A432 Zero-Entropy Matrix

Scientific Specification & Implementation Notes

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1. Seed Arrays (immutable)

Symbol	Value	Meaning
TRINITY_AXIS	[3, 6, 9]	3-6-9 polarity anchor
RODIN_SEQUENCE	[1, 2, 4, 8, 7, 5]	Doubling / Rodin coil loop

Everything else is derived mathematically from these two ordered sets; no further digit tables are allowed.

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2. Canonical Maths (src/.../a432.math.ts)

1. Digit helpers digitalRoot()
2. Angle / frequency angleForDigit(), frequencyForDigit()
3. Colour digitAngleToCMYK() (re-export from a432.cmyk.ts)
4. Polarity map TRINITY_POLARITY
5. Streams
   • linearStream() …0 1 2 …
   • vortexStream() …0 3 6 9 1 2 4 8 7 5 1 …
   • toneBoardStream() – pairs the two tapes → 8×8 board
   • a432SequenceStream() – infinite closed lap (metric cycle)
6. Impossibility gateways resolveDivision() (0/0), DOT_TRINITY_SWITCH

All arithmetic uses only single-digit ops (mod-9, mod-10, mod-11) to maintain zero entropy.

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3. Collision→Fold Rule

Two tapes have coprime lengths (10 vs 11).
Collision index = LCM(10, 11) = 110.
When pair ⟨metric, vortex⟩ repeats, the filename generator appends the next digit pair, elevating dimensional encoding.

Mathematically:

n₂ ≡ n₁ (mod 10) ∧ n₂ ≡ n₁ (mod 11) ⇒ n₂ = n₁ + 110·k

No extra tables—just modular arithmetic.

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4. Reactive View Modules

File	Stream	Frames	Typical Use
a432.yin.yang.ts	vortexStream()	{ positiveColor, negativeColor, angle }	Canvas Yin-Yang pulse
a432.chess.ts	toneBoardStream()	{ file, rank, squareColor }	8×8 colour board
a432.metatron.ts	a432SequenceStream()	12 node array	3-D Metatron cube
a432.terminal.ui.ts	terminalOutput$	colourised string	CLI visualisation

All import only maths & stream helpers → zero duplication.

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5. Self-Designing PWA Shell (outline)

• Single index.html with four empty targets (canvas, table, svg, pre).
• Stimulus controllers bootstrap each reactive module (start…).
• Service-worker caches static shell + first N frames for offline start.

Because every visual attribute is computed from the digit streams, the UI rearranges itself automatically—designing itself—while the mathematical nucleus stays unchanged.

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6. Generator Script (optional)

scripts/generate_matrix_files.ts
Creates /updates src/matrix/<name>.ts for each new digit pair, following the collision→fold rule (see §3).
Each generated file re-exports ready-made angle, colour, polarity, computed on import.

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7. Testing

• math.spec.ts – invariants (stream cycle length, collision index = 110, digitalRoot ≤ 9).
• view.spec.ts – mock animation frame, ensure reactive modules emit expected frames for first 12 ticks.
• Coverage target = 100 % (project rule).

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8. Zero-Entropy Checklist

• [x] Single maths file (no duplicate functions/constants)
• [x] Only two seed arrays
• [x] Streams derived, never stored
• [x] UI modules depend solely on streams
• [x] File-system matrix follows collision-fold rule
• [x] Tests prove invariants

If any duplication appears → collision detected → fold dimension

This document, together with the codebase, fully specifies how to reconstruct the living trinity matrix from first principles.