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möbius-color-duality

Möbius inversion for Gay.jl color duality - closes sparsification spine gap

Stars
23
Source
plurigrid/asi
Updated
2026-04-26
Slug
plurigrid--asi--m-bius-color-duality
View on GitHubRaw SKILL.md

// install — copy + paste into any project

mkdir -p .claude/skills && curl -fsSL https://raw.githubusercontent.com/plurigrid/asi/HEAD/plugins/asi/skills/möbius-color-duality/SKILL.md -o .claude/skills/m-bius-color-duality.md

Drops the SKILL.md into .claude/skills/m-bius-color-duality.md. Works with Claude Code, Cursor, and any agent that loads SKILL.md files from .claude/skills/.

Möbius Color Duality Skill

"Möbius inversion recovers local structure from global aggregates."

The Gap

The Amp thread corpus (1,807 threads) is 85.6% mapped to sparsification spine but has a critical gap:

Generation (Synthesis)     ████████░  49.2% ⭐ WELL-DEVELOPED
Validation (Verification)  ████░░░░░  21.6% ✓ SOLID
Execution (Control)        ███░░░░░░  15.2% ✓ ADEQUATE
Ontology (ACSet)           ██░░░░░░░   6.8% ⚠️ THIN
Decomposition (Hierarchy)  █░░░░░░░░   5.6% ⚠️ WEAK
Inversion (Duality)        ░░░░░░░░░   1.6% ❌ CRITICAL GAP

The system can generate but not invert. This skill closes that gap.

Core Insight

Forward (Generation): seed → color indices → structures
Backward (Inversion): structures → color distributions → recover seed

Implementation

Module: lib/gay_möbius_inversion.py (490 lines)

Key classes:

  • ColorMöbiusInverter: Numerical inversion for color spaces
  • TriadicColorInverter: GF(3) ternary extension

Status

✓ Core implementation: Möbius function, forward/backward inversion
✓ Duality graph generation: Contravariant functor structures
⊘ GF(3) integration: Ternary state extension
⊘ Amp corpus application: Test on actual thread colorization

Sparsification Spine Integration

Tier: Layer 5 - INVERSION (Duality/Reversal)
Trit: +1 (PLUS/Generator)
Coverage: Begins to fill 1.6% → expand to 10%+ target