Agent skill
m-bius-color-duality-plurigrid-asi-2
Install this agent skill to your Project
npx add-skill https://github.com/majiayu000/claude-skill-registry/tree/main/skills/other/m-bius-color-duality-plurigrid-asi-2
SKILL.md
=======
origin/feature/skill-connectivity-hub-20251226 metadata: trit: 1 polarity: PLUS source: 'Amp thread corpus analysis - fills critical Inversion layer' technologies:
- Python
- Number theory
- Category theory (contravariant functors)
<<<<<<< HEAD
origin/gayish ======= origin/feature/skill-connectivity-hub-20251226
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 spacesTriadicColorInverter: 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
<<<<<<< HEAD <<<<<<< HEAD
SDF Interleaving
This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Primary Chapter: 3. Variations on an Arithmetic Theme
Concepts: generic arithmetic, coercion, symbolic, numeric
GF(3) Balanced Triad
möbius-color-duality (−) + SDF.Ch3 (○) + [balancer] (+) = 0
Skill Trit: -1 (MINUS - verification)
Secondary Chapters
- Ch6: Layering
Connection Pattern
Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.
origin/gayish ======= origin/feature/skill-connectivity-hub-20251226
Recommended Agent Skills
Expand your agent's capabilities with these related and highly-rated skills.
majiayu000/claude-skill-registry
agent-ops-spec
Manage specification documents in .agent/specs/. Use when user provides requirements, acceptance criteria, or feature descriptions that need to be tracked and validated against implementation.
majiayu000/claude-skill-registry
agent-ops-state
Maintain .agent state files. Use at session start, after meaningful steps, and before concluding: read/update constitution/memory/focus/issues/baseline consistently.
majiayu000/claude-skill-registry
agent-ops-spec
Manage specification documents in .agent/specs/. Use when user provides requirements, acceptance criteria, or feature descriptions that need to be tracked and validated against implementation.
majiayu000/claude-skill-registry
agent-ops-testing
Test strategy, execution, and coverage analysis. Use when designing tests, running test suites, or analyzing test results beyond baseline checks.
majiayu000/claude-skill-registry
agent-ops-testing
Test strategy, execution, and coverage analysis. Use when designing tests, running test suites, or analyzing test results beyond baseline checks.
majiayu000/claude-skill-registry
agent-ops-state
Maintain .agent state files. Use at session start, after meaningful steps, and before concluding: read/update constitution/memory/focus/issues/baseline consistently.
Didn't find tool you were looking for?