Born-Compatible Record Measures and the Classical Concentration Limit: Separate Theorems and Their MTT Interface

The Born rule and the emergence of classical behavior are related, but they are not the same mathematical problem. The first fixes outcome probabilities for a declared quantum preparation and instrument. The second asks when retained records and observables are well approximated by one stable classical alternative. We formulate their interface without identifying them. Standard Gleason-type results recover trace probabilities only after additive or effect-noncontextual probability assumptions are supplied; they do not select an MTT source measure. The current q79 program now provides a stronger, domain-specific result: its canonical binary one-anchor Fock recorder emits an exact stopped-output measure and second-moment capture descent from the selected normal state, without an added Born axiom, stochastic primitive, fit, or observed probability on that domain. General apparatus contexts and objective single-history actualization remain open. Separately, we prove exact concentration and persistence bounds. If one record has probability at least 1 minus epsilon, the law is within epsilon in total variation of a deterministic record, bounded observables differ by at most epsilon times their oscillation, and a record with per-step escape probability at most eta survives n steps with probability at least 1 minus epsilon minus n times eta. These statements define a controlled classical limit. They do not derive the outcome weights or select one realized history.