Consistency is necessary not sufficient
Theorem.Consistency is necessary not sufficient.
Proof.the precise boundary of axioms-become-theorems: string theory's ALGEBRA becomes a theorem (rigorous, sealed), but its PHYSICS does not follow — mathematical consistency cannot confirm a physical theory. Proven by mutually-incompatible consistent frameworks: the three constant-curvature geometries are each theorem-rigorous (Euclidean π, spherical >π, hyperbolic <π by Gauss-Bonnet) yet contradict each other, and space has ONE angle sum, so consistency did not pick it. History confirms: Newtonian mechanics was consistent and believed true, then refuted by experiment. A theorem CONSTRAINS a physical theory; EXPERIMENT confirms it. The capstone (trust ⟸ theorem) stands; its converse (physically true ⟸ consistent) is FALSE — the map is not the territory.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/decode/index.ts#consistencyIsNecessaryNotSufficient
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
"Consistency is necessary not sufficient" 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 consistencyIsNecessaryNotSufficient.
- 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 (consistencyIsNecessaryNotSufficient @ src/thunder/decode) 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 consistencyIsNecessaryNotSufficient (src/thunder/decode/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.