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ERGODIC local update step gadget via Blume-Capel dynamics with GF(3) conservation.
Coordinates multi-agent systems using GF(3) trit assignments (-1,0,+1) and conservation checks (sum ≡0 mod 3) for triadic compositions. For ALIFE diffing, counterfactual navigation, categorical rewriting.
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ERGODIC local update step gadget via Blume-Capel dynamics with GF(3) conservation.
This gadget serves as the neutral coordinator in triadic systems.
Combines:
crdt_egraphKey Insight: Trits are generated in triplets that algebraically sum to zero.
Given two random trits t₁, t₂, the third is computed as:
t₃ = -(t₁ + t₂) mod 3
This guarantees: t₁ + t₂ + t₃ ≡ 0 (mod 3) for every triplet.
| Gadget | Trit | Pattern | Polarity |
|---|---|---|---|
| BLUE | -1 | a ⊕ (b ⊕ c) → (a ⊕ b) ⊕ c | Negative |
| GREEN | 0 | a ≡ a | Neutral |
| RED | +1 | (a ⊕ b) ⊕ c → a ⊕ (b ⊕ c) | Positive |
# Run 9 local update steps with seed 0x42D (1069 decimal)
bb scripts/local_compositionality_gadget.bb --seed 1069 --steps 9
# Run with hex seed
bb scripts/local_compositionality_gadget.bb --seed 0x42D --steps 9
# Run 27 steps (9 complete triplets)
bb scripts/local_compositionality_gadget.bb --seed 12345 --steps 27
ALWAYS conserved: ∑ gadget_trits ≡ 0 (mod 3)
Enforced by triplet structure: For every 3 steps, sum = 0.
When steps isn't a multiple of 3, the partial triplet still sums to 0 (mod 3) because each complete triplet contributes 0 to the running sum.
| Parameter | Value | Meaning |
|---|---|---|
| J | 1.0 | Exchange coupling |
| Δ | 0.0 | Tricritical point |
| Spectral Gap | 1/4 | Rapid mixing guarantee |
All seeds produce GF(3)-conserved outputs:
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis 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
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.