Dimensional Decoherence and Gravity as Frozen Ricci Flow Geometry

This work presents a novel five-dimensional (5D) geometric framework in which gravity in four-dimensional spacetime arises as the residual curvature left after a higher-dimensional Ricci-flow-like collapse.The additional coordinate ψ\psiψ is interpreted as a quantum-coherence or informational dimension whose evolution smooths curvature irregularities — a geometric analogue of quantum decoherence.When this flow halts, the geometry “freezes,” leaving behind the static 4D curvature observed as classical gravity.Numerical ψ–flow simulations confirm that: Curvature flattens toward equilibrium (Ricci-flow smoothing). The effective gravitational coupling GeffG_{\mathrm{eff}}Geff increases as the collapse completes. Black holes emerge as fixed points of the flow, representing complete decoherence of the extra dimension.The framework unifies ideas from General Relativity, Ricci flow, Kaluza–Klein geometry, and quantum decoherence, offering a geometric mechanism for the emergence of spacetime curvature.