The substrate's own notion of volume is not chosen. On the sector the programme works with, it is forced to be the same measure the Born rule uses.
unitaryFlowSetup_liouville_isForcedKahlerVolumeAn underlying deterministic world needs a way of saying how much of it is of one kind rather than another, and that means a notion of volume that the motion does not distort as it flows. Classical mechanics has one and calls it after Liouville. The worry is that such a volume might be picked to order, tuned to produce whatever answer was wanted. On the space this programme uses, it cannot be: the space and its symmetry leave exactly one option.
This is the hinge between the ontic story and the probability story. The substrate carries a finite Liouville measure and a motion that preserves it; the epistemic side needs the Fubini-Study measure to turn regions into Born weights. On the identity-projection sector those two are proved to be the same object, so the ruler used for probability is the substrate's own volume rather than a second, convenient assumption. It is also the honest reply to the standard objection that typicality arguments smuggle in the measure they justify.
For the unitary-flow sector the Liouville measure is the Fubini-Study measure, and it is the forced Kahler volume: the sector's typicality measure is determined by the state space and its unitary symmetry rather than posited. Scope to disclose: measure-preservation of the flow is carried as a structure field for physical admissibility (an ontic postulate), not derived; what is proved is that IF the sector is this one, the volume is forced.
Source links are pinned to a commit, so they do not drift. The anchors above are checked mechanically against the Lean tree on every build. The mathematics is not, and cannot be: that is a human responsibility and it rests with the author.