0 · Build a probe from finite stages

A probe begins with one box. Each new stage divides the boxes into smaller ones. A point in the finished probe is a path that makes one compatible choice at every stage.

Try this. Add one stage at a time. Notice that every stage has finitely many boxes, even though the completed probe has no last stage. Change the number of pieces to compare different branching patterns.

The standard name for this object is a profinite set. The browser builds the same finite sets and transition maps as the Python code, and the tests compare their results.