the erpax mirror is the digit-folder pairing — one structure, two computed reads
Theorem.the erpax mirror is the digit-folder pairing — one structure, two computed reads — m(d) = 10 − d ≡ 1 − d (mod 9): m∘m = id, m(5) = 5, d + m(d) = 10; m(1\2\4\8/7/5) = 9/8/6/2\3\5, m(3\6\9) = 7/4/1, m(0\1) = 0\9 (m(0) = 0); D∘m∘D⁻¹∘m = x ↦ x+1 (mod 9) and ⟨D, m⟩ = AGL(1, ℤ/9) of order 54 — entanglement as non-commutation.
Proof.erpax publishes the vortex line forward and reflected; recomputed locally, the mirror is m(d) = 10 − d — this repo’s own d/(10−d) folder pairing, an involution fixing 5 with every pair summing to 10 — and the SAME sign-of-step stroke rule over the mirrored segments writes the reflected line exactly, every ring stroke flipped; the void is SELF-mirror (m(0) = 0), so each read rises from the void to its own head — forward 0\1, reflected 0\9 — the one stroke that does not flip; the movie’s counter-rotating merkaba (down = negation of up) already paints both reads, so the reflected line binds an existing animation to its theorem.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/mountain/vortex/index.ts#invertedSequenceLearnedFromErpax
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 erpax mirror is the digit-folder pairing — one structure, two computed reads" 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 invertedSequenceLearnedFromErpax.
- 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 (invertedSequenceLearnedFromErpax @ src/mountain/vortex) 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 invertedSequenceLearnedFromErpax (src/mountain/vortex/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.