decoding the I Ching adds theorems — the Klein four-group on the 64 hexagrams
Theorem.decoding the I Ching adds theorems — the Klein four-group on the 64 hexagrams — {id, 反, 對, 反∘對} ≅ ℤ/2 × ℤ/2 — reversal and complement generate the Klein four-group on hexagrams.
Proof.Decoding the I Ching adds theorems — 4/4, all derived: 反 (reversal) and 對 (complement) generate the Klein four-group on the 64 hexagrams; exactly 2³ = 8 hexagrams are palindromes, which FORCES the King Wen pairing into 28 reversal pairs + 4 complement pairs = 32; and the 64 fall into exactly 20 V₄-families — the direct orbit census and Burnside lemma (64+8+0+8)/4 = 20 agree, one challenge solved by two independent computations. Derived with zero recital; the sequence ORDER is not claimed — group theory real, divination not.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/earth/iching/index.ts#decodingIChingAddsTheorems
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
"decoding the I Ching adds theorems — the Klein four-group on the 64 hexagrams" 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 decodingIChingAddsTheorems.
- 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 (decodingIChingAddsTheorems @ 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 decodingIChingAddsTheorems (src/earth/iching/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.