A Transdimensional Scalar-Time Derivation of the Casimir Effect: Compatibility, Corrections, and Testable Predictions in TSFT

We present a proof program deriving the Casimir effect within Time-Scalar Field Theory (TSFT), where vacuum fluctuations emerge as constrained modes of a scalartime coherence field Θ. Starting from TSFT postulates, we recover the standard attractive pressure P(a) = − π2ℏc 240a4 in the ideal limit via mode quantization and renormalization interpreted as coherence-baseline selection. TSFT-specific corrections—a coherence gap inducing exponential suppression at large separations and a modulation signature under external temporal perturbations—yield falsifiable predictions distinguishable from QED. Proposed experiments using AFM and lock-in detection are outlined, positioning TSFT as empirically viable for unified physics.