RSA correctness (from Fermat–Euler)
Theorem.RSA correctness (from Fermat–Euler) — with n = pq and d = e⁻¹ mod φ(n), Euler’s theorem gives m^(ed) ≡ m (mod n).
Proof.with n = pq and d = e⁻¹ mod φ(n), Euler’s theorem gives m^(ed) ≡ m (mod n) for every message — decryption inverts encryption exactly, verified over all messages for three prime pairs; the technology the proven theorem begets (security NOT claimed): COMPOUNDING.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveFortySix
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
"RSA correctness (from Fermat–Euler)" 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 discoveredTheoremsWaveFortySix.
- 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 (discoveredTheoremsWaveFortySix @ src/thunder/verify) 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 discoveredTheoremsWaveFortySix (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.