A Curvature-Dependent Gravito-Temporal Collapse (GTC): Degeneracy Mechanism for Singularity Resolution and Dark Sector Unification

We propose the Gravito-Temporal Collapse (GTC) framework as a robust Effective Field Theory (EFT) extension to General Relativity. The core hypothesis is that spacetime undergoes a continuous dimensional phase transition (4D -> 1D) when the Kretschmann curvature scalar approaches a critical Planckian threshold. We derive a stable metric degeneracy factor D(K) from a constrained variational principle with a positive-definite potential, ensuring the suppression of spatial geometry in the deep collapse regime. This mechanism resolves classical singularities while generating a residual scalar degree of freedom which unifies the Dark Sector. We demonstrate that: (1) In the galactic weak-field limit, the scalar field naturally adopts a logarithmic profile, reproducing the flat rotation curves associated with Dark Matter/MOND phenomenology. (2) On cosmological scales, an inverse power-law potential drives cosmic acceleration (w approx -1). (3) The model satisfies stringent Solar System constraints (Cassini) via a Chameleon screening mechanism, imposing a strict bound on the matter coupling. Finally, we discuss the implications for gravitational wave astronomy, predicting post-merger echoes with a time delay of approx 30ms, subject to reflectivity constraints.