Limits and successor problems

The closed result is Theorem thm:main. The structural class is declared, not reconstructed from its five requirements. The first four requirements give diagonal anchoring at arbitrary finite sizes. Records connect coherent whole-register readout to those diagonal laws; composability gives partial readout; continuation tests give positive-branch residual rays.

The proof order does not establish that records are necessary. It also does not assert that the first four requirements already determine coherent probabilities or updates.