Extrema-Frame Foreground-Background Theory

EF-FG is a downstream application of the unified realization framework to finite scalar fields, showing that the theory developed from pushdown normalization extends beyond automata. It builds a self-dual foreground/background semantics with observer-relative ownership and exact common-realization uncertainty, yielding an exact record-chain reduction, tractable local algorithms, NP-complete global ownership problems even on shallow trees, and common-realization obstructions of unbounded order. Its main contribution is both a new foreground/background theory and a concrete demonstration that the semantic–physical realization framework transfers to a genuinely different mathematical domain.