Establishment of Static Gravity through the Extension of the Minimal Length

Establishment of Static Gravity through the Extension of the Minimal Length This paper investigates how a static gravitational potential can emerge from the existence of a fundamental minimal length. When physical states evolve through discrete updates constrained by the minimal length, the spatial structure itself acquires a non‑continuous character. By extending this discrete structure to spatial configurations, the study derives a source‑based Poisson equation that governs the static gravitational potential. The analysis shows that the minimal‑length framework naturally leads to a 1/r potential when the internal density scales as 1/r2. This result is fully consistent with the Newtonian limit of general relativity, demonstrating that static gravity can be reconstructed without assuming a pre‑existing geometric spacetime. The work provides a conservative and coherent approach in which static gravitational behavior arises from the intrinsic structure of discrete spatial updates, offering a source‑based interpretation of gravity that precedes the geometric formulation of general relativity.