Emergent Gravity from Entropy Gradients: A Relational–Thermodynamic Hypothesis Minimum Relational Universe Programme — Phases III & IV

The goal of the Minimum Relational Universe programme has been to start with almost nothing — only nodes, directed relations, local update rules, energy cost, decay, and persistence — and ask whether meaningful structure can emerge without being predefined. Phases I and II showed that the answer is a qualified yes: the model earned stable persistence, ordered dependency, playhead-like traversal, sustained traversal ecologies, lineage replication, proto-regulation, and early anticipatory behaviour. One question nonetheless remained open after Version 8: how does ecology-level forecasting become a clean local predictive advantage? This paper proposes and tests a physical answer. The central hypothesis is that gravity-like attraction is not fundamental in the substrate but emerges from entropy gradients generated by persistent low-entropy structures. In that picture, movement down an entropy gradient is thermodynamically favourable, and the local survival advantage of gradient-following can be measured directly. The paper proceeds in two phases. Phase III (Sections 3–4) develops the theoretical framework, maps simulation parameters to physical quantities, and reports the first positive results on a sparse graph substrate. Phase IV (Section 5) upgrades to a 3D Euclidean substrate, removes designated mass nodes, and adds stronger diagnostics: paired baselines, isolated-source ablation, graph-density convergence testing, and a decomposed force metric that separates directional alignment from distance-scaling claims. Section 6 then extends the programme to a preliminary orbital analysis. The resulting picture is deliberately narrower than the strongest earlier versions of the claim: the present evidence supports emergent attractive dynamics in the toy substrate, while the bridge to quantitative physical gravity remains open. 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.