Structural Formulation of Forbidden Physics: Operator-Theoretic Obstructions and the Admissible Kernel

The designation of a physical theory, state, or process as "forbidden" is frequently treated in the scientific literature as a heuristic judgment or a localized phenomenological rule. This manuscript formalizes forbiddenness not as a qualitative suspicion, but as a strict operator-theoretic obstruction. By introducing a universal, non-negative constraint operator, we establish that admissible physics is strictly confined to its null space. Any state or trajectory occupying the orthogonal complement of this space is mathematically classified as forbidden. We derive the forbiddenness functional and establish the coercive penalty dynamics that actively repel unphysical trajectories. Furthermore, the manuscript proves that persistent constraint violation induces irreversible decoherence and strict entropy production. The framework explicitly enumerates the individual constraint operators that enforce fundamental physical laws—including symmetry, causality, unitarity, and thermodynamics—and maps this architecture directly to fluid dynamics, providing a formal model for variance-dominated cascade arrest in the Navier-Stokes equations. Finally, the manuscript extends this rigorous boundary to the sociology of scientific evaluation. It formalizes "gaslighting" in peer review as a strict mathematical mismatch—the application of an evaluation operator that cannot be derived from the governing constraints of the theory. It concludes by defining "calculated cruelty" as a derived structural regime: the persistent local minimization of a system after all coherent pathways for global correction have been irreversibly destroyed. Physics is not forbidden because it is unpopular or unfamiliar; it is forbidden precisely when it violates the operator-closed constraints that define admissible evolution.