This paper proposes and validates a ”relation-first” physical framework in whichgravity is not a fundamental interaction but an emergent phenomenon of relationalstructure in the low-energy limit. We construct a discrete system model based onrelational matrix evolution and find through numerical simulations that the systemnaturally emerges with a power-law gravitational potential function φ(r) ∝ r−0.813(R2 = 0.684), stably deviating from the classical Newtonian gravitational potential(φ ∝ r−1) by approximately 18.7%. Further analysis suggests that this exponentmay correspond to an effective spatial dimension D ≈ 2.813 or some quantumgravity correction. We also find that the traditional concept of ”force” fails in therelational framework and propose redefining ”force” as the gradient of relationaldensity. We provide complete numerical implementations and systematic analyses,offering new numerical evidence and computational frameworks for modified gravitytheory and quantum gravity research.Keywords: relational physics, emergent gravity, modified gravity, numericalsimulation, power-law potential, quantum gravity, higher-dimensional space