A Non-Idempotent Boundary Logic for Indeterminate Event Prediction

This work presents a non-idempotent boundary logic designed to model, analyze, and determine indeterminate events within structured sequences. The framework defines a hierarchy of boundary-differentiation operators (&¬, &¬₂, &¬₃, …) that capture intensities of non-classical negation and delineate transitional states between actualized and latent forms of an event. Shadow structures encode non-actualized variants of a term, enabling the system to track expansions, reductions, and cross-cap transitions (T₁,₃) across multiple representational layers. Using these components, we derive an explicit algorithm for predicting the next event after a branching point. The algorithm employs boundary operators, morphism families, shadow-expansion dynamics, and coarse invariants to reconstruct a unique (&¬₃)-state representation of the upcoming event. This establishes a deterministic solution to the classical problem of predicting future contingents without resorting to probabilistic heuristics.