Paper D: Calibration of Holosphere Thermodynamics Fixing Constants from Vacancy–Defect Dynamics

This paper completes the calibration of Holosphere thermodynamics by fixing three constants that govern its surface first law: the entropy–area coefficient η, the reduced coherence temperature Θ_coh, and the vacancy strain energy ε₀. Building on Papers A–C, which established the vacancy law, the flux–drift decomposition, and the surface first law, we determine these constants through a combination of geometric reasoning, statistical fluctuation analysis, and phenomenological anchoring to quantum electrodynamics. The entropy–area coefficient η is fixed at 1/4 by comparison to the Bekenstein–Hawking entropy bound, demonstrating a holographic correspondence between Holosphere vacancies and black hole thermodynamics. The reduced coherence temperature Θ_coh is defined by the variance of intra–shell defect drift and validated through numerical simulations, linking Holosphere dynamics to effective temperatures in non-equilibrium systems. The vacancy strain energy ε₀ is calibrated phenomenologically using the anomalous magnetic moment of the electron, providing a bridge between Holosphere energetics and QED. While ε₀ remains the most fragile element of the calibration, we outline in Appendix B a recursive renormalization hypothesis that could naturally bridge Planck and QED scales. Together, these results close the A–D foundational sequence and establish a parameter-free Holosphere thermodynamic framework, preparing the ground for applications in emergent gravity, fluid dynamics, and recursive scaling in future work.