From Transition Selection to Evaluation Validity in Time-to-Event Prediction

Time-to-event prediction increasingly uses adjacent states as temporal super vision, yet logging, filtering, and event-triggered acquisition can alter which transitions enter the learning channel. We study the target-specific question of what a transition-selection mechanism must preserve for acquired transitions to remain valid for an expected time-to-absorption target. For a proper finite absorbing process, we distinguish transition-distribution, target-Bellman, and deployment-evaluation validity, and show that Bellman validity holds exactly when the retention propensity is conditionally orthogonal to the successor time-to-event value. Any remaining local distortion propagates through the acquired-process resolvent and is then filtered by the deployment evaluation geometry, yielding an exact nested hierarchy and a full-support collapse result. Exact rational constructions, 500 deterministic random-kernel checks, and controlled Monte Carlo illustrations verify the identities and demonstrate all four operational regimes: distribution-valid, Bellman-valid but distribution-invalid, evaluation-valid but Bellman-invalid, and evaluation-invalid.