Is this skill compatible with formal logic tools?

Absolutely. It includes scripts for Julia validation and miniKanren relations, making it suitable for projects requiring rigorous structural coherence.

What is GF(3) in the context of this skill?

GF(3) refers to the Galois Field of three elements (-1, 0, +1), which is used here as a mathematical framework to balance agent roles and ensure logical consistency in multi-step operations.

Can I use this for visual debugging?

Yes, the skill includes deterministic color mapping via Gay.jl, allowing you to assign specific hex codes to trits for clear visual identification of system states.

How does the conservation check work?

For any group of three operations or agents to be validly composed, the sum of their assigned trits must be congruent to 0 modulo 3. This prevents logical gaps and ensures system equilibrium.

What are the primary agent roles supported?

The system utilizes three core roles: Generator (+1) for creation, Transformer (0) for processing/maintenance, and Absorber (-1) for validation and consumption.

GF(3) Tripartite Orchestration

Name: GF(3) Tripartite Orchestration
Author: plurigrid

byplurigrid

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Data Science & ML

Coordinates multi-agent systems and state transitions using GF(3) Galois Field conservation principles.

About

This skill implements a mathematical framework for multi-agent coordination based on GF(3) (Galois Field of 3 elements). It provides a structured approach to assigning agent roles—Generator (+1), Transformer (0), and Absorber (-1)—ensuring compositional coherence through conservation checks. By mapping operations to deterministic colors and triadic patterns, it enables robust orchestration for complex tasks like ALIFE structural diffing, categorical rewriting, and counterfactual navigation, making it an essential tool for developers building sophisticated autonomous systems that require formal balance and logical integrity.

Key Features

Trit assignment (-1, 0, +1) for defining agent roles and operational semantics
2 GitHub stars
Support for ALIFE structural diffing across behavioral and morphological vectors
Deterministic color mapping via Gay.jl for visual state and transition tracking
GF(3) conservation verification to ensure triadic system balance (Σχ ≡ 0 mod 3)
Integration with Julia and miniKanren for formal logic and relation validation

Use Cases

Ensuring mathematical coherence in monoidal category diagrams and categorical rewriting
Managing 'world-hopping' navigation to explore parallel possibilities in complex decision trees
Orchestrating three-agent teams (Explorer, Processor, Validator) for balanced AI workflows

About

Key Features

Trit assignment (-1, 0, +1) for defining agent roles and operational semantics
2 GitHub stars
Support for ALIFE structural diffing across behavioral and morphological vectors
Deterministic color mapping via Gay.jl for visual state and transition tracking
GF(3) conservation verification to ensure triadic system balance (Σχ ≡ 0 mod 3)
Integration with Julia and miniKanren for formal logic and relation validation

Use Cases

Ensuring mathematical coherence in monoidal category diagrams and categorical rewriting
Managing 'world-hopping' navigation to explore parallel possibilities in complex decision trees
Orchestrating three-agent teams (Explorer, Processor, Validator) for balanced AI workflows