Emergent Gravity from a Discrete Coordinate Network with a Presentist Temporal Metric: A Self-Consistent Derivation

We present a self-consistent discrete model of quantum gravity where spacetime is not a fundamental continuum but emerges as an effective description of a connected weighted graph at the Planck scale. In this framework, gravity is interpreted as an emergent phenomenon arising from changes in local edge lengths and clock rates in response to the energy-matter distribution. Key results of the work include:1. An exact combinatorial derivation of the macroscopic stiffness constant k = c^4/G from the network's rigidity percolation threshold under quantum edge-state constraints.2. Elevation of the stochastic Langevin graph dynamics to a rigorous path integral using the Martin–Siggia–Rose–Janssen–de Dominicis (MSRJD) formalism, showing that the full Regge action generates the exact stationary distribution.3. Microscopic derivation of the Born rule and wavefunction superposition through environment-induced decoherence via fluctuating spatial edges.4. Derivation of the continuum Einstein field equations and Schwarzschild metric without fine-tuning or background-space dependence. The theory is ultraviolet-finite, background-independent, and preserves local Lorentz invariance in the continuum limit with Planck-suppressed quadratic corrections. Quantifiable experimental predictions are provided, including gravitational-wave echoes from stellar-mass black holes (~10^5 Hz) and cosmological decoherence-induced line broadening of light (Δλ/λ ~ 10^-10 over 1 Gpc).