What is the primary purpose of the Möbius Path Filter?

It identifies and classifies paths in a dependency graph to differentiate between optimal linear chains and problematic circular or redundant paths using number theory.

Can this be used for general software dependency management?

Yes, while it is optimized for theorem proving and topological logic, the underlying graph classification can be applied to any system with complex dependency structures.

Does it handle large-scale graphs?

The skill is optimized for precision in logic segments. While path enumeration is computationally intensive, it provides rapid analysis for the complex sub-graphs typically found in theorem verification.

How does Möbius inversion apply to graph paths?

It assigns weights based on prime factorization where μ(n)=+1 indicates a prime path to keep, μ(n)=-1 suggests a need for rewriting, and μ(n)=0 flags redundancy.

Which programming language does this skill support?

This skill is specifically designed for Julia-based environments and utilizes native Julia functions for mathematical analysis and graph traversal.

Möbius Path Filter

Name: Möbius Path Filter
Author: plurigrid

byplurigrid

•

データサイエンスとML

Classifies and filters dependency graph paths using Möbius inversion to optimize proof structures and resolve circular logic.

The Möbius Path Filter is a specialized tool for analyzing complex dependency graphs, specifically designed for theorem proving and topological analysis. By applying Möbius inversion weights to geodesic paths, the skill identifies prime paths that form stable linear chains while flagging redundant or cyclical dependencies that require rewriting. It is particularly useful for developers and mathematicians working on proof verification systems or complex logic engines who need to ensure optimal graph structures and maintain a high spectral gap in their dependency models.

主な機能

01Generation of human-readable dependency analysis reports

02Seamless integration with safe-rewriting advisors for remediation

037 GitHub stars

04Automated detection of circular and redundant proof dependencies

05Prime factorization for geodesic path weighting

06Möbius inversion-based path classification (μ(n) scoring)

ユースケース

01Optimizing theorem dependency graphs for automated reasoning systems

02Analyzing topological structures in mathematical chemistry models

03Identifying and resolving circular logic in complex software architectures

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi mobius-path-filter

For use in Claude.ai and ChatGPT

Download Skill