PHAT

PHAT is a layer below every other library profiled here. It does not build complexes, does not read structures, and does not produce a barcode from a point cloud. It takes a boundary matrix and reduces it, and it exposes the choices that step involves rather than making them for you: standard, twist, chunk, and spectral-sequence reduction algorithms over several column representations, with optional parallelism.

That is a narrow interface and a deliberate one. Reduction is where persistence computation actually spends its time, and the algorithm and data structure that win depend on the shape of the matrix — which is a property of the problem, not of the library. Most tools pick for you. This one is for when the pick is the thing you are studying, or when you have a complex from somewhere else entirely and want persistence out of it without adopting a framework.

Practically, that makes it a capability the corpus holds rather than a tool it runs. Nothing here uses PHAT as a step in a pipeline today; it is present because a foundry that only carries entry-point tools cannot answer questions about the layer underneath them.

Licensing

LGPL-3.0-or-later, which is redistributable copyleft with the isolate-and-notice obligations rather than a blocker. Nothing prevents this from reaching a public channel — the recipe simply has not been submitted.

In this corpus

phat-environment stages phat-recipe, which compiles the C++ with pybind11 and is verified green; that in-repo build is the only reason the fixture sits at L1 rather than L3. The technique is persistent-homology, which lists it as a building block rather than an entry point.