Hilbertian Meta-Quantum Causal Field Physics: A Bra-Ket Formalism with a Gradient-Projection Causal Hamiltonian

This manuscript introduces a Hilbertian version of Meta-Quantum Causal Field Physics, a proposed trans-quantum framework in which a physical event is represented not only as a quantum state but also as a causal-field state carrying a gradient direction, measurement-operational structure, and field-signature coordinate. The central formal object is an extended ket |Psi_MQC> in a multi-layer Hilbert space, together with a causal Hamiltonian defined by H_MQC = -grad F_C . x. In the one-dimensional operational reduction used here, the field-like signal F(t) is taken from a scaled proxy-strain channel and the causal Hamiltonian trace becomes H(t) = -t dF/dt. The supplied dataset contains 703 samples spanning t = 0.026 to 18.278 s. The analysis produced non-trivial causal-Hamiltonian signatures, with H ranging from -118.81 to 114.84, mean H = -0.00144, mean |H| = 13.46, and a normalized bra-ket expectation value E_MQC = <Psi|H|Psi> = 0.005534. These results support first-level internal-operational validation: the formalism is mathematically computable, produces measurable signatures from the supplied data, and admits a bra-ket expectation-value representation. The manuscript does not claim absolute certainty or final external experimental closure; instead, it frames the result as model-based compatibility and internal validation of a newly proposed Hilbertian causal-field structure.