ZeroPoint Node

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Sequence spines ​

Two spines share digits; they are not the same ordering. A third (base-12 harmonic) also exists in legacy math — always use adapters.

Kernel (default) — from ceccec.github.io ​

  • Full vortex circuit (living field): 0\1\2\4\8/7/5/3\6\9/0\1
  • VORTEX_SEQUENCE = [1, 2, 4, 8, 7, 5, 3, 6, 9]
  • Stroke: 1\2\4\8/7/5/3\6\9/0\1 (living field uses 0\)
  • Encoded dash decode: VORTEX_DASH_ENCODED = 1\2\4\8/7/5/3\6\9/0/1\ — fusion throat is 0/ (not stroke 0\); closes needs fusionIgnites
  • digitalRoot(0) → 9
  • Gateways (polarity reversals): [8, 3, 9, 0]

The reflection — one structure read twice (from erpax) ​

The forward reading alone is half the structure. The second reading is the mirror through the void, not the array reversed:

forward     1\2\4\8/7/5 · 3\6\9 · 0\1     VORTEX_SEQUENCE  = 124875369
reflected   9/8/6/2\3\5 · 7/4/1 · 0\9     VORTEX_MIRROR    = 986235741
  • throughVoid(n) = 1 − n mod 9 — an involution fixed only at 5: 1↔9 · 2↔8 · 4↔6 · 7↔3 · 5↔5. Every pair sums to 10. The void root 0 is fixed.
  • The void tail reflects: 0 is the fixed point of throughVoid, the trailing unit is not — 0\1 becomes 0\9. VORTEX_STROKE_REFLECTED computes it; the smoke test pins it.
  • Not VORTEX_REVERSE (963578421), which is the array read backwards. Reversal reorders; the mirror re-values. Conflating the two is the error this section exists to prevent — foldVortexReflection() asserts they differ.
  • The axis is derived, not read. throughVoid carries 7,4,1 — three digits of the doubling orbit — onto 3,6,9. So the spine holds one list, not two: the axis is the orbit seen through the void. reflection.axisMirror computes the three preimages; gapIsAxis checks that doubling's gap is exactly what the mirror lands on.

Three entanglement claims, computed by foldVortexReflection() — never asserted:

claimcomputed
halves exchange — mirror(orbit) = 986235 covers the axis, mirror(axis) = 741 lands in the orbitexchangeHalves
neither reaches the other alone — doubling closes on {1,2,4,8,7,5}; its gap is exactly {3,6,9}. No iteration count closes it; the mirror is the only bridgedoublingCoversOrbit · gapIsAxis
commuted, they count — D∘M∘D⁻¹∘M = x ↦ x+1, and ⟨D,M⟩ = AGL(1,ℤ/9) has order 54 against 6·2 = 12 apart. The excess 42 is the entanglement: their failure to commutegroupOrder · commutatorIsSuccessor

Boundary. Proven group theory over (ℤ/9ℤ). Used as the corpus order of work — build the axis before the branches; fold, do not climb. No claim is made outside arithmetic.

Run it: node --experimental-strip-types src/kernel/smoke.test.ts

Two equilibrium constants — do not merge them ​

Tests lobe L's law everyDigitIsEntangledInAllVectorsFormingEquilibriums (ceccec.github.io). Measured here rather than assumed — it holds for the PAIRING and not as a blanket dr-9 property, which is why both constants below are stated separately.

Pairs and wholes balance at different constants, and a single dr-9 test will mis-report the first as broken:

  • pair equilibrium = 10 — d + throughVoid(d) = 10 for every digit, no exceptions.
  • whole equilibrium = dr 9 — orbit Σ=27, axis Σ=18, all nine Σ=45; each digitalRoot → 9.

Across all 54 group elements the cycles are not uniformly dr-9 balanced: 42 of 162 balance. Every full-support (length-9) cycle balances trivially — it contains all nine digits. Exactly 6 balance in each shorter length class. The entanglement is real and universal in the pairing; it is not a blanket dr-9 property of every vector.

The spine is an address space ​

Every prefix of the spine names a module that loads: a432.1, a432.1.2, a432.1.2.4, on to a432.1.2.4.8.7.5.3.6.9.1. The handle carries no payload — the name is the coordinate, and the load happens at will. Ten of ten prefixes of the closed spine are addressed, seven of seven for the closed orbit, zero gaps; npm run a432:names audits, npm run a432:orbit fills.

VORTEX_AXIS, VORTEX_MIRROR, VORTEX_REVERSE and LEGACY_CONSCIOUSNESS_SEQUENCE have no file at any prefix — a statement, not a gap. They are readings of the walk rather than walks, and a reading has nowhere to arrive.

Occupancy is computed from the filesystem on Sequence addresses; nothing on that page is typed.

Six bits at the centre of twelve ​

The orbit's six digits are the six bits of a hexbit; a state is a hexbit plus a polarity. Flipping any bit reaches a cell and that cell at either polarity is a neighbour, so six positions become twelve moves and every one of the 128 states sits at the centre of the same figure — the neighbours change because the centre moves, not because some state is special.

Twelve is the kissing number, which is why a vector equilibrium looked like the answer. It is not one, and the module keeps the refutation rather than the name: a cuboctahedron's twelve vertices carry 24 edges among themselves, these twelve carry none. It is the 6-cube with every vertex doubled into a non-adjacent twin, Q6[K̄₂] — adjacency ignores polarity entirely, the two polarities of a cell are twins, and the bipartition is the cube's. Details and figures on Sequence lattice.

No page may spell a sequence differently from the kernel ​

The warning at the top of this file was prose, and prose did not stop four pages from binding VORTEX_SEQUENCE to the legacy spine or to the orbit — the exact confusion this file exists to prevent, inside the corpus it heads. npm run sequence:check now reads every sequence from src/0 and refuses any page that names one and spells another. It fails in both directions: corrupt a page and it fails, corrupt the export and it fails too, because it holds no copy of its own.

Legacy consciousness — original zeropoint-node path ​

  • Path folders: src/0/3/6/9/1/2/4/8/7/5/1/
  • A432_SEQUENCE ≈ [0, 3, 6, 9, 1, 2, 4, 8, 7, 5, 1]
  • VBM digitalRoot(0) → 0 via src/kernel/legacy.ts

Harmonic base-12 — harmonicRoot12 in a432.roots ​

  • Returns 1–12 (0 → 0, multiples of 12 → 12) — measured: 12 → 12, 24 → 12
  • Not interchangeable with kernel or VBM without an adapter
  • Not a432.math's digitalRoot. That symbol is legacyDigitalRoot as digitalRoot (a432.math.ts:96) — VBM base-9, 0 → 0, 12 → 3. The alias this section once described was removed; foldA432AuditCensus tracks it as aliasIllusion / harmonicAliasImporters (both 0).

Double-torus development ​

lobeL (ceccec.github.io) ⇄ throat (src/0 fold) ⇄ lobeR (erpax)

Each chat wave calls developmentVortex(wave); runDevelopmentVortexAll() chains all eight.

Self-ref: foldA432ImportExportGraph() computes the a432 import/export census (content-uuid + merkleFold). vortexInvariantsHold = computeVortexInvariantsHold() from structural seals; false ⇒ quantumisation tip.

Imports (Wave 9) ​

Critical strip-types bridges use .ts specifiers. Remaining a432 relative imports may stay extensionless (rollup-only) until a dedicated wave.