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.

About

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

Implements cohesive modalities (♯, ♭, ʃ) for discrete and continuous data embedding.
2 GitHub stars
Enforces linear modality (♮) for strict one-use interaction resource management.
Generates Mermaid and DisCoPy diagrams for visualizing categorical type structures.
Provides cross-language integration for Ruby, Julia (ACSets), and Hy/DisCoPy.
Validates interaction entropy through GF(3) triad placement and spectral verification.

Use Cases

Implementing verified state-space trajectories in topological computing environments.
Generating structural diagrams and ACSet schemas for complex categorical systems.
Formalizing quantum-classical interaction protocols with strict linear resource tracking.

About

Key Features

Implements cohesive modalities (♯, ♭, ʃ) for discrete and continuous data embedding.
2 GitHub stars
Enforces linear modality (♮) for strict one-use interaction resource management.
Generates Mermaid and DisCoPy diagrams for visualizing categorical type structures.
Provides cross-language integration for Ruby, Julia (ACSets), and Hy/DisCoPy.
Validates interaction entropy through GF(3) triad placement and spectral verification.

Use Cases

Implementing verified state-space trajectories in topological computing environments.
Generating structural diagrams and ACSet schemas for complex categorical systems.
Formalizing quantum-classical interaction protocols with strict linear resource tracking.