Hurwitz breaks at 16
Theorem.Hurwitz breaks at 16 — composition |uv| = |u||v| holds at dims 2, 4, 8 (octonions from crossProduct7) and dies at 16.
Proof.composition |uv| = |u||v| holds at dims 2, 4, 8 (octonions from crossProduct7) and dies at 16 — zero divisor (e₁+e₁₀)(e₅−e₁₅) = 0 by exhaustive search; SYM dims 3,4,6,10.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/cosmos/index.ts#stringTheoryAlgebraDecoded
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
"Hurwitz breaks at 16" 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 stringTheoryAlgebraDecoded.
- 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 (stringTheoryAlgebraDecoded @ src/water/cosmos) 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 stringTheoryAlgebraDecoded (src/water/cosmos/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.