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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数据科学与机器学习

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

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.

主要功能

01Trit assignment (-1, 0, +1) for defining agent roles and operational semantics

022 GitHub stars

03Support for ALIFE structural diffing across behavioral and morphological vectors

04Deterministic color mapping via Gay.jl for visual state and transition tracking

05GF(3) conservation verification to ensure triadic system balance (Σχ ≡ 0 mod 3)

06Integration with Julia and miniKanren for formal logic and relation validation

使用场景

01Ensuring mathematical coherence in monoidal category diagrams and categorical rewriting

02Managing 'world-hopping' navigation to explore parallel possibilities in complex decision trees

03Orchestrating three-agent teams (Explorer, Processor, Validator) for balanced AI workflows

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi gf3-tripartite

For use in Claude.ai and ChatGPT

Download Skill