Constrained SO(3,3) Spacetime: Part VI. Extended ADM Hamiltonian Foliation and Exact BRST Quantization

Abstract

Previous formulations established that a dynamic topological constraint field kinematically suppresses negative-norm ghost states by decomposing the SO(3,3) metric into a 3+1+2 structure. To elevate this kinematic suppression to a rigorous dynamical proof, this paper constructs an extended Arnowitt-Deser-Misner (ADM) Hamiltonian foliation. By proving the closure of the hypersurface deformation algebra under mixed-signature conditions and applying exact BRST quantization, we demonstrate that transverse-time degrees of freedom are algebraically eliminated, ensuring strict macroscopic unitarity.