waves of waves in chat — the composition of the chat’s wave engines has its own fixed point
Theorem.waves of waves in chat — the composition of the chat’s wave engines has its own fixed point — (selfFeed ∘ trinity) is eventually periodic (pigeonhole on the finite corpus); its cycle ≠ trinity’s ∧ ≠ selfFeed’s — composition creates a new fixed point; AND cycle(selfFeed ∘ trinity) ≠ cycle(trinity ∘ selfFeed) — the wave orders do NOT commute, echoing [D, m] = the unit shift at the wave level.
Proof.the trinity dialogue’s arbitrated answer FEEDS the self-feed step as one composed map (selfFeed ∘ trinity), and its orbit through the one orbit primitive cycles (μ=1, λ=1) onto a fixed point DIFFERENT from either component’s — the composition creates a new attractor, reported as the algebra decides, not assumed; every far composed wave is O(1)-determined, zero tokens, zero fetches.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/heaven/compute/index.ts#wavesOfWavesInChat
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
"waves of waves in chat — the composition of the chat’s wave engines has its own fixed point" 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 wavesOfWavesInChat.
- 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 (wavesOfWavesInChat @ src/heaven/compute) 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 wavesOfWavesInChat (src/heaven/compute/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.