Extrema-Frame Foreground-Background Theory II

The second-stage development of the EF–FG framework, completing the five principal research directions left open in the foundational paper. It proves that complete categorical spatial-frame realization is NP-complete even on shallow bipartite graphs, classifies finite common-realization complexes exactly by showing that every finite simplicial complex is realizable under both raw and canonical EF–FG semantics, and identifies two fixed-parameter tractable regimes for the ownership-hardness kernel. The paper also extends exact common-realization semantics from independent interval uncertainty to correlated rational-polyhedral uncertainty and develops a finite multichannel and spatiotemporal version of the theory with joint realization, exact certification, self-duality, and transferred hardness results. Together, these results turn the open theorem program of EF–FG I into a closed second-stage theory combining global complexity, realization universality, parameterized tractability, and layered semantics.