3 parallel agents explore codebase improvements via GF(3) balanced prime geodesics
Trit: 0 (ERGODIC - navigates between generation and validation)
Coordinator Color: #D06546 (burnt sienna, transport of earth)
Seed: 1069 (0x42D)
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 (⊖) ─────┘
| 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 |
See PRIME_GEODESICS.md for full mathematical foundation.
| 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 | 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 |
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
seed_{n+1} = (seed_n ⊕ (trit_n × γ)) × MIX mod 2⁶⁴
At every step of the walk:
trit_generator + trit_coordinator + trit_validator ≡ 0 (mod 3)
(+1) + (0) + (-1) = 0 ✓
Like the Three Chromatic Samovars:
just chromatic-walk seed=1069
Generator proposes a codebase change with +1 trit.
Coordinator structures the proposal, deriving the interface.
Validator checks invariants and reduces.
If GF(3) = 0 at walk end, the improvement is committed.
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
three-match (-1) ⊗ chromatic-walk (0) ⊗ gay-mcp (+1) = 0 ✓ [Core Walk]
ramanujan-expander (-1) ⊗ ihara-zeta (0) ⊗ moebius-inversion (+1) = 0 ✓ [Prime Netting]
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 |
As the 0 goblin, Chromatic Walk provides:
Step 1: #46F27F (mint green) ○ Transport
Step 2: #E2282A (vivid red) ○ Derive
Step 3: #EE55F2 (hot pink) ○ Navigate
| 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)
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Category:developer