Deterministic Systems Intelligence: Admissible-State Operators for Feasibility-First Inference in Sequential Systems

Sequential systems are commonly analysed with probabilistic, state-space, dynamical and learning-based methods, yet these approaches may define state spaces broader than the states that an active system can actually reach under structural constraints, regimes and accumulated history. This creates a systems-representation problem: inference can remain technically valid while operating over infeasible states or transitions. Deterministic Systems Intelligence (DSI) is developed as a systems-science framework for addressing that problem by operationalising admissibility as an explicit pre-inferential systems layer. DSI distinguishes conceivable from admissible state spaces and defines a set-valued admissible-state operator constructed from clock, regime, memory and constraint predicates. Six scoped methodological propositions specify implications for feasibility, masking, regime transition, memory, optimisation and admissibility-consistent explanation. The framework is positioned relative to cybernetics, viability and reachability theory, state-space modelling, nonlinear dynamics, time-series analysis and machine learning, with explicit boundaries on what DSI inherits and what it adds. A fully specified sequential-system example demonstrates how identical observed emissions can yield different admissible futures under different clocks, regimes and histories, while comparative evaluation criteria are defined for admissibility construction and inferential withholding. DSI is proposed as a complementary admissibility layer that makes representational feasibility explicit before downstream estimation, prediction, optimisation or release governance.