Part 3 of 10 - Unified Spacetime Theory’s “The Mechanical Foundations of a Unified Spacetime” -NEW Version 12.50 (replaces V11.55)- AbstractWithin Unified Spacetime Theory (UST), this paper gives a self-contained, mechanical account of spin-one-half. The derivation uses only the dynamics of a single continuous medium—no spinors, no representation theory, no quantum postulates—and shows how a stable, helical mode in that medium carries the spin-½ magnitude. The logic is minimal: a robust energy split, a kinematic link between rotation rate and stored energy, and a careful transport from the saturated mode to its gentle, linear limit. Taken together, those pieces pin down the spin value without importing extra structure. Relationship to the Foundations PaperThis work is built on the UST “Foundations” paper, which sets the core framework (the medium, its moduli and density, the light-cone speed as a material property, and the USEMP constitutive principle). Readers new to UST should treat the present spin-½ paper as a focused application within that framework. Scope fences that defer holonomy/statistics and other background structure point to the Foundations companion for details.Citation: Unified Spacetime Theory Foundations: The Mechanical Origins of Spacetime - Unifying Forces and Deriving Lorentz Symmetry (v4.10), doi: 10.5281/zenodo.17795775. What This Paper Does States the assumptions and scope up front and keeps to them. Builds the time-evolution system from first principles and identifies the conserved quantities it implies. Derives the spin-½ magnitude for the helical ground state and shows how the result persists when transported to the linear regime. Presents a conservative, background-gradient force that falls straight out of the same mechanics and invites analogue-tabletop testing. Documents a full verification pipeline (meshes, refinements, acceptance gates, and an error budget) so others can audit or reproduce the calculations. Why This MattersThe usual story of spin-½ leans on abstract algebra. Here it emerges from a concrete mechanical model with a single universal signal speed (the medium’s light-cone speed). In calm, uniform conditions the familiar kinematics reappear; away from that limit the model stays within measurable, material-like quantities. The result is a transparent route to a core quantum feature from everyday mechanics. Scope and Future WorkThe immediate next release in this series is the Black Holes and Quantum Gravity paper, developing a singularity-free core and a mechanical emission mechanism within the same framework. Following that, focused companions are planned on Dark Mass (scalar bulk solitons), the Strong Force, and the History of the Universe. Each will keep to the same discipline: no added fields, no ad-hoc rules, and results that are testable and reproducible. ReproducibilityA reference solver, data checks, and audit artifacts are provided so that an independent reader can retrace every step with stated tolerances. Unit mapping to SI is kept separate from the dynamics for clarity. Coming NextThe series “The Mechanical Foundations of a Unified Spacetime” is organized as a ten-paper sequence, all built on the same mechanical medium developed here. Following Foundations, Lorentz Invariance, and Spin-1/2, the subsequent papers are:4. Black Holes and Quantum Gravity: The Mechanical Origin of Hawking Radiation5. Dark Mass: Scalar Solitons in Unified Spacetime Theory6. History of the Universe7. The Strong Force8. The Weak Force9. Emergence of Quantum Dynamics10. The Particle Zoo: Deriving the Mass Spectrum Together they extend the same underlying medium to all sectors of physics, always with the goal of giving a minimal, reproducible, and testable mechanical account of observation rather than stitching together separate theories. Foundations Paperhttps://doi.org/10.5281/zenodo.17887509 Black Hole and Quantum Gravity Paperhttps://doi.org/10.5281/zenodo.17804079 Dark Mass paper: https://doi.org/10.5281/zenodo.18474582 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 Mechanical Strong Force in Unified Spacetime Theory: Flux Tubes and Confinement from Torsional Saturation https://doi.org/10.5281/zenodo.18602945 Contactjared@ustphysics.org