The Non-Existence of Absolute Physical Constants: A Rigorous Informational-Oscillatory Framework

We establish through rigorous mathematical proof that no physical constant can be ‘absolute’ in the sense of being simultaneously determinable with infinite precision, independent of measurement scale, and independent of cosmological epoch. Our framework rests on three pillars: (i) information-theoretic bounds (Bekenstein-Holographic principle), (ii) renormalization group analysis, and (iii) functional analysis of oscillatory operators on Sobolev spaces. We introduce the Dynamic Zero Operator (DZO)—a rigorously defined linear operator on H²(ℝ) with oscillatory kernel—and prove that: (a) Borwein π-algorithms converge to DZO fixed points, (b) Riemann zeta zeroes are DZO eigenvalues for specific kernel choice, (c) the geometric constant π is not absolute but emerges as scale-dependent projection π_eff(Λ, R). This establishes a profound trinity: Borwein algorithms ↔ DZO spectral theory ↔ ζ(s) zeroes, unified by modular symmetry and phase cancellation. We provide: (1) complete proof that ΛCDM parameters (H₀, Λ) cannot be fundamental constants, (2) numerical example demonstrating π_eff(Λ) dependence, (3) testable predictions linking Borwein convergence to GUE statistics. This falsifies ΛCDM as currently formulated and provides foundation for scale-dependent effective cosmology.