The moment heist

Matching the averages still leaves room for very different distributions.

These distributions agree on a set of moments, yet put their probability mass in different places. The experiment looks for the largest gap that can hide behind the same summary statistics.

The actual two moment-matched distributions on an eleven-point grid — 01 Two distributions from the saved eleven-point grid agree on moments zero through three. Their distance is 99/400, the certified diameter for this finite case.

What to look for

On the selected eleven-point grid, the two shown distributions sit 99/400 apart in Wasserstein distance. Exact primal and dual calculations certify the finite-grid maximum.

Under the hood

A working engine, interactive experiment and exact exported examples.

A certificate audit and proof notes that identify established background and limits.

Each finite-grid calculation has a pair of distributions that achieves the distance and a dual certificate that puts a matching ceiling on it.