The Inapplicability of Canonical Quantization to Embedding Gravity: A General Theorem and Its Realization in the Quantum Blueprint Formalism

In canonical quantum gravity, the Wheeler–DeWitt (WDW) equation ĤΨ = 0 arises from applying Dirac constraint quantization to the ADM Hamiltonian formulation of general relativity. The resulting equation is timeless, generating the problem of time—widely regarded as the deepest conceptual obstacle to quantum gravity. This paper proves a general theorem: for any theory in which the Einstein equation arises as a Gauss–Codazzi identity of an embedding V ↪ M, the Dirac constraint quantization of the gravitational sector is structurally inapplicable. The proof identifies three prerequisites of the Dirac procedure (a dynamical gravitational Hamiltonian, the metric as a fundamental variable, and time as a gauge-eliminable parameter) and shows that all three fail generically in embedding gravity, because the Einstein equation is a geometric identity of the embedding, the metric is the induced metric on the submanifold, and its status as a constraint arises from coordinate freedom on a pre-existing manifold that the embedding approach replaces with derivation. This general theorem (Theorem 3.1) applies to all embedding gravity theories: Regge–Teitelboim gravity, Randall–Sundrum braneworlds, DGP gravity, information-geometric embeddings, and the Quantum Blueprint Formalism (QBF). For each, we verify the failure of the prerequisites explicitly. For the QBF—the most complete realization, in which the embedding is derived from transcendental conditions on coherent structure—the theorem acquires additional force: time is not merely non-gauge but ontologically prior to spacetime via the circulation component of the Mother Equation. Three testable consequences are identified that distinguish embedding gravity from WDW-based approaches: the absence of a discrete area spectrum, the absence of third-quantization effects, and a minimum decoherence rate at absolute zero.