the hexagram orbit census — twelve fours and eight twos complete the 64
Theorem.the hexagram orbit census — twelve fours and eight twos complete the 64 — 64 = 12·4 + 8·2 — the hexagram orbits under {反, 對} (twelve 4-orbits, eight 2-orbits).
Proof.The hexagram orbit census — 2/2: under the Klein four-group of 反 and 對 the 64 hexagrams decompose into exactly 12 orbits of size 4 and 8 orbits of size 2, no fixed points (12·4 + 8·2 = 64; 20 orbits, matching the Burnside average sealed independently), and the small orbits sit exactly on the 16 symmetric hexagrams — palindromes pairing by complement, anti-palindromes by the composite. Exhaustive enumeration, every count refutable.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/earth/iching/index.ts#hexagramOrbitCensusTwelveFoursEightTwos
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
"the hexagram orbit census — twelve fours and eight twos complete the 64" 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 hexagramOrbitCensusTwelveFoursEightTwos.
- 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 (hexagramOrbitCensusTwelveFoursEightTwos @ src/earth/iching) 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 hexagramOrbitCensusTwelveFoursEightTwos (src/earth/iching/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.