Emergent Gravity from Basin-Fixed Point Framework

This manuscript develops a unified emergent‑gravity model based on the basin–fixed point framework, in which gravity and spacetime curvature arise from the collective dynamics of discrete relational energy minima (“basins”) rather than a fundamental geometric manifold. Building on earlier work showing how quantum mechanics emerges from basin fixed‑point structure, this paper extends the formalism to gravitational and cosmological scales and introduces two additional axioms governing collective curvature and scale‑dependent renormalization. Within this framework, effective mass arises from the Hessian (local curvature) of each basin’s energy functional, while gravitational attraction originates from adjacency‑driven energy gradients between basins. In the continuum limit of densely packed basins, these interactions reproduce Newton’s inverse‑square law and the weak‑field structure of the Einstein equations without assuming spacetime geometry as a fundamental entity. The gravitational constant itself emerges from microscopic basin parameters, requiring no independent coupling constant. The paper further demonstrates how homogeneous basin distributions generate FLRW‑like expansion, while density fluctuations naturally seed cosmological structure formation and CMB anisotropies. At high densities, the discrete nature of basins regulates curvature and prevents classical singularities, replacing them with finite, high‑connectivity phases and producing soft‑horizon behavior in compact objects. The framework also offers qualitative explanations for intermediate‑mass black hole stability windows, mass gaps, gravitational‑wave ringdown structure, and near‑horizon deviations from general relativity. Overall, this work provides a minimal, falsifiable, and observationally testable emergent‑gravity model in which spacetime curvature, inertia, and gravitational dynamics arise from the topology and energy landscape of discrete basin interactions.