Pt-5 of 10 - V4.93 Dark Mass as Bulk Compression: Scalar Solitons in Unified Spacetime Theory

Part 5 of 10 - Unified Spacetime Theory’s “The Mechanical Foundations of a Unified Spacetime” Reason for new version: V4.93 is a symbol-hygiene and scope-clarity update to eliminate an ambiguity around the symbol α. In the prior version, α appeared in two unrelated roles: it was (i) listed in the front-matter “vault constants” set and (ii) used in Appendix D as the conventional light-bending (deflection) angle α(b). That overlap could be misread as introducing an extra UST constant or a tunable knob, even though Appendix D’s α(b) is strictly an observable/diagnostic angle. In V4.93, α was removed from the paper’s vault-constant list, and the Appendix D bending-angle notation was renamed to - Δθ(b) - with a brief notation lock clarifying it is an observable deflection angle, not a UST constant. No physics claims, derivations, numerical results, or conclusions were changed - only notation and front-matter bookkeeping were corrected to preserve the vault-lock discipline and prevent cross-paper symbol collisions. V4.93 Dark Mass as Bulk Compression: Scalar Solitons in Unified Spacetime Theory Abstract Unified Spacetime Theory treats the vacuum as a real physical medium whose internal mechanical states can store energy and influence gravity-like behavior. In this view, what is usually called dark matter is not a new particle or hidden force. It is a stable, long-lived form of vacuum compression: a localized “squeeze” state that carries mass-energy but does not interact with light in the way ordinary matter does. Because the vacuum does not support freely propagating compression radiation, these compressed regions cannot easily shed energy and collapse into thin rotating disks. Instead, they naturally persist as extended, diffuse halos that provide the gravitational scaffolding around galaxies. This paper develops the bulk-compression branch of the theory and shows how such halos arise as finite-energy, stable configurations. The same nonlinear saturation mechanism that stabilizes the compressed core also enforces a universal upper limit on the central density, producing flat inner profiles consistent with observed galaxy cores. Finally, the work connects halo structure to both galaxy rotation patterns and gravitational lensing through a single, unified physical mechanism, and it derives a clear, testable scaling relation linking core size to total halo mass. Coming Next: This is Part 5 of the series “The Mechanical Foundations of a Unified Spacetime.” Following the Foundations (1), Lorentz Invariance (2), Spin-1/2 (3), and Black Holes (4); the next papers following this Dark Mass paper, in order, are The Mechanical History of the Universe (6), The Strong Force (7), The Weak Force (8), Emergence of Quantum Dynamics (9), and finally The Particle Zoo (10). Together they extend the same underlying medium to cosmology, the strong and weak interactions, and the full particle spectrum, always with the goal of giving a minimal, reproducible, and testable mechanical account of observed physics. Foundations paper - Hooke's Law/USEMP and Lorentz Invariance papers:https://doi.org/10.5281/zenodo.17887509 Spin 1/2 paper https://doi.org/10.5281/zenodo.17795865 Black Hole and Quantum Gravity paperhttps://doi.org/10.5281/zenodo.17804079 Mechanical History of the Universe https://doi.org/10.5281/zenodo.18102268 Cosmological Redshift from Homogeneous Dilation in Unified Spacetime Theory (companion paper for History paper) https://doi.org/10.5281/zenodo.18174406 Contact: jared@ustphysics.org