Measurement flow

In plain terms

Here is the problem. Saying "measurement is de-isolation dynamics" is a picture. The debt behind the picture: exhibit actual dynamics -- one map, deterministic, respecting the arena's volume -- that couples a system to a pointer and sorts trajectories into outcome blocks with the right sizes.

This theorem pays that debt at the projective level. The flow exists, is measure-preserving, is provably not the identity, and after it runs, the arena decomposes into pointer blocks -- one per outcome -- whose volumes are exactly the Born weights. Repeat preparations and the block frequencies converge to those weights almost surely.

No collapse anywhere: one deterministic map, run once per trial, plus ignorance of the starting point.

In CSD

This is the LF5 tier: the von Neumann measurement scheme realised dynamically on the dilated arena, closing the gap between the kinematic volume results and the de-isolation picture. The dilation that abstract measurement theory cites is here an actual flow, and the per-microstate outcome map -- which block a given starting point lands in -- is delivered by the pointer-partition theorems, discharging an outcome-function debt the corpus had carried explicitly.

Its honest boundary is equally explicit: the flow realises measurement dynamics at the projective level; deriving the record layer's fibre mechanism from such dynamics is the stated open frontier.

Mathematically

measurement_flow_born_frequency: the de-isolation flow is Fubini-Study measure-preserving with pointer-block volumes equal to the Born weights, and empirical block frequencies converge almost surely, for every unit preparation -- the earlier genericity hypothesis retired by the unconditional volume engine. The disjointness of the pointer blocks and the outcome map per microstate are separate, reusable theorems.