Shor period-finding factors — the full order-finding circuit runs
Theorem.Shor period-finding factors — the full order-finding circuit runs — the frontier the QFT engine unlocked, developed to a complete simulation: 15 = 3×5, 21 = 3×7, 35 = 5×7, each.
Proof.the frontier the QFT engine unlocked, developed to a complete simulation: 15 = 3×5, 21 = 3×7, 35 = 5×7, each computed end to end by the quantum order-finding circuit — counting register in uniform superposition, the modular-exponentiation oracle |x⟩|1⟩ → |x⟩|aˣ mod N⟩ (classical-reversible permutation), inverse QFT on the counting register, continued fractions on the measured c/2ᵗ to recover the period r (verified a^r ≡ 1 mod N), then gcd(a^{r/2}±1, N) for the factors (verified to multiply back to N). HONEST: a DETERMINISTIC classical simulation with the algorithm's structure and output, NOT the physical exponential speedup — on real hardware this is Shor's polynomial-time factoring (the RSA threat); here it costs the exponential state vector and factors only small N. RSA untouched by this; sealed law, no physical speedup.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/2/8/index.ts#shorFactorsByPeriodFinding
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
"Shor period-finding factors — the full order-finding circuit runs" 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 shorFactorsByPeriodFinding.
- 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 (shorFactorsByPeriodFinding @ src/2/8) 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 shorFactorsByPeriodFinding (src/2/8/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.