plurigrid 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 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:
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
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
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
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.