Re-Phase Vol.5.4 Information-Adapted Selection — Selector Classes, Retention, and Safe Forgetting

Re-Phase Vol.5.4 moves from single-path compatibility lifting (Vol.5.3) to family-level selector existence: given a family of admissible base paths, can one information-constrained rule choose a compatible lift for every member at once? The opening principle is that fiberwise liftability does not imply information-adapted selection — below the offline top class, a memoryless, lookback, causal, retained-coordinate, or quotient-restricted selector may fail to exist even when every fiber is nonempty. The volume defines selector classes as factorization conditions through information maps, introduces selector inconsistency, bridge-valid selection, non-blocking continuation, retained-coordinate versus selector-memory separation, and safe forgetting relative to selector preservation, with finite toys A–F witnessing each gap and the target-sound-versus-selector-preservation boundary identified as the main open question.