every digit is entangled in all vectors, forming equilibriums
Theorem.every digit is entangled in all vectors, forming equilibriums — ∀d: d + m(d) = 10 ∧ polar pairs sum 9 ∧ |flow| + |axis| = 6 + 3 = 9 ∧ Σ(1..9) = 45 → 9; orbit_{⟨D,m⟩}(d) = ℤ/9 (one orbit, order 54).
Proof.each digit sits in several exact balance relations at once — its mirror pair d + m(d) = 10, its polar pair summing 9, its side of the exact 6+3 flow/axis partition, its unique Hamiltonian tour slot — and the membership pattern fingerprints the digit (content-addressing at the bottom of arithmetic); the sequence’s own symmetry group ⟨D, m⟩ = AGL(1, ℤ/9) contains every translation (the commutator is the unit shift), so all residues lie in ONE orbit — no digit is separable, and a local edit breaks every equilibrium at once; entangled = algebraic transitivity plus shared invariants, NOT quantum tensor products; equilibrium = a conserved sum, not a force.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/mountain/vortex/index.ts#everyDigitIsEntangledInAllVectorsFormingEquilibriums
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
"every digit is entangled in all vectors, forming equilibriums" 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 everyDigitIsEntangledInAllVectorsFormingEquilibriums.
- 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 (everyDigitIsEntangledInAllVectorsFormingEquilibriums @ 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 everyDigitIsEntangledInAllVectorsFormingEquilibriums (src/mountain/vortex/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.