--- name: chromatic-walk description: 3 parallel agents explore codebase improvements via GF(3) balanced prime geodesics version: 1.0.0 --- # Chromatic Walk Skill **Trit**: 0 (ERGODIC - navigates between generation and validation) **Coordinator Color**: #D06546 (burnt sienna, transport of earth) **Seed**: 1069 (0x42D) --- ## Overview Chromatic Walk enables **3 parallel agents** to explore codebase improvements using GF(3)-balanced derivation chains. Each agent holds a trit polarity, and together they form a self-boiling triad. Walks are **prime geodesics**: non-backtracking paths that are unambiguously traversable in p-adic number systems. ``` Generator (⊕) ─────┐ ├──→ GF(3) = 0 ──→ Prime Geodesic Coordinator (○) ────┤ │ Validator (⊖) ─────┘ ``` --- ## The 3-Agent Structure | Role | Trit | Color | Action | Responsibility | |------|------|-------|--------|----------------| | **Generator** | +1 | #D82626 (Red) | Create | Propose code changes, new patterns | | **Coordinator** | 0 | #26D826 (Green) | Transport | Formalize structure, derive next seed | | **Validator** | -1 | #2626D8 (Blue) | Verify | Check invariants, reduce to essence | --- ## Prime Geodesic Foundation See [PRIME_GEODESICS.md](./PRIME_GEODESICS.md) for full mathematical foundation. ### Why Non-Backtracking? | Property | Prime Path | Composite Path | |----------|------------|----------------| | Factorization | **Unique** | Multiple | | p-adic valuation | **Well-defined** | Ambiguous | | Möbius μ(n) | ≠ 0 | = 0 (filtered) | | Ihara zeta | **Contributes** | Ignored | **Key insight**: Chromatic walks are prime geodesics in derivation space, traversable unambiguously by zeta functions. ### Zeta Function Traversability | Zeta | Domain | Primes | |------|--------|--------| | Riemann ζ(s) | ℤ | Prime numbers | | Ihara ζ_G(u) | Graphs | Non-backtracking cycles | | Dedekind ζ_K(s) | Number fields | Prime ideals | | Selberg Z(s) | Manifolds | Prime geodesics | --- ## Seed Chaining Across Agents Each agent derives its seed from the shared genesis, offset by the golden ratio: ```ruby genesis = 0x42D # 1069 γ = 0x9E3779B97F4A7C15 # Golden ratio constant seed_generator = genesis # +1 stream seed_coordinator = genesis ^ γ # 0 stream seed_validator = genesis ^ (γ << 1) # -1 stream ``` ### Derivation Chain (per step) ``` seed_{n+1} = (seed_n ⊕ (trit_n × γ)) × MIX mod 2⁶⁴ ``` --- ## GF(3) Conservation Invariant At every step of the walk: ``` trit_generator + trit_coordinator + trit_validator ≡ 0 (mod 3) (+1) + (0) + (-1) = 0 ✓ ``` ### Self-Boiling Property Like the Three Chromatic Samovars: - Generator provides +1 (creative surplus) - Validator provides -1 (critical reduction) - Coordinator provides 0 (transport without change) --- ## Walk Protocol ### Phase 1: Genesis ```bash just chromatic-walk seed=1069 ``` ### Phase 2: Propose (Generator leads) Generator proposes a codebase change with +1 trit. ### Phase 3: Formalize (Coordinator transports) Coordinator structures the proposal, deriving the interface. ### Phase 4: Verify (Validator constrains) Validator checks invariants and reduces. ### Phase 5: Commit (combined) If GF(3) = 0 at walk end, the improvement is committed. --- ## Commands ```bash just chromatic-walk seed=1069 # Initialize walk just chromatic-walk-step seed=1069 # Run single step just chromatic-walk-verify seed=1069 # Verify GF(3) conservation ``` --- ## Triad Bundles ``` three-match (-1) ⊗ chromatic-walk (0) ⊗ gay-mcp (+1) = 0 ✓ [Core Walk] ramanujan-expander (-1) ⊗ ihara-zeta (0) ⊗ moebius-inversion (+1) = 0 ✓ [Prime Netting] ``` --- ## Goblin Integration Chromatic-walk is the **0 Coordinator** in the goblin triad: ``` shadow-goblin (-1) ⊗ chromatic-walk (0) ⊗ agent-o-rama (+1) = 0 ✓ ``` | Role | Trit | Color | Action | |------|------|-------|--------| | Shadow Goblin | -1 | #F0D127 | Validates walks | | **Chromatic Walk** | **0** | **#46F27F** | **Transports derivations** | | Agent-O-Rama | +1 | #E7B367 | Generates proposals | ### Coordinator Capabilities As the 0 goblin, Chromatic Walk provides: - **Transport**: Move context between generator and validator - **Derive**: Compute next seed in derivation chain - **Navigate**: Traverse between realms (Beautiful Realms) - **Balance**: Ensure triad sums remain at GF(3) = 0 ### Color Stream (Seed 1069, Stream 2) ``` Step 1: #46F27F (mint green) ○ Transport Step 2: #E2282A (vivid red) ○ Derive Step 3: #EE55F2 (hot pink) ○ Navigate ``` ## Related Skills | Skill | Relation | |-------|----------| | **unworld** | Seed chaining foundation | | **ihara-zeta** | Non-backtracking enumeration | | **ramanujan-expander** | Spectral gap verification | | **moebius-inversion** | Composite filtering | | **gay-mcp** | Deterministic color generation | | **shadow-goblin** | Validates walks (-1) | | **agent-o-rama** | Generates proposals (+1) | --- **Skill Name**: chromatic-walk **Type**: Multi-Agent Prime Geodesic Exploration **Trit**: 0 (ERGODIC) **GF(3)**: Conserved by construction **Backtracking**: Forbidden (composites are p-adically imprecise) ## Scientific Skill Interleaving This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem: ### Stochastic - **simpy** [○] via bicomodule - Stochastic processes ### Bibliography References - `graph-theory`: 38 citations in bib.duckdb ## SDF Interleaving This skill connects to **Software Design for Flexibility** (Hanson & Sussman, 2021): ### Primary Chapter: 10. Adventure Game Example **Concepts**: autonomous agent, game, synthesis ### GF(3) Balanced Triad ``` chromatic-walk (+) + SDF.Ch10 (+) + [balancer] (+) = 0 ``` **Skill Trit**: 1 (PLUS - generation) ### Secondary Chapters - Ch4: Pattern Matching ### Connection Pattern Adventure games synthesize techniques. This skill integrates multiple patterns. ## Cat# Integration This skill maps to **Cat# = Comod(P)** as a bicomodule in the equipment structure: ``` Trit: 0 (ERGODIC) Home: Prof Poly Op: ⊗ Kan Role: Adj Color: #26D826 ``` ### GF(3) Naturality The skill participates in triads satisfying: ``` (-1) + (0) + (+1) ≡ 0 (mod 3) ``` This ensures compositional coherence in the Cat# equipment structure.