Emergent Gravity and Orbital Mechanics from a Relational Thermodynamic Substrate Minimum Relational Universe Programme — Phases III–IV and the World-Body Line

The Minimum Relational Universe (MRU) is a computational programme testing whether a minimal relational substrate — only nodes, directed relations, local updates, energy cost, decay, and persistence — can generate gravity-like attraction and orbital mechanics without importing them as assumptions. This paper reports the complete arc of results from Phase III through the v13.4 world-body model. Phase III established emergent gravity on a sparse Barabási–Albert graph: a 1/r entropy density profile (Pearson r = 0.64–0.77), gravity-well clustering (occupation fraction 0.65–0.73), and positive selection pressure on gradient-sensing nodes (5/6 seeds). It identified the decay length ξ = √(D/λ) as the critical parameter separating long-range from short-range gravity. Phase IV advanced to a 3D Euclidean substrate with universal emission. Under strengthened diagnostics — paired baselines, isolated-source ablation, graph-density convergence testing, and a decomposed force metric — the results are: (1) 75% of local entropy gradients align toward the emission-weighted centre of mass with near-zero seed variance (range 0.04); (2) inward gradient magnitude correlates with 1/r² from the peak emitter (mean r = 0.54); (3) log-log slope excess is primarily a discrete-graph artefact (~70%), with slopes converging monotonically toward ideal values as node density increases; (4) field-on runs produce excess cluster contraction of +0.081 over paired baselines (6/6 seeds); and (5) gradient-sensing shows a paired selection uplift of +0.033 (95% CI +0.028 to +0.038). The orbital mechanics line established that the Yukawa entropy field supports indefinitely stable orbits above a sharp stability threshold at ξ/r ≈ 5. A five-test diagnostic progression identified four layered constraints on carrier-based orbital mechanics. The resolution was a structural separation: the orbit belongs to the world-body and the gravitational field; the biosphere is a passenger powered by stellar input. In the v13.4 world-body model, self-sustaining orbital world-bodies with internal biospheres achieve pass fraction 1.000, tangential fraction 0.932, L-sign consistency 1.000, and L-magnitude CV 0.000 through 8000 steps (92+ revolutions) with zero washout. A biosphere may coexist within the orbiting world and weakly regulate its long-timescale structural persistence, but it does not consume or steer the orbit. DISCLAIMER Generative AI was used to assist with [literature screening / coding support / draft language revision]. All AI-assisted outputs were independently checked by the author, and the author takes full responsibility for the final analysis and text. This is encompassing all the work that has been done and will be done. All code is under MIT licensing. All research papers are under Creative Commons License. All code, outputs and notes are included in the reproducibility bundle zip file.