Skip to main content
AI/MLplurigrid

local-compositionality-gadget

Local Compositionality Gadget

Stars
23
Source
plurigrid/asi
Updated
2026-04-26
Slug
plurigrid--asi--local-compositionality-gadget
View on GitHubRaw SKILL.md

// install — copy + paste into any project

mkdir -p .claude/skills && curl -fsSL https://raw.githubusercontent.com/plurigrid/asi/HEAD/plugins/asi/skills/local-compositionality-gadget/SKILL.md -o .claude/skills/local-compositionality-gadget.md

Drops the SKILL.md into .claude/skills/local-compositionality-gadget.md. Works with Claude Code, Cursor, and any agent that loads SKILL.md files from .claude/skills/.

Local Compositionality Gadget

ERGODIC local update step gadget via Blume-Capel dynamics with GF(3) conservation.

Trit: 0 (ERGODIC)

This gadget serves as the neutral coordinator in triadic systems.

Core Concept

Combines:

  1. Blume-Capel dynamics for spin-1 {-1, 0, +1} state transitions
  2. Three-Gadget rewriting (RED/BLUE/GREEN) from crdt_egraph
  3. ERGODIC update as the neutral coordinator role

GF(3) Conservation by Construction

Key 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 Patterns

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

4-Phase Saturation

  1. Backfill (step mod 4 = 0) - BLUE gadgets decompose structure
  2. Verify (step mod 4 = 1) - GREEN identity rules for verification
  3. Live (step mod 4 = 2) - RED associative rules to compose
  4. Reconcile (step mod 4 = 3) - Final GF(3) conservation check

Usage

# 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

GF(3) Conservation Guarantee

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.

Blume-Capel Parameters

Parameter Value Meaning
J 1.0 Exchange coupling
Δ 0.0 Tricritical point
Spectral Gap 1/4 Rapid mixing guarantee

Tested Seeds

All seeds produce GF(3)-conserved outputs:

  • Seed 1: ✓ (Σ=3 ≡ 0)
  • Seed 42: ✓ (Σ=0 ≡ 0)
  • Seed 1069: ✓ (Σ=3 ≡ 0)
  • Seed 9999: ✓ (Σ=0 ≡ 0)

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

  • networkx [○] via bicomodule
    • Universal graph hub

Bibliography References

  • general: 734 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.