Relativistic Scalar Strain Architecture: Vacuum Stress Saturation Monograph Vol. I and attribute Ravinder Singh (ORCID: 0009-0002-6532-7699).

This repository presents the official preprint, numerical codebase, and verification engine for Volume I of the Relativistic Scalar Strain (RSS) architecture operating under the Vacuum Stress Saturation (VSS) model. The RSS framework reformulates space-time as a non-linear elastic continuum characterized by a constitutive vacuum strain saturation limit. By replacing passive vacuum assumptions with geometric boundary conditions, the framework completely eliminates dark matter particles and ad-hoc dark energy fluids, deriving all observed gravitational dynamics across dwarf galaxies, spiral galaxies, galaxy clusters, and cosmological horizons directly from visible baryonic mass distributions with zero free parameters, zero halo fitting, and zero arbitrary switches. Theoretical Pillars & Mathematical Foundations Universal Critical Threshold: Derived strictly from first principles using spherical horizon geometry and fundamental SI constants: $$a_{\\text{crit}} \\equiv \\frac{c \\cdot H_0}{2\\pi} \\approx 1.0422 \\times 10^{-10}\\text{ m/s}^2$$ Master Constitutive Relation: A unified non-linear field equation governing celestial kinematics across four orders of mass magnitude: $$g_{\\text{obs}}\\left(1 - e^{-g_{\\text{obs}}/a_{\\text{crit}}}\\right) = g_{\\text{bar}}$$ Geometric Vacuum Saturation: Exact horizon boundary saturation replacing the cosmological constant ($\\Lambda$): $$\\Omega_{\\text{vac}} = 1 - \\frac{1}{\\pi} \\approx 0.6817 \\quad (68.17\\%)$$ Empirical Validation Suite Solar System Screening: Demonstrates exponential strain suppression ($\\Delta g/g < 10^{-14}$) in high-acceleration regimes ($g_{\\text{bar}} \\gg a_{\\text{crit}}$), guaranteeing strict compliance with GR and Cassini tracking precision. Galactic Kinematics: Exact scale-invariant flat rotation curve predictions ($V_{\\text{RSSV}} = (G M_{\\text{bar}} a_{\\text{crit}})^{1/4}$) validated against all 175 galaxies in the SPARC database ($N=4.000$). Cluster Hydrostatics & Lensing: Accurate hydrostatic ICM gas profiles ($N=2.000$) and conformal metric photon deflection ($N=0.500$) without invoking NFW halos or collisionless particle halos. Cosmological Closure: Direct geometric closure ($\\Omega_m + \\Omega_{\\text{vac}} \\equiv 1.0$) falling directly within Planck 2018 observational confidence limits. Included Software & Asset Registry The submission includes a zero-configuration Python execution pipeline (Run_all.py), an automated mathematical ledger writer (equations_results.txt), a 7-module automated pytest verification suite, and an interactive 3D cosmological simulation engine (section_07) with photorealistic spectral star rendering and dynamic lensing visualization.