UST Core Mechanics: Numerical Validation of Light‑Speed, Hydrostatics, Gravity, and Dispersion

This file contains the full numerical verification script for Unified Substrate Theory (UST). It runs in SageMath and outputs hard numerical values confirming each core UST constraint without relying on symbolic algebra. The script verifies: the substrate sound‑speed/light‑speed equivalence the corrected hydrostatic density profile and its asymptotic restoration the Newtonian limit of the substrate potential the longitudinal and transverse wave dispersion relations, including viscous damping All calculations are performed using fixed numerical constants, and the script prints the resulting values directly. This provides a clear, reproducible numerical check showing that UST’s baseline equations behave exactly as expected: the substrate wave‑speed matches light‑speed, the density profile compresses correctly in a gravitational well, the potential reduces to −G·M/r, and the wave modes propagate and damp with the correct magnitudes. This file is intended as a simple, transparent numerical validation of the foundational UST mechanics. This work is part of a larger collection of UST documents. The other versions available in the DOI record are not revisions of this document. They are separate papers written for different purposes. Some versions present the full mathematical proofs behind the update rules, others provide a technical physical description of substrate behavior, and others are formal proof papers built around the Universal Balance Laws. Together, these documents form a complete set: a plain‑language booklet, a physical description paper, and full mathematical proof papers, each offering a different perspective on the same underlying theory. If you have questions or want to discuss the work, you can contact me directly at dustin@unifiedsubstratetheory.com Don't be shy. I want to discuss science. It is fun and should be. Reachout and lets get started on new discoveries.