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.

Conceptual Structure of the ToE–2PS Framework: Baryonic Matter Distribution ↓ Baryonic Acceleration (g_bar) ↓ Scalar Coherence Field Λ Response ↓ Additional Acceleration (g_Λ) ↓ Effective Acceleration g_obs = g_bar + g_Λ ↓ Emergent RAR Relation Baryonic matter generates a gravitational field that induces a response in the scalar coherence field Λ. This response produces an additional acceleration , leading to the effective gravitational acceleration . The resulting dynamics naturally reproduce the Radial Acceleration Relation (RAR) observed in galactic rotation curves, providing an emergent explanation consistent with the ToE–2PS toroidal hypercoherence model.