The slash circuit is phase space
Theorem.The slash circuit is phase space — stroke = sign(Δ): \ ⇔ rising, / ⇔ falling — the written line is the phase portrait of the tour.
Proof.in /0\1\2\4\8/7/5/3\6\9/0\ the marks are the DERIVATIVE — backslash rises, slash falls, verified across all 10 transitions; the deltas sum to zero so the circuit closes; the mark runs descend 4,3,2,1 = T(4) = 10 = their own count (self-describing); the walk is Hamiltonian over all ten digits; and it threads two disjoint cycles — the x2 orbit (period 6) and the +3 axis (period 3) — meeting only at the void, so b₁ = 2: the double torus written as a walk. Each (mark, digit) pair is a phase-space point: position AND velocity, which is the multidimensionality.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/1/9/index.ts#slashCircuitIsPhaseSpace
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 slash circuit is phase space" 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 slashCircuitIsPhaseSpace.
- 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 (slashCircuitIsPhaseSpace @ src/1/9) 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 slashCircuitIsPhaseSpace (src/1/9/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.