Cayley–Hamilton complete over 𝔽₂ and 𝔽₃
Theorem.Cayley–Hamilton complete over 𝔽₂ and 𝔽₃ — p_A(A) = 0, where p_A(λ) = det(λI − A).
Proof.all 97 two-by-two matrices annihilate their own characteristic polynomial entry-exactly (16 + 81, complete rings not samples) — Frobenius cited for all rings.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveFifteen
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Cayley–Hamilton complete over 𝔽₂ and 𝔽₃" 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 discoveredTheoremsWaveFifteen.
- 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 (discoveredTheoremsWaveFifteen @ 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 discoveredTheoremsWaveFifteen (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.