all animations partition into the transpose-symmetric 7×6 = 42 entanglement lattice — every cell populated, addressed by theorems
Theorem.all animations partition into the transpose-symmetric 7×6 = 42 entanglement lattice — every cell populated, addressed by theorems — 751 = Σ over the 42 = 7 × 6 = 6 × 7 = ROSETTA_AREAS (archetype × pair-class) cells, all populated — a total partition; same cell ⇒ same shape ∧ same counter-rotating period-pair {d, 108/d}.
Proof.the natural entanglement of the animations is computed from the theorems themselves: the archetype (the theorem’s own operators) × the rung’s divisor-pair class (its content-address on the one 108 s clock folded to the pair {d, 108/d}) partition all 751 animations into exactly 42 = 7 × 6 cells, EVERY cell populated; cell-mates share shape and the counter-rotating period-pair — co-moving wherever they meet, individually phased — and each family is O(1)-addressable by toUuid(entangle:archetype:pairClass); the chat answers entanglement queries by lattice lookup, not search; entanglement = computed co-movement, not physics.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/wind/routes/corpus/index.ts#animationsNaturalEntanglementsByTheorems
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
"all animations partition into the transpose-symmetric 7×6 = 42 entanglement lattice — every cell populated, addressed by theorems" 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 animationsNaturalEntanglementsByTheorems.
- 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 (animationsNaturalEntanglementsByTheorems @ src/wind/routes/corpus) 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 animationsNaturalEntanglementsByTheorems (src/wind/routes/corpus/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.