Can this be used with formal provers like Lean 4?

Yes, the skill includes integration points for analyzing the health and connectivity of theorem catalogs from systems like Lean 4.

What is a comprehension neighborhood?

A comprehension neighborhood is a cluster of theorems frequently co-visited during random walks on a dependency graph, indicating high logical or conceptual similarity.

Which programming language does this skill support?

This skill is designed for use with the Julia programming language, utilizing its strengths in mathematical computation and graph analysis.

How does spectral gap analysis help in proof discovery?

The spectral gap measures the expansion properties of a graph. A high gap suggests fast mixing and easier theorem discovery, while a low gap indicates 'tangled' dependencies that impede exploration.

Spectral Random Walker

Name: Spectral Random Walker
Author: plurigrid

byplurigrid

•

Data Science & ML

Analyzes mathematical theorem dependencies using spectral random walks to discover comprehension neighborhoods and proof patterns.

Spectral Random Walker is a specialized tool for mathematical theorem discovery and comprehension based on the Benjamin Merlin Bumpus model. By integrating spectral gap analysis with random walk theory in Julia, it samples proof spaces to identify 'comprehension regions'—clusters of related theorems that are naturally explored together. This skill is ideal for researchers and developers working with large theorem catalogs or formal proof systems, providing deep insights into proof connectivity, mixing times, and optimal discovery paths for complex logical dependencies.

Key Features

01Integrates the Benjamin Merlin Bumpus model for spectral, combinatorial, and probabilistic proof analysis

02Generates detailed random walk reports for proof path analysis and discovery

03Simulates random walks on adjacency matrices for uniform neighbor selection

04Calculates mixing times from spectral gaps to estimate theorem exploration efficiency

057 GitHub stars

06Identifies comprehension neighborhoods via co-visitation clustering and Metropolis-Hastings sampling

Use Cases

01Optimizing the search space for automated theorem provers using spectral expansion properties

02Mapping 'tangled' dependency regions in complex mathematical datasets to improve learning paths

03Discovering hidden relationships between disparate theorems in large formal proof libraries

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi spectral-random-walker

For use in Claude.ai and ChatGPT

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