When should I use the Local Compositionality Gadget?

This skill is ideal for projects involving topological data structures, complex graph rewriting, or distributed systems requiring rigorous triadic consistency and ergodic stability.

How does the four-phase saturation cycle work?

The cycle uses four steps: Backfill (decomposition), Verify (identity check), Live (composition via associative rules), and Reconcile (final conservation check).

What do the RED, BLUE, and GREEN gadgets represent?

BLUE gadgets (-1) represent negative polarity and decompose structure; GREEN gadgets (0) are neutral and verify identity; RED gadgets (+1) are positive and compose structure via associative rules.

What is GF(3) conservation in this context?

GF(3) conservation is an algebraic guarantee where trits (-1, 0, +1) are generated in triplets that sum to zero mod 3, ensuring balanced and reversible state transitions.

Local Compositionality Gadget

Name: Local Compositionality Gadget
Author: plurigrid

byplurigrid

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Data Science & ML

Manages ergodic local updates using Blume-Capel dynamics and GF(3) conservation for topological graph rewriting.

The Local Compositionality Gadget is a specialized tool designed for performing ergodic state updates within triadic systems. It leverages Blume-Capel dynamics and GF(3) algebraic conservation to ensure structural integrity across four-phase saturation cycles (Backfill, Verify, Live, and Reconcile). By generating trits in balanced triplets where the sum is always zero modulo 3, it maintains zero-sum equilibrium in graph-based data structures, making it highly effective for managing complex CRDT e-graphs and topological state transitions in decentralized environments.

Key Features

01Deterministic state reconciliation using hex or decimal seeding

02Integrated Three-Gadget rewriting patterns (RED/BLUE/GREEN)

03Four-phase saturation cycle for structural decomposition and composition

04GF(3) algebraic conservation for guaranteed state consistency

05Ergodic local update steps based on Blume-Capel spin-1 dynamics

062 GitHub stars

Use Cases

01Simulating topological state transitions in complex triadic systems

02Maintaining algebraic consistency in distributed CRDT e-graphs

03Implementing ergodic update steps for mathematical graph modeling

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi local-compositionality-gadget

For use in Claude.ai and ChatGPT

Download Skill