Orig-Final N-FIELD Phenomenological Vacuum Energy Regularization for Nanoscale Quantum Experiments

The Author presents a vacuum energy regularization framework using a smooth multiplicative UV regulator with methods to address ultraviolet divergences in quantum field theory. This work introduces a previously undisclosed functional form Nref (T, E) =k/ (T/T0) m+ (E/EP) nNₑ₄₅ (T, E) = k/ (T/T₀) ᵐ + (E/EP) ⁿ (T, E) =k/ (T/T0) m+ (E/EP) n where parameters (k, m, nk, m, nk, m, n) are mathematically constrained by the regulator structure rather than freely fitted. The framework yields a finite vacuum energy density ρvac=ℏc123 πH−2ₕ₀₂ = c123\, H^-2ρvac=123πℏcH−2 and makes concrete predictions for: Casimir force deviations at sub-10 nm separations (power-law corrections) Bell test correlations via detector inefficiencies (S=22 η2S = 22\, ²S=22η2) All results are derived from standard real-analysis, respect quantum-mechanical bounds, and make no claims of solving the cosmological constant problem or introducing new physics.