What programming languages are supported by this skill?

It includes specific integration patterns and boilerplate for Ruby, Julia (via Catlab.jl), and Hy (using DisCoPy for categorical composition).

How does this skill help with diagram generation?

The skill provides automated templates and commands to export interaction data into Mermaid syntax, DisCoPy SVG, and ACSet schemas for immediate visual verification of your logic.

What is Cohesive Linear HoTT?

Cohesive Linear Homotopy Type Theory (LHoTT) is a mathematical framework that combines cohesive ∞-topos theory with linear logic to model systems requiring both continuous/discrete structures and one-time use resources.

What is GF(3) triad placement?

It is a balancing mechanism used to ensure compositional coherence, where interactions are assigned values that must sum to zero (mod 3) to maintain system equilibrium.

What is the purpose of the linear modality (♮)?

The linear modality ensures that a resource or interaction can be used exactly once, preventing accidental copying or deletion in formal state-space transitions.

Cohesive Linear HoTT Formalizer

Name: Cohesive Linear HoTT Formalizer
Author: plurigrid

byplurigrid

•

Data Science & ML

Implements Cohesive Linear Homotopy Type Theory patterns for formalizing interaction entropy and generating categorical diagrams.

This skill synthesizes Urs Schreiber's cohesive ∞-topos framework with Mitchell Riley's linear HoTT to provide a robust environment for quantum-classical bridging. It enables developers to implement complex modal operators—Sharp, Flat, Shape, and Linear—for sophisticated discrete-continuous data handling. By enforcing linear resource conservation and providing automated Mermaid and DisCoPy diagram generation, it allows for the formal verification of interaction protocols and topological structures within Claude Code.

Key Features

01Implements cohesive modalities (♯, ♭, ʃ) for discrete and continuous data embedding.

022 GitHub stars

03Enforces linear modality (♮) for strict one-use interaction resource management.

04Generates Mermaid and DisCoPy diagrams for visualizing categorical type structures.

05Provides cross-language integration for Ruby, Julia (ACSets), and Hy/DisCoPy.

06Validates interaction entropy through GF(3) triad placement and spectral verification.

Use Cases

01Implementing verified state-space trajectories in topological computing environments.

02Generating structural diagrams and ACSet schemas for complex categorical systems.

03Formalizing quantum-classical interaction protocols with strict linear resource tracking.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi lhott-cohesive-linear

For use in Claude.ai and ChatGPT

Download Skill