Entropic Hysteresis of Spacetime: A Quantum Gravity Framework for Dark Matter and Dark Energy

We propose that both dark matter–like phenomena (galaxy rotation curves, cluster lensing) and dark energy–like acceleration (cosmic expansion) arise from a single, irreversible entropic mechanism. Our framework integrates: Verlinde’s Entropic Gravity and SEAT (Scaling Entropy-Area Thermodynamics): Interpreting gravitational attraction as a manifestation of entropy gradients on holographic boundaries. Irreversibility (Hysteresis) of Spacetime: Large-scale rearrangements in matter trigger a pinned scalar field SSS, leaving residual stress-energy that mimics dark matter halos and stable vacuum-like energy. Loop Quantum Gravity (LQG) Spin-Foam Barriers: Discrete spin-network states create combinatorial energy barriers, preventing the reversion of pinned states and ensuring hysteresis. We provide: A detailed mathematical account of Verlinde’s entropic force derivation and the SEAT framework. An expanded partial EPRL-FK spin-foam summation on a larger 40^3 lattice. A comprehensive HPC PDE code demonstration coupling entropic partial flips with a gravitational Poisson solver in a 256^3 domain. A robust rotation-curve fit to multiple SPARC data galaxies, including NGC 2403. A refined numerical argument for vacuum-energy fine-tuning, presenting a spin-foam degeneracy function g(ρvac)g(\rho_{\mathrm{vac}})g(ρvac). An exploration of the implications on fundamental cosmological issues, including the Hubble tension. We conclude by outlining how large-scale HPC cosmic runs, exhaustive spin-foam amplitude calculations, and full multi-galaxy or supernova MCMC fits can further validate or refute this irreversible entropic interpretation of the dark sector. Keywords: Entropic Gravity, SEAT, Dark Matter, Dark Energy, Loop Quantum Gravity, Spin-Foam, Hysteresis, HPC PDE Simulations, Vacuum Fine-Tuning, Hubble Tension, Cosmology, Observational Data, SPARC, EPRL-FK