On the Non-Quantizability of Gravity and Constraint-Induced Rigidity of Physical Structure

Description This work proves a closure theorem for primitive attempts to quantize gravity. It shows that, when quantization is formulated in standard mathematical-physics terms, any same-domain construction mapping classical gravitational structure to quantum structure must diverge in a finite set of technical loci. These loci include representation choice, observable assignment, constraint closure, state-space definition, measure or inner-product selection, boundary extraction, and admissible continuation. Using the AASC (admissibility, standing, reference, irreversibility) framework, the paper demonstrates that these divergences are not arbitrary but structurally exhaustive. Each divergence is mapped to a finite normal-form class and shown to collapse under admissibility constraints: either by introducing auxiliary structure, changing scope, performing post hoc repair, or reducing extensionally to an already admissible realization. Consequently, gravity is not quantizable as a primitive same-domain operation. The positive result is a constraint-induced rigidity theorem. It establishes that admissibility-preserving physical structure must be constructed as a constraint-native realization, rather than by quantizing a classical theory. Within such realizations: general relativity appears as an interior constrained Hamiltonian projection, quantum mechanics appears as an interior Hilbert/Schrödinger projection together with boundary-level measurement/record structure, and both are understood as bookkeeping projections of a common admissibility-bearing quotient architecture. The result does not deny the utility of canonical, path-integral, or other quantization techniques as effective tools. It shows instead that these procedures cannot serve as primitive foundations for quantum gravity within an admissibility-preserving framework. The paper replaces the question “how to quantize gravity” with a well-posed alternative: how to construct admissibility-preserving realizations whose projections reproduce both gravitational and quantum structure. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility Admissibility and Constraint-Induced Rigidity of Physical Quotient Structure