Why use SplitMix64 for parallel execution?

SplitMix64 allows the AI to fork seeds into three independent, deterministic streams, ensuring that parallel operations are reproducible across different substrates like Python and Julia.

What programming languages does this skill support?

The skill provides implementations and bridge types for Python, Julia, Modelica (replaces Wolfram), and the Narya proof assistant.

How does GF(3) conservation work within the skill?

It ensures every decision trifurcates into three parallel paths—Validator (MINUS), Coordinator (ERGODIC), and Executor (PLUS)—where the sum of the trits always equals zero (mod 3).

What is an Ordered Locale in this context?

An Ordered Locale is a topological structure used here to model software dependencies and MCP servers as open sets with directional 'way-below' relations, providing a foundation for causal structure.

Ordered Locale & Triadic Topology

Name: Ordered Locale & Triadic Topology
Author: plurigrid

byplurigrid

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Data Science & ML

Implements point-free topology and triadic GF(3) logic to manage causal structures and deterministic parallel execution for MCP servers.

This skill provides a rigorous mathematical framework based on ordered locales and directed topology for AI agent interactions. By modeling MCP servers as open sets and utilizing bridge types for dependencies, it enables deterministic, parallelized decision-making via a triadic GF(3) system. It is specifically designed for developers working with formal methods, the Narya proof assistant, or complex multi-language substrates (Python, Julia, Modelica) where causal consistency and reproducible parallel execution are critical.

Key Features

01GF(3) arithmetic conservation ensuring compositional coherence across software systems.

02Native integration with the Narya proof assistant and Emacs Proof General.

03Triadic decision-making framework (MINUS/ERGODIC/PLUS) for parallel task execution.

04Deterministic parallelization via SplitMix64 across multiple programming substrates.

052 GitHub stars

06Point-free topology implementation using Heunen-style ordered locales.

Use Cases

01Implementing reproducible triadic scheduling for parallel AI agent workflows.

02Designing causal structures for complex Model Context Protocol (MCP) server dependencies.

03Formalizing directed homotopy theory and bridge types within Narya proof scripts.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi ordered-locale

For use in Claude.ai and ChatGPT

Download Skill