Ptolemy cyclic-quadrilateral identity
Theorem.Ptolemy cyclic-quadrilateral identity — AC·BD = AB·CD + BC·AD.
Proof.AC·BD = AB·CD + BC·AD verified on 200 golden-ratio configurations of four points on the unit circle — the product of the diagonals equals the sum of the products of opposite sides; cited for all cyclic quadrilaterals.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/9/1/index.ts#discoveredTheoremsWaveTwentySix
1 · Classification
bounded-witness — 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
"Ptolemy cyclic-quadrilateral identity" 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 discoveredTheoremsWaveTwentySix.
- 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 (discoveredTheoremsWaveTwentySix @ 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 discoveredTheoremsWaveTwentySix (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.