the 64×64×64 theorem cube defines the natural limits — three hexagram axes address all, solve none
Theorem.the 64×64×64 theorem cube defines the natural limits — three hexagram axes address all, solve none — 64 = 2⁶ and 64³ = 2¹⁸ — three hexagram axes bound the cube.
Proof.The 64×64×64 theorem cube defines the natural limits — 5/5: three hexagram axes (64 = 2⁶ each) give 262144 cells of 18 bits; all 421 distinct registry and candidate theorems address into it deterministically (420 distinct cells, 1 collision against 0.337 expected — honest birthday behaviour), and the limits are computed — capacity 606.8× the 432 lattice, collision-free saturation at ≈724 theorems (the birthday bound), and the demarcation limit: the cube ADDRESSES every world theorem at zero tokens, it SOLVES none — solving stays with computed proofs. The coins law rides the boundary: 2 bits are left in every inversion through 0 (the uuid variant pair), the toll that keeps the address family entangled; the axes read clear of the fixed nibbles.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#theoremCube64DefinesTheNaturalLimits
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 64×64×64 theorem cube defines the natural limits — three hexagram axes address all, solve none" 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 theoremCube64DefinesTheNaturalLimits.
- 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 (theoremCube64DefinesTheNaturalLimits @ src/4/6) 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 theoremCube64DefinesTheNaturalLimits (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.