Fibonacci partial sum F_{n+2}−1
Theorem.Fibonacci partial sum F_{n+2}−1 — Σ_{k=1}^n F_k = F_{n+2} − 1, exact in BigInt to n = 80 (Σ_{1..10} = 143 = F₁₂ − 1).
Proof.Σ_{k=1}^n F_k = F_{n+2} − 1, exact in BigInt to n = 80 (Σ_{1..10} = 143 = F₁₂ − 1).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveForty
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
"Fibonacci partial sum F_{n+2}−1" 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 discoveredTheoremsWaveForty.
- 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 (discoveredTheoremsWaveForty @ 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 discoveredTheoremsWaveForty (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.