This paper studies a narrow operational question relevant to relational and closed-system approaches to physics: whether present accessible data determine a unique past. The central claim is modest. In general, direct reconstruction of the past from the present is ill-posed. Trajectory-dependent memory reduces ambiguity, but does not in general eliminate it. The resulting operational problem is therefore branch selection under a specified readout, rather than inversion of the present state alone. To formalize this claim, a minimal retrodictive-relational apparatus is introduced in which an observer is modeled as a subsystem endowed with a readout channel and record structure, without appeal to consciousness or external absolute time. The apparatus defines admissible pasts, historical ambiguity, branch-conditioned retrodiction, and readout-dependent value functions. Two experimental families are then incorporated. In reconstruction experiments across four synthetic modes, direct reverse reconstruction is generally weak, with improvement over baseline observed only in a minority of cases. In branch/readout experiments, erased readout outperforms path-like readout in a coherence-preserving regime, with a representative V4 result given by , , and . The relevance to quantum gravity is conceptual rather than dynamical: if time and observables are relational, then retrodiction should also be formulated relationally.
Yernar Seksenbayev (Fri,) studied this question.