how long does a stage survive?

A stage is supposed to leave the field for the next stage to work on. Whether it does is not a matter of design intent: two Gibbs chains driven by the same random numbers coalesce, and once they have, the later chain has forgotten which field it started from. So "history" survives exactly as long as the chains stay apart. This measures that directly.

A, stage 1 lays its marks, then stage 2 settles. B, stage 1 lays nothing, then stage 2 settles. Same seed, same stage count, same random numbers, same everything else, so any disagreement between A and B is stage 1 and nothing else. C, same as A at a different seed: the scale of two unrelated worlds, which is what disagreement looks like when it means as much as it can.