Class-Relative Certification of Open-Loop Backward Signaling from a Committed Record: Exact Ordinary-Route Bounds and Anytime-Valid Evidence

This preprint develops a rigorous framework for certifying open-loop backward signaling from an earlier committed record while distinguishing it from ordinary explanations such as postselection, hidden memory, conditioning, fine-tuning, and measurement dependence. For explicitly defined alternative classes, the paper derives exact finite-alphabet bounds on the observable record distributions, characterizes the corresponding feasible region through three operational cuts, and proves constructive converses showing that every point inside the region admits an ordinary-route realization. It also introduces a scaled gauge of class-relative violation, transport-based robustness bounds, and projection-closed e-processes that provide anytime-valid sequential evidence under optional stopping. Worked examples and exact rational checks illustrate how the framework can be applied in finite-data experiments. The resulting certification is deliberately class-relative: rejection of an audited ordinary-route class does not by itself identify a unique physical mechanism or establish retrocausality in an unrestricted open world. Instead, the framework specifies what must be committed, randomized, retained, audited, and statistically demonstrated before backward signaling becomes a defensible interpretation rather than an artifact of selection or hidden dependence.