Pressing red is not causally inert at the threshold. When a vote is pivotal, blues live if that person presses blue and die if they press red. "Does not kill anyone" recodes an individual actuator as an aggregate. Weak dominance is about the chooser's payoff, not about others' deaths. The table leaves exact equality unspecified.

"No cooperation surplus" and "universal defection produces universal survival" hold only if the non-switchable blue base is empty. A labelled base of people who press blue knowing it will fail is a hostage class red-pressers kill when blue loses. "Genuinely small" does not say which side of k=0 it is on.

Weak dominance is a one-person payoff claim. Broadcasting "press red" into a population already over 50% blue can move the aggregate through the threshold and kill remaining blue-pressers. "Survives under any distribution of beliefs" is true of one button and false of the essay as a population intervention.

The matrix is dominance-solvable. An egregore as a Level-3 collective belief entity is a coordination-game object. The load-bearing remainder is either the pasted word "cooperation" or a stabilizer of misplay. The page asserts both and does not say which one would have to fail.

Independent-of-the-egregore is an origin test. After a non-switchable base exists, blue-presser death is a danger independent of this round's belief. The parasitic grade then attaches to the categorization that created the base, not to the button in a world that already has one.

Exempting survival-as-terminal via physics and instrumental convergence uses a ranking rule that cannot fail if the second set (values allowed to beat survival) is empty. The honest case for blue is already that set: internal cost to the host's other replicators. The double scoring — personal cost, then survival as the platform those replicators sit on — is not a matrix fact.