Can I use this for formal mathematical proofs?

Yes, the skill includes Narya proof assistant definitions and bridge types, specifically designed for formal verification and synthetic infinity-category theory.

How does this skill manage MCP servers?

It treats MCP servers as open sets within a topological locale, utilizing the 'way-below' relation to model and navigate complex dependencies and causal structures.

What is GF(3) conservation?

GF(3) conservation is a constraint where every triadic interaction must sum to zero (mod 3), ensuring compositional coherence and stability across the system's architecture.

What is a 'Trit' in the context of this skill?

A Trit is a value in ternary logic (-1, 0, +1) used to trifurcate decisions into validation, coordination, and execution paths while maintaining GF(3) conservation.

Which programming languages are compatible with this skill?

The skill provides cross-substrate implementations for Python, Julia, Modelica, and Emacs, ensuring reproducible logic via SplitMix64.

Ordered Locale Topology & Triadic Systems

Name: Ordered Locale Topology & Triadic Systems
Author: plurigrid

byplurigrid

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データサイエンスとML

Implements point-free topology and triadic decision-making for formal verification and MCP server orchestration.

The Ordered Locale skill integrates advanced mathematical frameworks—including Heunen-style ordered locales and GF(3) triadic logic—directly into Claude's workflow. It allows developers to model Model Context Protocol (MCP) servers as topological open sets and manage dependencies through formal 'way-below' relations. By trifurcating every decision into parallel Validator, Coordinator, and Executor paths, it ensures GF(3) conservation and deterministic parallel execution across Python, Julia, and Modelica. This skill is particularly valuable for users working with directed homotopy theory, causal structures, or formal proofs within the Narya proof assistant.

主な機能

01Triadic Decision Logic: Trifurcates workflows into MINUS (Validator), ERGODIC (Coordinator), and PLUS (Executor) paths.

028 GitHub stars

03Narya Proof Integration: Supports bridge types and formal 'way-below' relations for rigorous verification.

04GF(3) Conservation: Enforces mathematical balance (sum ≡ 0 mod 3) across all system interactions.

05MCP Server Indexing: Models servers as open sets in a locale using deterministic creation-time coloring.

06Deterministic Parallelism: Uses SplitMix64 to ensure identical execution results across Python, Julia, and Modelica substrates.

ユースケース

01Orchestrating complex MCP server dependencies using topological 'way-below' relations.

02Formally verifying causal structures and sheaves in directed homotopy theory projects.

03Implementing high-integrity parallel logic in distributed systems via triadic scheduling.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi ordered-locale

For use in Claude.ai and ChatGPT

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