A Parameter-Free Unification of Quantum Mechanics and General Relativity

Big update today Changelog — Version 2.0 (Extended) This version refines the original formulation of the parameter-free unification of quantum mechanics and general relativity based on the Planck two-measure: σ_P = ℓ_P · t_P = ħ G / c⁴. The effective cosmological term has been normalized using the Friedmann equation: Λ_eff = 3 / (c R t), which refines — but does not alter — the original structure Λ ∝ 1 / (c R t).This normalization step is analogous to fixing a coupling constant through a boundary condition, not to introducing any free parameter. The formulation simultaneously:• regularizes vacuum energy through covariant heat-kernel averaging,• resolves classical singularities via Planck-covariant source smearing,• determines the cosmological constant geometrically,• and connects the fine-structure constant α ≈ 1/137 to holographic microstructure. This framework unifies quantum theory, gravitation, and cosmology in a single informational-geometric structure and yields parameter-free predictions for cosmic acceleration, large-scale structure, and galactic dynamics. New in this version — Simulations and Physical Tests (Appendices):• Appendix A — Cosmological tests: Supernovae Ia (Pantheon+), BAO (BOSS/eBOSS/SDSS), CMB acoustic scale, linear structure growth fσ₈, weak-lensing convergence spectra C_ℓ^κ, and the micro–macro invariant δ. All tests show O(1%) agreement with ΛCDM at the background level, without introducing fit parameters. • Appendix B — Regularized black holes: Numerical solutions of spherically symmetric collapse with σ_P–regulated cores remove the classical singularity and replace it with a finite curvature spike at r ≈ ℓ_P. The event horizon remains unaffected, while the interior geometry becomes smooth and causal. • Appendix C — Primordial black holes and Hawking evaporation: Hawking temperature and evaporation dynamics were simulated for regularized Planck-scale cores embedded in a Λ_eff background. The result: the horizon temperature remains essentially classical, but the late-time evaporation phase acquires a finite-core spectral imprint. The information content is stored and released unitarily through the Planck core, offering a resolution of the Hawking information paradox without introducing new fields.