What is persistent homology in the context of coding?

It is a mathematical method that identifies structural features, such as dependency cycles, that persist across different levels of code complexity, helping distinguish core architecture from incidental code patterns.

How does this skill help with refactoring?

It identifies 'stable' cycles (persistent β₁ features) which represent deep-seated circular dependencies that are the most critical targets for decoupling and architectural cleanup.

Can it analyze compiled code without source files?

Yes, the skill integrates with radare2 to analyze binary call graphs and function sizes, building a topological map of the compiled software's structure.

Does it support version comparison?

Yes, it uses the Stability Theorem and bottleneck distance to compare persistence diagrams between different versions, highlighting which structures were preserved, lost, or added.

What are Betti numbers in software analysis?

In this context, β₀ represents independent clusters of code components, β₁ indicates 1-dimensional holes or circular dependencies, and β₂ identifies higher-order structural voids.

Topological Code Analyzer

Name: Topological Code Analyzer
Author: plurigrid

byplurigrid

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Analytics & Monitoring

Analyzes code and binary structures using persistent homology to identify stable topological features and cyclic dependencies.

The Persistent Homology skill leverages Topological Data Analysis (TDA) to map the structural evolution of codebases and binaries across varying complexity thresholds. By calculating Betti numbers and generating persistence diagrams, it distinguishes robust architectural patterns from transient code noise, allowing developers to pinpoint deep-seated cyclic dependencies and structural voids. This tool is essential for high-level architectural auditing, binary security analysis via radare2 integration, and ensuring structural stability across software versions using mathematical bottleneck distance metrics.

Key Features

01Complexity Filtration: Tracks code structure across nested cyclomatic complexity thresholds.

02Stability Verification: Measures structural changes between versions using bottleneck distance metrics.

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04Betti Number Calculation: Quantifies connected components, cycles, and higher-order structural voids.

05Persistence Diagrams: Maps the 'birth' and 'death' of structural features to isolate stable patterns.

06Radare2 Integration: Performs deep topological analysis on compiled binaries for structural auditing.

Use Cases

01Verifying architectural integrity and structural stability during major version migrations.

02Identifying and refactoring persistent cyclic dependencies in complex legacy codebases.

03Performing topological security audits on binaries to find hidden structural anomalies.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi persistent-homology

For use in Claude.ai and ChatGPT

Download Skill