Multi-Scale Validation of the Ratioat-Octonionic Entropy Law: Convergence with Gravitational-Wave Astronomy, Relativistic Tests, and Astrophysical Imaging

This work presents the Ratioat–Octonionic Emergence Framework, an independently developed mathematical theory whose axioms include a discrete scaling constant α=7/11\alpha = 7/11α=7/11, an octonionic structural backbone, and a codified set of 61 Universal Laws of Emergence. The central axiom, the Ratioat–Octonionic Entropy Law, reduces in the black-hole limit to the Bekenstein–Hawking entropy formula, thereby recovering Hawking’s area theorem. The framework is tested across nine empirical domains: Binary black-hole mergers (horizon areas, LIGO/Virgo) Inspiral chirp mass consistency Ringdown spectroscopy Binary neutron star tidal deformability (GW170817) Hulse–Taylor pulsar orbital decay Event Horizon Telescope shadow diameter (M87*) Relativistic redshift of S2 near Sgr A* Cassini Shapiro delay Gravity Probe B geodetic and frame-dragging precession Across all cases, the framework reproduces precision results in the GR limit while offering falsifiable departures tied to the universal scaling constant α=7/11\alpha = 7/11α=7/11. The paper includes appendices listing all 61 Universal Laws, a worked example for GW150914, and a policy impact letter situating the framework as a resource for physicists, engineers, mathematicians, and educators. Licensing: Open educational and research use is permitted under CC BY 4.0 (with attribution). Commercial applications require a separate license from the author. This release is intended both as a rigorous validation of the Ratioat–Octonionic Entropy Law against historical gravitational data, and as a public resource for advancing multi-disciplinary innovation.