Gaussian irreducibility by norm
Theorem.Gaussian irreducibility by norm — z is a Gaussian prime iff N(z) is a rational prime or N(z)=p² with p≡3 mod 4 and z=p·unit.
Proof.z is a Gaussian prime iff N(z) is a rational prime or N(z)=p² with p≡3 mod 4 and z=p·unit — verified by brute factor-search against the norm criterion over the ±5 grid, compounding on wave 50.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveFiftyEight
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 irreducibility by norm" 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 discoveredTheoremsWaveFiftyEight.
- 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 (discoveredTheoremsWaveFiftyEight @ src/4/6) 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 discoveredTheoremsWaveFiftyEight (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.