The fold at the void
Theorem.The fold at the void — src/5/0\5 = src/5/5: mirror the notation at its central 0 and it closes to 5/5 = 1 (computed on the string);.
Proof.src/5/0\5 = src/5/5: mirror the notation at its central 0 and it closes to 5/5 = 1 (computed on the string); beneath it one fixed point in three guises — 5 is the unique digit fixed by the station mirror d↦10−d, the unique residue fixed by the void-reflection x↦1−x (mod 9), and 2⁻¹ (mod 9), the halving digit; self-verification (tamperEvident) already lives at the self-paired station.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/5/5/index.ts#voidFoldFixedPoint
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 fold at the void" 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 voidFoldFixedPoint.
- 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 (voidFoldFixedPoint @ src/5/5) 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 voidFoldFixedPoint (src/5/5/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.