Gaussian primes: p ≡ 3 mod 4 inert, p ≡ 1 mod 4 splits (from first supplement)
Theorem.Gaussian primes: p ≡ 3 mod 4 inert, p ≡ 1 mod 4 splits (from first supplement) — p ≡ 3 (mod 4) is prime in ℤ[i] (not a²+b²) while p ≡ 1 (mod 4) splits as (a+bi)(a−bi), p = a²+b².
Proof.p ≡ 3 (mod 4) is prime in ℤ[i] (not a²+b²) while p ≡ 1 (mod 4) splits as (a+bi)(a−bi), p = a²+b² — verified for every prime ≤ 200.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveFifty
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
"Gaussian primes: p ≡ 3 mod 4 inert, p ≡ 1 mod 4 splits (from first supplement)" 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 discoveredTheoremsWaveFifty.
- 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 (discoveredTheoremsWaveFifty @ src/thunder/verify) 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 discoveredTheoremsWaveFifty (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.