Reconstruction of the Schwarzschild Weak-Field Limit in Geometric Response Cosmology (GRC): A Flat Substrate with Emergent Time

The Schwarzschild metric constitutes the exact solution of Einstein's equations for a non-rotating spherical body. In the weak-field limit (rₛ/r ≪ 1), this metric predicts three observable phenomena: gravitational time dilation (redshift), Shapiro time delay, and angular deflection of light. In the standard framework, these phenomena require a four-dimensional pseudo-Riemannian geometry with two independent metric components (gₜₜ and gᵣᵣ). In this work we demonstrate that the weak-field limit of Schwarzschild emerges mechanically in Geometric Response Cosmology (GRC) from a single hypothesis: the conservation of the velocity-vector norm in a flat, absolute spatial substrate. The effective propagation velocity of the photon, modulated by the local gravitational resistance of the substrate, quantitatively reproduces the three classical phenomena without invoking geometric curvature. This result constitutes a complete ontological reconstruction of the weak-field gravitational regime from a continuous-medium mechanics.