HomologyState

Full diagram at f, each bar annotated with its representative cycle (the class's generator at birth for a finished bar; the still-open generator for an essential class).

Query values across successive calls must be non-decreasing: this mutates state by advancing the underlying stream, never rewinding it, so diagramAt(3.0) followed by diagramAt(1.0) does not recompute the state as of 1.0 -- it reports whatever was still open at 3.0 as if newly queried at 1.0. Pre-existing behavior, inherited unchanged from the algorithm this replaces.