How does this skill handle diagram generation?

The skill includes templates and commands to convert interaction data into Mermaid flowcharts, state diagrams, and DisCoPy-compatible SVG exports.

What is the significance of the GF(3) Triad?

It uses ternary logic (mod 3) to ensure that groups of interactions maintain a zero-sum invariant, which is used for spectral verification and system consistency.

What programming languages does it support?

While it is a logic-based skill, it provides specific implementation examples and integration logic for Ruby, Julia, and Hy (Lisp on Python).

What is LHoTT Cohesive Linear?

It is a framework that combines Linear Homotopy Type Theory with cohesive modalities to model complex interactions where resource use and topological structure are critical.

LHoTT Cohesive Linear

Name: LHoTT Cohesive Linear
Author: plurigrid

byplurigrid

•

データサイエンスとML

Implements Cohesive Linear Homotopy Type Theory patterns to formalize interaction entropy and generate complex structural diagrams.

概要

This skill synthesizes Urs Schreiber’s cohesive ∞-topos framework with Mitchell Riley’s linear HoTT to provide a specialized environment for modeling quantum-classical bridging and interaction entropy. It enables the use of formal modal operators—Sharp, Flat, Shape, and Linear—to maintain structural integrity and resource conservation within codebases. By utilizing GF(3) triadic invariants and automated diagram generation, it provides a rigorous foundation for developers working on topological computing, formal verification, and advanced mathematical modeling.

主な機能

Modal Operator Implementation: Supports ♯ (Sharp), ♭ (Flat), ʃ (Shape), and ♮ (Linear) modalities for type-theoretic precision.
2 GitHub stars
GF(3) Spectral Verification: Validates interaction consistency using ternary logic and Ramanujan gap verification.
Automated Diagram Generation: Exports interaction sequences to Mermaid, DisCoPy, and SVG formats for visual documentation.
Linear Resource Enforcement: Manages 'one-use' interaction logic to ensure linear logic constraints are met without duplication.
Multi-Language Synthesis: Provides implementation patterns for Ruby, Julia (ACSets), and Hy/DiscoHy integration.

ユースケース

Verifying data integrity and interaction conservation in multi-agent systems via triadic invariants.
Formalizing state transitions in quantum-classical hybrid systems using topological types.
Generating architectural diagrams for complex categorical logic and homotopy type theory research.

概要

主な機能

Modal Operator Implementation: Supports ♯ (Sharp), ♭ (Flat), ʃ (Shape), and ♮ (Linear) modalities for type-theoretic precision.
2 GitHub stars
GF(3) Spectral Verification: Validates interaction consistency using ternary logic and Ramanujan gap verification.
Automated Diagram Generation: Exports interaction sequences to Mermaid, DisCoPy, and SVG formats for visual documentation.
Linear Resource Enforcement: Manages 'one-use' interaction logic to ensure linear logic constraints are met without duplication.
Multi-Language Synthesis: Provides implementation patterns for Ruby, Julia (ACSets), and Hy/DiscoHy integration.

ユースケース

Verifying data integrity and interaction conservation in multi-agent systems via triadic invariants.
Formalizing state transitions in quantum-classical hybrid systems using topological types.
Generating architectural diagrams for complex categorical logic and homotopy type theory research.