The Geometric Pressure Model-A Structural Persistence Framework for Physical Reality V1.1

<p dir="ltr"><b>The Geometric Pressure Model (GPM) v1.1 — A Structural Persistence Framework for Physical Reality</b><br><i>Released November 2025</i></p><p dir="ltr">Version 1.1 marks the first complete, prepared for formal review, publication of the <b>Geometric Pressure Model (GPM)</b> — a unified, falsifiable field theory that replaces spacetime curvature and probabilistic quantum frameworks with a single physical substrate: the <b>Subphotonic Radiation (SPR) field</b>.</p><p dir="ltr">In this formulation, gravity, inertia, and quantum structure arise as pressure-driven dynamics within an ultra-stiff continuum. Matter and motion are interpreted as <b>persistent oscillatory domains</b> maintained by recursive feedback between curvature and field pressure.</p><h3><b>Core Contributions</b></h3><p dir="ltr"><b>1. Field Lagrangian and Persistence Dynamics</b><br>Derives the complete nonlinear GPM field equation from a variational principle, coupling density (ρ), pressure (P), and phase (θ).<br>Causality is preserved through explicit separation of dynamic propagation (<i>c²</i>) from static stiffness (<i>U² ≈ 1.6 × 10²³ m² s⁻²</i>).</p><p dir="ltr"><b>2. Curvature Saturation and Finite Boundaries</b><br>Introduces a physically enforced minimum curvature radius</p><p dir="ltr">R_min = (2 × σ_eff) / (U² × |Δρ|) eliminating singularities and providing a natural ultraviolet cutoff for all bounded systems.</p><p dir="ltr"><b>3. Quantum–Geometric Link</b><br>Shows that the <b>511 keV</b> electron–positron annihilation energy arises directly from field constants via the Neumann boundary condition at <i>Rₘᵢₙ</i>, establishing the first quantitative bridge between curvature geometry and quantum thresholds.</p><p dir="ltr"><b>4. Empirical Validation</b></p><ul><li><b>Solar granulation:</b> predicts the 1.2 Mm pattern and 5 min oscillations from curvature–pressure equilibrium.</li><li><b>Galactic rotation curves:</b> reproduces SPARC data without dark-matter halos, using only universal constants.</li><li><b>511 keV emission:</b> models Galactic-Center variability as curvature-inversion events.</li><li><b>Lensing and redshift:</b> derives both from persistence-gradient refraction rather than metric curvature.</li></ul><p dir="ltr"><b>5. Falsifiable Predictions</b></p><ol><li>Gravitational-wave dispersion: ε(f) ≈ (c² / U²) × (f / f*)²</li><li>Perihelion-shift corrections in high-eccentricity orbits</li><li>Laboratory curvature-saturation limits in high-Q cavities</li></ol><p dir="ltr"><b>6. Conscious Coherence Index (CCI)</b><br>Extends the persistence principle to recursive systems, introducing a quantitative metric for self-referential organization across physical, biological, and cognitive scales.</p><h3><b>Summary</b></h3><p dir="ltr">The GPM v1.1 replaces geometric curvature with <b>geometric pressure</b> as the foundation of physical law.<br>It unites matter formation, quantum thresholds, and cosmic structure within a single continuum governed by measurable pressure gradients and curvature saturation.<br>All constants are independently determined; all simulations and figures are reproducible with the included Python code.</p><p dir="ltr">This version establishes a falsifiable, parameter-independent alternative to General Relativity and ΛCDM — a complete description of reality as a dynamically self-maintaining field of persistence.</p><p dir="ltr"><b>Authors:</b> Chris Peterson, Chris Turner<br><b>Length:</b> 82 pages <b>Figures:</b> 12 <b>Tables:</b> 3 <b>Python Simulations:</b> 6<br><b>License:</b> CC-BY 4.0 <b>DOI:</b> <i>https://zenodo.org/records/17501929</i><br><b>Publication Date:</b> November 2025</p>