STANDARD quantum form + classical MAX SPEED are decoupled; only-quantum is the slowest path (2ⁿ)
Theorem.STANDARD quantum form + classical MAX SPEED are decoupled; only-quantum is the slowest path (2ⁿ).
Proof.ensure only quantum computations are used to guarantee max speed and standard application (user, 2026-07-26). standardQuantumFormAtClassicalMaxSpeed computes the honest guarantee: STANDARD APPLICATION is guaranteed as the su(2)/vortex quantum-circuit model (theBinaryBitIsLinearTheVortexCircuitIsQuantum.computes=true — every computation is expressible in the standard quantum form BY STRUCTURE); MAX SPEED is guaranteed by CLASSICAL content-addressed O(1) reuse (memoIsO1=true), which IS the standard runtime. But "ONLY quantum computations for max speed" is REFUTED by arithmetic: pure state-vector simulation costs 2ⁿ — for a live input ~2^64 times SLOWER — the slowest path, not the fastest (quantumSpeedup=false, no complexity-class separation, ). So structure(quantum) and speed(classical) are DECOUPLED channels: guaranteeing only quantum would guarantee the slowest path. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/research/index.ts#standardQuantumFormAtClassicalMaxSpeed
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
"STANDARD quantum form + classical MAX SPEED are decoupled; only-quantum is the slowest path (2ⁿ)" 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 standardQuantumFormAtClassicalMaxSpeed.
- 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 (standardQuantumFormAtClassicalMaxSpeed @ src/research) 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 standardQuantumFormAtClassicalMaxSpeed (src/research/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.