Same state, different history

Two panels build the identical final graph—three objects and two relations—through different sequences of Pop, Refuse, Bind, and Collapse. Step through both, then compare what their histories retain.

Path A

Path B

What replay shows

Both logs terminate at the same rendered state: objects a, b, and c, with admitted relations a–b and b–c. Inspection of the current graph alone cannot distinguish the paths.

Path B, however, records a Refuse of a–c. That relation was considered and excluded. Path A never considered it and therefore contains no corresponding historical fact.

Replay recovers this difference. Under Spherepop the structures are not identical, because identity is indexed by history rather than present state.