Orbital Stability Transition in a Yukawa Entropy Field An ongoing experimental note for the Minimum Relational Universe programme

This note reports a clean Branch A result for the Minimum Relational Universe (MRU) orbital programme. Using an analytic softened Yukawa entropy field, a zero-noise tracer-particle setup, a Verlet integrator, and a short formation perturber, the scan shows that orbital behaviour is governed primarily by the dimensionless ratio ξ/r, the field decay length relative to orbital radius. The outcome is not a gradual loss of orbital quality but a sharp practical transition: below ξ/r ≈ 5, orbits destabilise in a substantial fraction of runs; above roughly ξ/r ≈ 7, no tracer exceeds the eccentricity threshold within the tested horizons. In the stable regime, the local orbital eccentricity settles near 0.19 and the growth rate of eccentricity is effectively zero, indicating long-lived precessing Yukawa orbits rather than secular degradation. The result materially changes the earlier diagnosis of the MRU orbital programme. It supports the claim that the field itself can sustain orbit-like motion, while leaving the full carrier layer as the remaining bottleneck. The paper therefore presents a strong, publishable narrow result: a falsifiable orbital-stability boundary in ξ/r for the Yukawa entropy field, together with a clear statement of what has and has not yet been established. 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.