Cognitive Engineering Framework and Temporal Semantic Dominance Principle: BLOC Theory V2.1

BLOC Theory v2.1 develops a mathematically closed operator–geometric frame work for Human–AI cognitive systems and establishes a formal theory of semantic irreducibility under computational transformation. The framework addresses a fundamental unresolved problem in AI cognition: whether semantic meaning can be losslessly reconstructed after discrete computational encoding and organizational projection. The theory is built on three coupled mathematical foundations. First, a Hilbert space semantic architecture rigorously defines all cognitive, organizational, and computational spaces with explicit topology, norm, metric, and duality structure. Second, a category-theoretic inter-theory hierarchy formally links BLOC, DAIS-10, KAD Theory, and SFPM-10 through explicitly constructed categories, functors, and compositional operator mappings. Third, the framework proves two central structural theorems. TheSemantic Separation Theorem proves that Human semantic meaning and machine aligned computational representations are separated by a strictly positive lower bound ε =distIm(Algn ◦F),Im(M) > 0, derived constructively from compactness and semantic-image disjointness. This establishes semantic irreducibility as a mathematical consequence of operator geometry rather than a philosophical claim about AI limitation. The Projection Closure Theorem further proves that all managerial and organizational interpretations are bounded, non expansive projections of irreversible operator-level transformations in semantic Hilbert space. The framework additionally introduces a canonical embedding for Unified Intel ligence dynamics, a tensor-interaction formalism for Human–AI coupling, a Riesz grounded phenomenological integral, and a functorial semantic-drift architecture across governance layers. Six application theorems are derived as strict logical consequences of the axiomatic system, including irreducible alignment distortion, governance driftpropagation, diagnostic semantic incompleteness, and order-sensitive knowledge integration. BLOC Theory v2.1 therefore establishes a formally verifiable foundation for computable cognitive engineering, in which Human–AI systems operate under provable geometric, categorical, and information-theoretic constraints. The theory reframes AI alignment not as perfect semantic equivalence, but as bounded-error optimization under mathematically unavoidable semantic separation.Beyond its theoretical contribution, the framework provides a computable managerial architecture for organizational decision systems operating under AI-mediated work flows. The theory enables formal analysis of governance drift, alignment degradation, knowledge propagation, semantic risk accumulation, and bounded decision distortion across complex enterprises. As a result, BLOC Theory v2.1 provides organizations with a mathematically grounded foundation for AI governance, cognitive risk man agement, strategic decision engineering, and Human–AI operational design, allowing institutions to measure, constrain, and optimize semantic reliability under provable structural limits.