Asi möbius-color-duality

Möbius inversion for Gay.jl color spaces — recovers seeds from color distributions

install

source · Clone the upstream repo

git clone https://github.com/plurigrid/asi

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/plurigrid/asi "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/m-bius-color-duality" ~/.claude/skills/plurigrid-asi-mobius-color-duality-37add7 && rm -rf "$T"

manifest: skills/m-bius-color-duality/SKILL.md

source content

Möbius Color Duality

Numerical Möbius inversion applied to color spaces: given observed color distributions (global aggregates), recover the generating seed (local structure).

Module

lib/gay_möbius_inversion.py

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ColorMöbiusInverter

TriadicColorInverter

Key Classes

```
ColorMöbiusInverter
```
— numerical forward/backward inversion for color spaces. Forward: seed to color indices to structures. Backward: structures to color distributions to recovered seed.
```
TriadicColorInverter
```
— extends inversion to GF(3) ternary color states.

Usage

from lib.gay_möbius_inversion import ColorMöbiusInverter

inverter = ColorMöbiusInverter()
# Forward pass: seed -> color distribution
distribution = inverter.forward(seed)
# Backward pass: distribution -> recovered seed
recovered = inverter.invert(distribution)

Integration

This fills the "Inversion (Duality)" layer of the sparsification spine (was at 1.6% coverage). The system can generate color structures but this module enables the reverse — recovering seeds from observed colorizations.