ix-topo

name	ix-topo
description	Topological data analysis — persistent homology, Betti numbers, point cloud topology
disable-model-invocation	true

Topological Data Analysis

Compute topological features of point cloud data using persistent homology.

When to Use

When the user has point cloud data and wants to detect topological features (connected components, loops, voids), compute Betti numbers, or generate persistence diagrams.

Capabilities

• Persistent homology — Birth-death pairs across filtration radii
• Betti numbers at radius — Count of H_0 (components), H_1 (loops), H_2 (voids) at a given scale
• Betti curve — How Betti numbers evolve as radius increases
• Vietoris-Rips complex — Build simplicial complex from distance threshold

Key Concepts

• β₀ = connected components, β₁ = loops/tunnels, β₂ = voids
• Long-lived features (large death-birth) are topologically significant
• Short-lived features are likely noise

Programmatic Usage

use ix_topo::pointcloud::{persistence_from_points, betti_at_radius, betti_curve};
use ix_topo::simplicial::{rips_complex, SimplexStream};

MCP Tool

Tool name: ix_topo Operations: persistence, betti_at_radius, betti_curve