Gravity and Thermodynamics from Pruning: Newton's Law, Keplerian Orbits, and the Unruh Temperature from SR Causal Flux Conservation

We demonstrate that two foundational results of gravitational physics — Newton’s inversesquare force law and the Unruh temperature — emerge from a single principle of the Stochastic Rupture (SR) relational framework: conservation of causal pruning flux. For the gravitational sector, the pruning rate Γ = γ0/(1−χeff) near a point mass produces a radial gradient −dΓ/dr = γ0rs/r2 by elementary calculus. Numerical simulation on a 300 × 300 grid recovers F ∝ r −2.001 (< 0.05% error*), and leapfrog integration yields stable Keplerian circular orbits with δr/r < 0.1% over 27 complete revolutions. For the thermal sector, the linearized entropy transport equation is extended to the Cattaneo (telegrapher) equation, whose hyperbolic limit gives a wave equation with effective speed veff = √ηκ. Setting veff = c recovers the SR constraint c 2 = ηκ. The resulting causal cone structure, combined with standard mode decomposition for an accelerating observer, yields the Unruh temperature TU = ℏa/(2πckB) via the Bogoliubov coefficient |βΩω| 2 = (e 2πΩ/a − 1)−1 . All code is provided for reproducibility. No parameters were adjusted to obtain any of these results. *The force law exponent -2.001 reported in the simulations is a finite-difference artifact (grid spacing dx = 0.04, error O(dx^2) ~ 0.002). The analytical result F = gamma0 * r_s / r^2 is exact by elementary calculus; no approximation is involved. Higher grid resolution converges to -2.0000.