Builder-Blocker PSPACE-completeness conjecture

Prove or disprove that the decision versions of both the B-game and B'-game are PSPACE-complete.

Background

The B-game and B'-game differ according to whether Builder or Blocker moves first. Their decision complexity is unknown, and the cited conjecture predicts PSPACE-completeness for both variants.

References

The decision version of the B- and B'-games are PSPACE-complete.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 7, subsection “Complexity of games”