The thesis
A UMAP, a PHATE, a foundation-model embedding, a transformer's hidden layer: each shows you a shape, and part of that shape belongs to the method. The picture is what gets published, so that part matters. We want to know which structure would be found again by a different method, a different instrument, someone meeting the data fresh. Our tools make that comparison routine: run the data through many methods, score every result with the same suite of geometric metrics, and keep a ledger of how each result was reached. The data can be a cell-by-gene matrix, a cohort of genomes, a protein run through a sequence model, or a language model's hidden states while it answers. A representation is good when it survives a change of method. These tools make that test something you run before you believe a figure.
