Composite Dual Scalar Field Theory (CDSF Theory): A Diffeomorphism-Invariant Bimetric Gravity Framework and Localized Stable Coupling Field Dynamics

Please note: The main manuscript is uploaded as "Composite Universe Theory.pdf", and the supplementary mathematical derivations for extreme boundary limits are provided in the attached file "CUT___Extreme_Boundary_Conditions.pdf". --- We present the formal, structural, and mathematical closure of the Composite Universe Theory (CDSF Theory), a unified, diffeomorphism-invariant bimetric gravitational framework. Spacetime is modeled via two concurrent geometric manifolds: the observable physical sheet (R) governed by the metric g_R and a complementary hidden sheet (I) governed by g_I. These sectors couple locally through an intermediary dynamical scalar field, exhibiting finite causal propagation bounded by the physical light-cone. We eliminate the ad-hoc hypotheses of independent dark matter and dark energy. Dark matter phenomena emerge as a kinetic consequence of the metric alienation tensor derived directly from the variation of the exact interaction Lagrangian, while dark energy arises from the non-linear saturation potential V(Φ) = V_0 [1 - exp(-Φ/Φ_0)]. A rigorous phase-space stability analysis proves the existence of stable attractor solutions, ensuring geometric protection against ghost instabilities. Finally, we execute a rigorous minimization protocol against the extensive real Pantheon Type Ia supernovae compilation (N = 1048). The Calibrated Composite Universe framework secures a highly robust reduced chi-square of χ² ≈ 1.007, establishing absolute statistical viability and validating the localized scalar coupling field dynamics without arbitrary fine-tuning.