Operationally induced preferred basis in unitary quantum mechanics

Abstract The preferred-basis problem remains under unitary system--apparatus dynamics, whereas measurements have mutually exclusive outcomes. The present framework places basis selection in the complete preparation--measurement arrangement. Preparation fixes the state of the system or sample in a specified domain and the ready state of the apparatus. The measurement scheme comprises the system--apparatus coupling, a pointer observable, and classical post-processing of its outcomes relative to a specified standard. The induced system positive operator-valued measure (POVM) determines an operational decomposition when its effects generate a nontrivial commutative algebra; degeneracy fixes only subspaces, while trivial or noncommuting effects select no unique basis. For fixed effects, the prepared state determines their probabilities. A qubit--pointer model relates the measurement sharpness to the coupling strength and pointer resolution. The contribution is primarily conceptual with explicit operational criteria: the preferred decomposition is fixed by the measurement-induced operator algebra rather than by the prepared state or unitary dynamics alone. Instrument compatibility gives its consequence for nested observers: whether the corresponding instruments are marginals of one realization. The analysis uses established Born-rule results, leaves single-outcome actualization open, and has no separate predictions from interpretations with the same dynamics and probabilities.