Gauss Eureka: every n is a sum of three triangular numbers
Theorem.Gauss Eureka: every n is a sum of three triangular numbers — 8n+3 = odd²+odd²+odd² (three squares forced odd by mod 8) with 2k+1 ↔ T_k gives three triangular numbers.
Proof.8n+3 = odd²+odd²+odd² (three squares forced odd by mod 8) with 2k+1 ↔ T_k gives three triangular numbers — verified by exhaustive witness for every n ≤ 300, compounding on the three-square theorem.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveFiftyTwo
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
"Gauss Eureka: every n is a sum of three triangular numbers" 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 discoveredTheoremsWaveFiftyTwo.
- 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 (discoveredTheoremsWaveFiftyTwo @ src/thunder/waves) 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 discoveredTheoremsWaveFiftyTwo (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.