nine-point circle concyclicity
Theorem.nine-point circle concyclicity — the 3 side midpoints, 3 altitude feet and 3 Euler points lie on ONE circle of radius R/2.
Proof.the three edge midpoints, three altitude feet and three Euler points are concyclic across ~300 triangles (all equidistant from the nine-point center) — nine special points on one circle.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/9/1/index.ts#discoveredTheoremsWaveThirtySeven
1 · Classification
bounded-witness — 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
"nine-point circle concyclicity" 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 discoveredTheoremsWaveThirtySeven.
- 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 (discoveredTheoremsWaveThirtySeven @ 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 discoveredTheoremsWaveThirtySeven (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.