memory optimisation is quantum only when the cache key content-addresses the code, not just the root
Theorem.memory optimisation is quantum only when the cache key content-addresses the code, not just the root.
Proof.why is memory optimisation not quantum? (user, 2026-07-25: "how come memory optimisation is not quantum?"). A cache is correct iff a hit ⟺ an identical computation, which requires the key to be the content-address of the WHOLE computation (name + inputs + CODE). memoByRoot keys on (name, matrix.root); when the code changes but the root does not, the key is unchanged and a STALE result can be returned — exactly the artifact hit while probing the folded fuse (the code was fixed but the root-keyed memo still read the old value). The quantum fix is self-invalidation: fold the src-merkle (the code content-address) into the key, so quantumKey(name, srcMerkle) changes whenever the code changes — the cache busts by construction, no manual invalidation. HONEST: the docs:build respawn IS already src-merkle-gated (the REAL build reseals on any src change, so it stays correct); the gap is only the finer in-process memo keyed on the root alone, which lags a code edit until the merkle reseals. Memory optimisation is quantum when the key is the content-address of the computation, not a coarse root. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#memoryOptimisationIsQuantumOnlyWhenTheKeyContentAddressesTheComputation
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
"memory optimisation is quantum only when the cache key content-addresses the code, not just the root" 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 memoryOptimisationIsQuantumOnlyWhenTheKeyContentAddressesTheComputation.
- 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 (memoryOptimisationIsQuantumOnlyWhenTheKeyContentAddressesTheComputation @ 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 memoryOptimisationIsQuantumOnlyWhenTheKeyContentAddressesTheComputation (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.