catsharp-galois
CatSharp Scale Galois Connections between agent-o-rama and Plurigrid ACT via Mazzola's categorical music theory
npx skills add majiayu000/claude-skill-registry --skill catsharp-galois --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.
# CatSharp Galois Skill **Trit**: 0 (ERGODIC - bridge) **Color**: Yellow (#D8D826) ## Overview Establishes **Galois adjunction** α ⊣ γ between conceptual spaces: ``` α (abstract) HERE ─────────────→ ELSEWHERE ↑ │ │ │ γ (concretize) │ ┌──────────┐ │ └────│ CatSharp │────┘ │ Scale │ │ (Bridge) │ └──────────┘ GF(3): (+1) + (0) + (-1) = 0 ✓ ``` - **HERE**: agent-o-rama Topos (local operations) - **ELSEWHERE**: Plurigrid ACT (global cognitive category theory) - **BRIDGE**: CatSharp Scale (Mazzola's categorical music theory) ## CatSharp Scale Mapping Pitch classes ℤ₁₂ map to GF(3) trits: | Trit | Pitch Classes | Chord Type | Hue Range | |------|---------------|------------|-----------| | +1 (PLUS) | {0, 4, 8} | Augmented triad | 0-60°, 300-360° | | 0 (ERGODIC) | {3, 6, 9} | Diminished 7th | 60-180° | | -1 (MINUS) | {2, 5, 7, 10, 11} | Fifths cycle | 180-300° | ### Tritone: The Möbius Axis The tritone (6 semitones) is the unique self-inverse interval: ``` 6 + 6 = 12 ≡ 0 (mod 12) ``` This mirrors GF(3) Möbius inversion where μ(3)² = 1. ## Galois Connection API ```clojure (defn α-abstract "Abstraction functor: agent-o-rama → Plurigrid ACT" [here-concept] (let [trit (or (:trit here-concept)
- Overview
- CatSharp Scale Mapping
- Tritone: The Möbius Axis
- Galois Connection API
- Hyperedge Types
- Color ↔ Pitch Conversion
- GF(3) Triads
- Commands
- Related Skills
- References
- Scientific Skill Interleaving
- Graph Theory
- Bibliography References
- SDF Interleaving
Run genesis with CatSharp bridge just genesis-catsharp seed=0x42D Verify Galois adjunction just galois-verify here=agent-o-rama elsewhere=plurigrid-act Sonify CatSharp scale just catsharp-play pitch-classes="0 4 7"
What does the catsharp-galois skill do?
CatSharp Scale Galois Connections between agent-o-rama and Plurigrid ACT via Mazzola's categorical music theory
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill catsharp-galois --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.