A Parameter-Free Unification of Quantum Mechanics and General Relativity

Changelog — Version 2.0 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. Version 1 This work presents a parameter-free unification of quantum mechanics and general relativity based on the Planck two-measure σₚ = ℓₚ · tₚ = ħ G / c⁴ This fundamental spacetime cell links quantum fluctuations, gravitational geometry, and cosmic expansion without introducing extra fields or adjustable parameters. The formulation simultaneously:• regularizes vacuum energy through covariant Heat-Kernel averaging,• resolves classical singularities via Planck-covariant source smearing,• determines the cosmological constant as Λ = 1/ (c R t) • and connects the fine-structure constant α ≈ 1/137 to holographic microstructure. This approach unifies microphysics, gravity, and cosmology in a single informational–geometric framework, providing testable predictions for cosmic acceleration, running couplings, and galactic dynamics without dark matter.