Thermodynamic Gravity and the Entropic Suppression of Cosmic Structure: A Holographic Resolution to the S8 Tension

🔵 THEORETICAL FRAMEWORK: The Holographic Capacitor instead, the entropic discharge targets the mass of the dark sector, sublimating Dark Matter to solve S₈. Q: Does Mass Fading mean Dark Matter is annihilating into photons? A: No. The particle number density (n) is strictly conserved in the comoving volume. The decay targets the rest mass (m) of the individual particles via a dynamically evolving Yukawa-like coupling to the background scalar field. The mass sublimates directly into the vacuum, conserving total energy between the dark sectors without producing a blinding gamma-ray signature. Q: Does this model predict a Big Rip? A: No, it predicts a Conformal Crossover. Because the framework is driven by the sublimation of mass (ṁ/m < 0), the universe does not rip apart. As t, the mass of the dark sector approaches strictly zero. This sets the stage for the universe to become entirely scale-free, satisfying the absolute boundary conditions required for Penrose's Conformal Cyclic Cosmology (CCC). Q: How was the screening law discovered? A: The core interaction was identified via blind Symbolic Regression (AI). We provided the AI with basic operators and data (Star Formation Rate, ₘ) and it independently rejected standard linear models, converging on the sharp transition and inverse-density relationship as the optimal mathematical solutions. This manuscript provides the formal derivation of that AI-discovered law from first principles. ⚠️ VERSION HISTORY / UPDATE LOG v3. 0 (The "Holographic Capacitor" Update) - Feb 2026: THEORETICAL CORRECTION: Completely updated the mechanism to align with the rigid "Geometric Stiffness" proven in the v118 MCMC runs (Paper I). The "Phantom Shredder" hypothesis has been officially retracted. NARRATIVE SHIFT: Dark energy is now mathematically formulated as the delayed discharge of the Holographic Capacitor, resolving the Coincidence Problem. Added rigorous derivations for the Mass Fading isomorphism and the Entropic Boost Factor. AI VALIDATION: Retained AI Symbolic Regression scripts (Placebo & Noise tests) confirming the density screening function. LICENSING: Source code remains strictly licensed for Academic Use Only. v2. 0 (The "Strong Phantom" Update) - Dec 21, 2025: Attempted to explain a deep phantom excursion (w -1. 5). Falsified by broader likelihood penalties in Paper I stress testing. v1. 0 (Superseded): Initial upload of the preliminary "Reciprocal Vacuum" framework. 3. Keywords: Thermodynamic Gravity, Holographic Capacitor, Coincidence Problem, Mass Fading, S8 Tension, Conformal Cyclic Cosmology, Symbolic Regression, AI in Physics 4. Version: 3. 0 5. Related Identifiers: Relation: Cites / Is Supplemented By Identifier: 10. 5281/zenodo. 18689530 (Paper 1)