| title | Realisations |
|---|
Each step: the realisation, the file that computes/proves it, and the result. Everything recomputes from the digit-folder mesh; see Compute.
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.
Self-sealing fraction product = 1; additive m(d)=10−d; multiplicative n↔n⁻¹.
→ src/5/vortex.lean (self_seal), SEQUENCE-DECODE.md §3.
The stroke-reversal digits of the cyclic walk.
→ SEQUENCE-DECODE.md §4.
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.
Three mod-3 cosets = three equilateral triangles; two counter-rotating flows.
→ SEQUENCE-DECODE.md §6.
Ten's-complement bonds d ↔ 10−d (sum 10 = carry); trinity = 3 outbound legs.
→ src/5/reflection.lean, SEQUENCE-DECODE.md §7.
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).
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.
A cube down its 3-fold axis is a hexagon → Seed (6+1) → Flower (19) → Fruit (13) → Metatron (78 lines). Verified projection. → animation.
5 = 2⁻¹, primitive root, the 10−d fixed digit; the still self-inverse pivot.
→ src/5/vortex.lean.
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}.
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.
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}.
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.
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}.
(ℤ/7)* ≅ C₆ ≅ (ℤ/9)*; ray-generator 3 (mod 7) ↔ 2 (mod 9).
→ src/7/rosetta.{ts,lean}.
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.