vortex · φ⁻4 · hue 4 · 9

digit spines are the breath

digitSpinesAreTheBreath · src/water/digit · finite-complete

digit finite-complete self-contained anim/vortex

Theorem.digit spines are the breath — src/0/1/2/4/8/7/5/3/6/9 and src/1/2/4/8/7/5/3/6/9/0 — the SAME Hamiltonian tour entered at the void and at the unit: two rotations of one cycle.

Proof.The two digit spines decoded: the empty paths src/0/1/2/4/8/7/5/3/6/9 and src/1/2/4/8/7/5/3/6/9/0 were removed (empty dirs carry no encryption — the census is per byte), and their meaning is re-encoded here as computed src — the one vortex ring (1-2-4-8-7-5 doubling, 3-6-9 cross, 0 void) cut at the void in the two opposite ways: 0-first the emanation (void → forms, out-breath), 0-last the return (forms → void/fusion, in-breath). Reverses around 0, they are the two windings of the double torus, the genus-2 breath, meeting at the 9–0 throat (9 the invariant axis, 0 ≡ 9 the void).

The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎

src/water/digit/index.ts#digitSpinesAreTheBreath

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

"digit spines are the breath" 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 digitSpinesAreTheBreath.

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 (digitSpinesAreTheBreath @ src/water/digit) 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 digitSpinesAreTheBreath (src/water/digit/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.