möbius-color-duality
Möbius inversion for Gay.jl color duality - closes sparsification spine gap
npx skills add majiayu000/claude-skill-registry --skill m-bius-color-duality --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# 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 ##
- The Gap
- Core Insight
- Implementation
- Status
- Sparsification Spine Integration
What does the möbius-color-duality skill do?
Möbius inversion for Gay.jl color duality - closes sparsification spine gap
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill m-bius-color-duality --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.