Constraint Projection in Discrete Ledger Systems: A Formal Model of Future-Balance Visibility with Sleep-Stage Predictions

We present a formal model in which future constraints become visible in the present without retrocausation. The model operates within Recognition Science (RS), a discrete-time framework whose axioms—a unique cost function, a forced golden-ratio scale, three spatial dimensions, and an 8-tick conservation period—have been published and machine-verified elsewhere [1-4]. Taking these axioms as given, we prove that any observation event within an 8-tick window creates a balance debt that the remaining ticks must discharge (Theorem [1]), and that this debt inflates the effective cost function monotonically (Theorem [2]). We call this cost inflation "Phantom Light"—the shadow of a future balance requirement visible in the present as a restriction on admissible trajectories.

We then model sleep stages by a monotone coherence ordering (an empirical input from polysomnography) and prove a robust visibility ordering: lower-coherence stages carry higher phantom magnitude, with N3 dominating N1 and REM (Theorem [3]). Under the canonical consecutive-integer budget used for illustration, N3 has twice the N1 phantom magnitude. Zero balance debt annihilates phantom light in every mode (Theorem [4]).

The model yields five falsifiable predictions, including a sleep-stage ordering of precognitive dream reports and a presentiment-scaling law. We also specify preregistered empirical proxies for the latent model variables, a blinded prospective dream-scoring protocol, and a small-effect power envelope for confirmatory studies. All theorems are machine-verified in the Lean 4 proof assistant (52 theorems, zero unproved placeholders, zero new axioms beyond the RS foundation). Each claim is classified as PROVED, MODELING CHOICE, or HYPOTHESIS in an explicit table (Section [5]). We discuss the relationship to Aharonov's Two-State Vector Formalism, to Hobson's AIM model of dream generation, and to the presentiment literature including both positive reports (Radin, Mossbridge) and critical responses (Wagenmakers, Alcock).