Measurement-Induced Entanglement Transitions and Basin Diagnostics Instruments, First Passage, and Protocol Limits

This paper replaces a universal identification of measurement-induced phase transitions, collapse thresholds, basin loss, and Zeno or anti-Zeno behavior by a typed, model-dependent framework. A hybrid monitored circuit is specified by its Hilbert space, unitary layers, measurement instrument, record law, conditioned trajectories, and averaged channel. The trajectory-averaged subsystem entropy is proved to differ from the entropy of the averaged state by a nonnegative Holevo quantity; consequently, the averaged channel does not retain the trajectory data that define the entanglement transition. Basin margins are retained as an effective model class only after a metric, boundary, generator, initial law, and stopping rule are fixed. For a stable Ornstein–Uhlenbeck coordinate with an absorbing boundary, we derive the exact mean first-passage integral and a basin-local contraction bound. The result is smooth in finite positive parameters and supplies no universal logistic knee. For a two-level system repeatedly projected at intervals of length tau, we derive the exact survival probability and its Zeno limit. Anti-Zeno enhancement is not universal and requires a specified reservoir or protocol. Measurement remains an ordinary physical interaction; outcome completion and the selection of one record are separate from an ensemble entanglement transition. The Modal Triplet Theory interpretation is conditional on a same-source map that emits the instrument, record weights, effective basin coordinate, and comparison errors.