Catalan conjecture 8 and 9 to 10⁶
Theorem.Catalan conjecture 8 and 9 to 10⁶ — 8 = 2³ and 9 = 3² are the ONLY consecutive perfect powers up to 10⁶.
Proof.8 = 2³ and 9 = 3² are the ONLY consecutive perfect powers up to 10⁶ — every perfect power enumerated, the sole unit gap; Mihailescu 2002 cited for all n.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentyFour
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Catalan conjecture 8 and 9 to 10⁶" 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 discoveredTheoremsWaveTwentyFour.
- 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 (discoveredTheoremsWaveTwentyFour @ src/9/1) 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 discoveredTheoremsWaveTwentyFour (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.