The central result of this work is a first-principles derivation of primordial quantum state selection in CPT-symmetric cosmology based on distributional gravitational regularity at a spacelike boundary. This work supersedes the phenomenological parametrization introduced in earlier CPT formulations by deriving the primordial quantum state from a variational principle at the CPT-symmetric boundary. In CPT-symmetric cosmology, the Big Bang is reinterpreted as a geometric junction rather than a physical singularity. While this framework constrains global spacetime structure, the primordial quantum state is often imposed as an external assumption. This paper replaces such ad hoc prescriptions with a dynamical selection principle derived from boundary regularity and energetic consistency. We formulate a variational principle over admissible Gaussian (Hadamard) states that enforces the canonical boundary constraint while penalizing adiabatic excitation. The variational problem is mode-local and algebraic. The boundary constraint fixes the squeezing phase discretely, while the squeezing amplitude is selected uniquely as the stable variational minimum within the Hadamard class. The boundary condition is implemented as a finite energetic penalty rather than a rigid kinematic constraint, reflecting the fact that exact enforcement would generically require infinite excitation energy. The resulting squeezing spectrum exhibits automatic ultraviolet admissibility, finite infrared saturation, and an emergent transition scale separating boundary-dominated and standard behavior. The selected squeezing amplitude represents the minimal entanglement cost required to maintain quantum continuity across the CPT-symmetric bounce. From the boundary-selected state we derive the primordial curvature power spectrum directly, obtaining a universal suppression factor that modifies long-wavelength modes while recovering the standard spectrum in the ultraviolet. The results are logically prior to effective boundary-entropy and dark-sector constructions and provide a technical foundation for subsequent regime-specific developments. This work is purely theoretical. It contains no Boltzmann evolution, no CMB angular power spectra, and no observational fitting. Physical consistency is established through parametric backreaction bounds and non-Gaussianity considerations. The result is a complete and falsifiable theory of primordial state selection that provides a clean interface to observational tests developed in a companion paper.
Mhamed Karrit (Wed,) studied this question.