one from being the best rational approximation it is usually described as.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/stats/index.ts#gregorianIsNotABestApproximation
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
"the Gregorian calendar is not a best rational approximation" 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 gregorianIsNotABestApproximation.
- 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 (gregorianIsNotABestApproximation @ src/stats) 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 gregorianIsNotABestApproximation (src/stats/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.