MRU v13.4: World-Body with Slow Biosphere Regulation An honest report on stable orbital world-bodies with internal biospheres that do not pay for the orbit

This report documents the current main-line ontology of the MRU orbital programme: a world-body that orbits conservatively in the Yukawa / entropy field and an internal biosphere that does not consume the orbit. The v13.4 model treats biology as a slow regulator of world condition rather than as a drain on orbital kinetic energy. Across 3200-step and 8000-step runs, the bare world-body, the world-body plus passive biosphere, and all tested regulator configurations retained pass fraction 1.000, tangential fraction 0.932, L-sign consistency 1.000, and L-magnitude CV 0.000. Weak regulator couplings produced only tiny changes in structural persistence and emission scale, while leaving the orbit effectively unchanged. The honest conclusion is narrower but cleaner than earlier carrier-wide formulations: the world orbits because of the field, and life may coexist within the world and weakly regulate its long-timescale condition without paying for or steering the orbit. The reports identify a sharp stability transition at ξ/r≈5. Yukawa Geometry: Below this value, orbits fail; above it, eccentricity locks (at approx. 0.116 in v12) and orbits become permanently stable. Recovery of Kepler: This mathematically recovers Keplerian behavior as the decay length ξ approaches infinity (the long-range gravity limit). 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.