persistent-homology

Persistent homology tracks topological features—components, loops, and voids—across nested complexity filtrations. It computes Betti numbers at each threshold and generates persistence diagrams showing birth-death pairs; features that persist across many levels are robust structural invariants, while short-lived features are noise.

Yes. Persistent homology works across source code, binary analyses, and CFGs by constructing filtrations from cyclomatic complexity thresholds. It identifies stable structural holes and robustness metrics across all three domains, integrated with radare2 for binary code analysis.

A filtration is a nested sequence of complexes built by incrementally raising a complexity threshold. In code analysis, filtration by cyclomatic complexity creates successive layers of the codebase; topological features that survive across layers indicate structural resilience and meaningful invariants.

Run a persistence analysis by defining a complexity-based filtration on your codebase. The Skill computes Betti numbers at each level, generates persistence diagrams, and outputs stable features and comparative metrics showing which structures persist across thresholds.

Betti numbers count topological features at each complexity level: the first Betti number counts connected components, the second counts loops, and the third counts voids. Tracking these across filtrations reveals how structural complexity and connectivity change, highlighting robust patterns and fragility points.

Persistence diagrams capture multi-scale structural stability that cyclomatic complexity or coupling metrics alone miss. Use them when you need to identify which architectural features remain invariant under varying complexity thresholds—essential for verifying robustness and distinguishing signal from noise in large codebases.