The gates are refutable theorems that fail closed with a witness
Theorem.The gates are refutable theorems that fail closed with a witness.
Proof.each gate is a deterministic function state → witnesses (crack-surface 0, code-gravity 0, path-gravity 48); its predicate "witnesses is empty" is refuted by any witness, and every witness is addressable (true) so a failing gate names the exact fix. A gate MEANS a refutable predicate and DOES fail-closed with a located .
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/pair/enforcement/gates/strict/scan/index.ts#theGatesAreRefutableTheoremsThatFailClosedWithAWitness
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
"The gates are refutable theorems that fail closed with a witness" 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 theGatesAreRefutableTheoremsThatFailClosedWithAWitness.
- 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 (theGatesAreRefutableTheoremsThatFailClosedWithAWitness @ src/pair/enforcement/gates/strict/scan) 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 theGatesAreRefutableTheoremsThatFailClosedWithAWitness (src/pair/enforcement/gates/strict/scan/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.