Variational Closure and UV/IR Scale Duality in Covariant Bitemporal Geometrodynamics: The Zero-Sum Field Operator, Sub-Planckian Fiber Geometry, and Dimensional Reduction of Physical Constants

Building upon the five foundational monographs of the Covariant Bitemporal Geometrodynamics (CBG) series (Papers I–V), this treatise formulates the formal variational closure (Cycle III) of the 5-dimensional geometric model on the manifold M_{3,2} = (R_{t1} x S^1_{t2}) x Sigma_3 with signature (-,-,+,+,+) and integer dimensions (d_t, d_s, D) = (2, 3, 5) (N_Cartan = 30, D_config = 17, Phi_infinity = 2.40287 x 10^-4). First, we expand the stationary variation delta S_JV = 0 of the 5D Master Action across all metric, holonomic, Schutz–Clebsch fluid, and Spin(3,2) = Sp(4,R) spinorial sectors to formulate the Zero-Sum Field Operator Identity Xi_{AB}[M_{3,2}] = 0, demonstrating how the total canonical Hamiltonian density vanishes identically on any spatial-fiber Cauchy hypersurface Sigma_3 x S^1_{t2} through the exact cancellation between gravitational-holonomic curvature and informational-fermionic stress-energy. Second, we analyze the extreme ultraviolet (UV) and infrared (IR) boundary regimes of the manifold, showing that the asymptotic sub-Planckian radius of the secondary temporal fiber R_{t2,infinity} = Phi_infinity * L_P = 3.8836 x 10^-39 m (circumference L_{t2,infinity} = 2.4402 x 10^-38 m) acts as a smooth geometric regulator below the Planck length L_P = 1.6163 x 10^-35 m, linked to the macroscopic Hubble horizon scale r_{H,0} = 1.373 x 10^26 m via an exact UV/IR reciprocity across the mesoscopic bounce fulcrum lambda_micro = sqrt(L_P * r_{H,0}) = 47.11 um (D_bounce = (2*pi/17) * lambda_micro = 17.41 um). Third, we examine the secular Casimir stability conditions of the compactified fiber Sigma_3 x S^1_{t2} and the geometric interpretation of dimensional SI units (c, hbar, G, k_B, e) as natural conversion factors within the M_{3,2} formalism.