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.

About

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

Deterministic state reconciliation using hex or decimal seeding
Integrated Three-Gadget rewriting patterns (RED/BLUE/GREEN)
Four-phase saturation cycle for structural decomposition and composition
GF(3) algebraic conservation for guaranteed state consistency
Ergodic local update steps based on Blume-Capel spin-1 dynamics
2 GitHub stars

Use Cases

Simulating topological state transitions in complex triadic systems
Maintaining algebraic consistency in distributed CRDT e-graphs
Implementing ergodic update steps for mathematical graph modeling

About

Key Features

Deterministic state reconciliation using hex or decimal seeding
Integrated Three-Gadget rewriting patterns (RED/BLUE/GREEN)
Four-phase saturation cycle for structural decomposition and composition
GF(3) algebraic conservation for guaranteed state consistency
Ergodic local update steps based on Blume-Capel spin-1 dynamics
2 GitHub stars

Use Cases

Simulating topological state transitions in complex triadic systems
Maintaining algebraic consistency in distributed CRDT e-graphs
Implementing ergodic update steps for mathematical graph modeling