A Minimal Scalar - Tensor Model for Toroidal Hypercoherence: An Emergent Explanation of the Radial Acceleration Relation

This work presents a minimal scalar–tensor formulation associated with the concept of toroidal hypercoherence within the ToE-2PS paradigm. The model introduces a scalar coherence field that effectively modifies gravitational dynamics in the quasi-static regime, naturally reproducing the Radial Acceleration Relation (RAR) observed in galactic rotation curves.

Within this framework, a characteristic acceleration scale emerges from the dynamics of the coherence field and exhibits correspondence with fundamental cosmological parameters, suggesting a possible connection between galactic dynamics and the large-scale structure of spacetime.

The formalism recovers the Newtonian limit in the high-acceleration regime and remains compatible with the standard relativistic structure in the weak-field limit, while simultaneously reproducing the observational phenomenology commonly associated with MOND-like behavior.

The resulting framework provides a unified phenomenological description linking galactic dynamics, gravitational lensing, and cosmological observables within a single coherence-based gravitational response.