three-match

npx skills add majiayu000/claude-skill-registry --skill three-match --agent claude-code

Same command for any agent — swap --agent for codex, cursor, copilot.

<!-- Propagated to codex | Trit: 0 | Source: .ruler/skills/three-match --> # Three-Match Skill: 3-SAT via Colored Subgraph Isomorphism **Status**: ✅ Production Ready **Trit**: -1 (MINUS - conservative/geodesic) **Principle**: Local constraints → Global correctness **Frame**: Non-backtracking geodesics with Möbius filtering --- ## Overview **Three-Match** reduces 3-SAT to 3-coloring which reduces to colored subgraph isomorphism. The 3-MATCH gadget enforces constraints LOCALLY via: 1. Non-backtracking geodesics (prime paths, μ(n) ≠ 0) 2. Möbius inversion filtering (back-and-forth cancellation) 3. GF(3) conservation (sum ≡ 0 mod 3) **Correct by construction**: If local geodesic constraints are satisfied, global 3-SAT solution is guaranteed. ## Core Formula ```ruby # Three colors match at depth d iff: # - Pairwise differences have 3-adic valuation ≥ d # - No backtracking (each color unique in path) # - GF(3) sum ≡ 0 (mod 3) v₃(|a - b|) ≥ d ∧ v₃(|b - c|) ≥ d ∧ v₃(|c - a|) ≥ d ``` ## Why Non-Backtracking? 1. **Prime paths**: μ(n) ≠ 0 ⟺ n is squarefree 2. **No revisiting**: Each state appears once in geodesic 3. **Möbius filtering**: Composites (backtracking) cancel out 4. **Spectral gap*

Run 3-MATCH demo
just three-match
Test gadget correctness
just test-three-match
Combine with unworld
just unworld-match