Pisano period π(10) = 60
Theorem.Pisano period π(10) = 60 — Fibonacci mod m is periodic with π(10) = 60, and π(m) is even.
Proof.Fibonacci mod m is periodic with π(10) = 60, and π(m) is even for every m > 2 (checked to m ≤ 50) — Fibonacci cycles modulo any base.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveThirtyThree
Figure — the proof, computed and plotted
F₀ = 0, F₁ = 1, Fₙ = (Fₙ₋₁ + Fₙ₋₂) mod 10 → period π(10) = 60
Computed by Fibonacci recurrence mod 10, exact — recomputed on every build, zero tokens.
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
"Pisano period π(10) = 60" 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 discoveredTheoremsWaveThirtyThree.
- 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 (discoveredTheoremsWaveThirtyThree @ src/9/1) 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 discoveredTheoremsWaveThirtyThree (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.