Structural–Informational Model of Space–Time Part II: A Physical Alternative to Singularity Surgery in Ricci Flow, A Universal Time Quantum and A Structural–Informational Interpretation of Gravity

This work proposes a structural–informational model of space–time that integrates Ricci flow, topological relaxation, and synchronization principles into a unified theoretical framework for describing the evolution of physical systems and interpreting the emergence of time, gravity, and large-scale cosmic structure. A concept of topological–geometric relaxation is introduced, in which physical evolution is interpreted as a process of harmonizing curvature, structure, and a characteristic time scale. The theoretical framework builds upon the Ricci flow formulation introduced by Hamilton and further developed by Perelman. Within the proposed Structural–Informational Model of Space–Time, this formalism is extended by introducing structural synchronization, leading to the Hamilton–Ricci–Perelman (HRP) flow as a physically motivated generalization of the classical Ricci flow. The HRP flow provides a unified description of geometric and structural evolution, in which topological transitions are treated as intrinsic features of the dynamical system rather than as the result of externally imposed surgery. The physical realization of HRP relaxation is associated with a postulated background pulsation of space–time at a characteristic frequency of approximately 0.06 Hz. Assuming the space–time medium to be nearly incompressible, oscillating particles and macroscopic bodies become synchronized through a mechanism analogous to Kuramoto dynamics. The synchronization time is determined numerically as the minimum of a combined residual functional incorporating both the HRP compatibility condition and a radial geometric constraint. The corresponding relaxation time increases monotonically with orbital radius. However, after normalization by the orbital-curvature factor, , the relaxation times of all planets converge to a common invariant value of ≈ 16.77 s. This invariant is interpreted as a structural quantum of time, according to which the planetary system represents a family of geometrically modulated realizations of a single relaxation scale. Within the proposed framework, gravity is interpreted as the physical manifestation of a topological–geometric relaxation process through which the space–time structure evolves toward dynamically synchronized states and maximal temporal coherence. The mathematical operations of smoothing, relaxation, minimization, and topological restructuring embodied in the HRP flow are interpreted, in accordance with Landauer's principle, as physical processes involving the redistribution of information and structural energy. In this context, deformation of the manifold metric is regarded as an informational flow associated with the structural energy of curvature. By combining Ricci-driven geometric relaxation with the synchronization functional , the HRP flow can be interpreted as a fundamental equation governing structural–informational interactions across a unified relaxation process, linking the elements of space–time, elementary particles, and macroscopic physical systems. On this basis, the existence of a fifth fundamental interaction—the structural–informational interaction—is hypothesized. Rather than competing with gravitational, electromagnetic, weak, and strong interactions, it is proposed as a higher-level organizing principle that manifests itself through the universal tendency of physical systems to evolve toward stable topological and geometric configurations.