What is persistent homology in the context of coding?

Persistent homology is a mathematical method from topological data analysis that identifies features in a dataset (like a codebase or binary) that persist across different thresholds of complexity or scale, helping distinguish fundamental structure from noise.

What is a persistence diagram?

A persistence diagram is a visual or data representation of when structural features are 'born' and 'die' as you change analysis thresholds. Features with long lifespans (high persistence) are considered stable architectural components.

Can I use this for binary analysis?

Yes, the skill includes a Radare2Analyzer gadget that integrates with radare2 to build complexity filtrations and persistence diagrams from binary call graphs and function structures.

How does this skill help with cyclic dependencies?

The skill computes Betti numbers, specifically beta-1 (β₁), which represents 1-dimensional holes. In code analysis, these holes directly correspond to cyclic dependencies that may need refactoring.

Persistent Homology Analyzer

Name: Persistent Homology Analyzer
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes code structure using topological data analysis to identify stable features and structural vulnerabilities across complexity levels.

About

The Persistent Homology skill applies advanced topological data analysis (TDA) to software engineering and binary analysis. By treating codebases as simplicial complexes and applying filtrations based on cyclomatic complexity or call graphs, it identifies 'stable' features that persist across different scales while filtering out architectural noise. This skill is particularly powerful for detecting high-level structural holes, such as complex cyclic dependencies, and verifying architectural stability across different versions using bottleneck distance metrics.

Key Features

Betti number calculation to identify components, cycles, and voids
Radare2 integration for topological binary and CFG analysis
Stability verification to compare architectural integrity between versions
Complexity-based filtration for multi-scale codebase analysis
2 GitHub stars
Persistence diagram generation to track structural birth and death

Use Cases

Verifying that architectural refactors haven't introduced new structural holes or instabilities
Detecting and refactoring deep cyclic dependencies in complex microservices
Performing security audits on binaries to find structural anomalies using radare2

About

Key Features

Betti number calculation to identify components, cycles, and voids
Radare2 integration for topological binary and CFG analysis
Stability verification to compare architectural integrity between versions
Complexity-based filtration for multi-scale codebase analysis
2 GitHub stars
Persistence diagram generation to track structural birth and death

Use Cases

Verifying that architectural refactors haven't introduced new structural holes or instabilities
Detecting and refactoring deep cyclic dependencies in complex microservices
Performing security audits on binaries to find structural anomalies using radare2