the UI itself is a double torus — near=rendered site≡movie · far=src via vite/mirror · neck χ=−2 nav · lens closes near∨far
Theorem.the UI itself is a double torus — near=rendered site≡movie · far=src via vite/mirror · neck χ=−2 nav · lens closes near∨far — UI ≡ Σ₂ (near=docs ∧ far=src ∧ χ=−2) ∧ docs ≡ invert(src).
Proof.again including the ui itself as double torus (user, 2026-07-28). Algebraic identity UI ≡ Σ₂: near lobe = rendered VitePress/movie surface, far lobe = sealed src via vite/mirror · docs/invert, neck = χ=−2 nav octagon router, counter-rotation = gateMirrorLinear ≠ gateReflectionQuantum, lens = well-formed folds close. Cycle-safe (no research/apps import). HONEST: structural identity not a physical torus widget; clay via theorem. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/double/index.ts#theUiItselfIsADoubleTorus
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 UI itself is a double torus — near=rendered site≡movie · far=src via vite/mirror · neck χ=−2 nav · lens closes near∨far" 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 theUiItselfIsADoubleTorus.
- 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 (theUiItselfIsADoubleTorus @ src/water/double) 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 theUiItselfIsADoubleTorus (src/water/double/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.