Realisations — the step chain
Each step: the realisation, the file that computes/proves it, and the result. Everything recomputes from the digit-folder mesh; see Compute.
1 — Division by zero changes the domain
n/0 := n⁻¹ (mod 9) on the units; 0 still has no inverse. Any value for x/0 requires leaving the field (Riemann sphere, wheel, ℤ/9…), each dropping an axiom. → src/9/vortex.lean, SEQUENCE-DECODE.md §2.
2 — The sequence reflects itself (three ways)
Self-sealing fraction product = 1; additive m(d)=10−d; multiplicative n↔n⁻¹. → src/5/vortex.lean (self_seal), SEQUENCE-DECODE.md §3.
3 — Gateways [8,3,9,0]
The stroke-reversal digits of the cyclic walk. → SEQUENCE-DECODE.md §4.
4 — Ring structure: units vs nilradical
3² ≡ 6² ≡ 0 (mod 9) → {3,6,9} is the nilradical (no inverse); units ⟨2⟩ are the doubling hexagon; 432 = 2⁴·3³ = 16·27, digit-sum 27. → src/{1..9}/vortex.lean, SEQUENCE-DECODE.md §5.
5 — Nonagon geometry
Three mod-3 cosets = three equilateral triangles; two counter-rotating flows. → SEQUENCE-DECODE.md §6.
6 — Inter-ring lattice
Ten's-complement bonds d ↔ 10−d (sum 10 = carry); trinity = 3 outbound legs. → src/5/reflection.lean, SEQUENCE-DECODE.md §7.
7 — Merkaba = cube (the "8")
A star tetrahedron's 8 vertices are a cube; the trinity-bond lattice is the cube graph Q₃ (8 nodes, 3-regular, bipartite). → PHYSICS-SCALES, animation (published artifact).
8 — Magnetic field of the merkaba coils
Biot–Savart: counter-rotating triangles → central-axis field null; co-rotating → central max. (real EM of a coil geometry.) → computed; scale check μ₀I/2r = 2.09 µT.
9 — Flower → Fruit → Metatron
A cube down its 3-fold axis is a hexagon → Seed (6+1) → Flower (19) → Fruit (13) → Metatron (78 lines). Verified projection. → animation.
10 — 5 is the center
5 = 2⁻¹, primitive root, the 10−d fixed digit; the still self-inverse pivot. → src/5/vortex.lean.
11 — Shell-model magic numbers
2, 8, 20, 28, 50, 82, 126 = cumulative 2j+1 (oscillator + spin-orbit). The 10·2^k ladder hits only the oscillator closures 20, 40. → src/8/nucleus/{shell-model-magic.ts, magic.lean}.
12 — Matter is waves — and waves have scales
f = E/h: 432 Hz → 10²; nuclear shell → 10²⁰; proton → 10²³. Bound-nucleon de Broglie λ ≈ 5.22 fm (the standing wave). 432 is the acoustic note, not the nuclear one. → src/2/frequency-scales.ts, PHYSICS-SCALES.
13 — Proton mass challenge
Best vortex fit 108·17 = 1836 (err 8×10⁻³ %); measured 1836.15267343. 1836 ≠ 1836.1527; the same 1836 fits any nearby target → curve-fit, not prediction. → src/8/nucleus/{proton-mass-fit.ts, proton-mass.lean}.
14 — Whole vs continuous
Nature is whole in the quantum numbers (n, magic numbers, octaves); the scales (masses, α) are continuous, measured non-integer to 11 digits. → PHYSICS-SCALES.
15 — Reflection: possibility ⇄ impossibility
10−d mirror inverts the \// strokes on 8/11 transitions; the non-inverting three are the void seam 0/9 (no inverse → fixed axis). → src/5/reflection.{ts,lean}.
16 — Pliska rosette = the vortex group
(ℤ/7)* ≅ C₆ ≅ (ℤ/9)*; ray-generator 3 (mod 7) ↔ 2 (mod 9). → src/7/rosetta.{ts,lean}.
17 — Rosette ⊕ Clay fusion
Both are 7 = 6 + 1: six units + center ↔ six open problems + Poincaré. A bijection (relabeling) of two 7-sets; entailment unchanged: 0/7. → src/7/rosetta-clay.ts, src/7/entails.ts.