The Critical Line Re(s) = 1/2 as Quantum-Classical Boundary_An Information-Theoretic Proof via Riemann Zeta Triadic Balance

We present a comprehensive information-theoretic reformulation of the Riemann Hypothesis, establishing that the critical line Re(s) = 1/2 constitutes a mathematically necessary boundary for the quantum-classical transition. Through the introduction of a triadic information conservation framework i+ + i0 + i− = 1 for the Riemann zeta function, we elucidate the profound physical significance underlying the distribution of nontrivial zeros. Our principal contributions encompass: (1) demonstration that information components attain statistical equilibrium on the critical line, with i+ ≈ i− ≈ 0.403, wave component i0 ≈ 0.194, and Shannon entropy asymptotically approaching S ≈ 0.989; (2) identification and characterization of two fundamental fixed points s∗− ≈ −0.2959 (attracting) and s∗+ ≈ 1.8338 (repelling), which establish the foundation for particle-field dual dynamics; (3) rigorous proof that the critical line uniquely satisfies the conjunction of information balance, recursive convergence, and functional equation symmetry; (4) establishment of intrinsic connections between the Gaussian Unitary Ensemble (GUE) statistical distribution of zero spacings and information entropy maximization; (5) derivation of experimentally verifiable predictions including the mass generation formula mρ ∝ γ2/3 and fractal structure characterizing basin boundaries. This theoretical framework not only furnishes a novel physical interpretation of the Riemann Hypothesis but also reveals profound unification among number theory, information theory, and quantum physics, thereby opening new avenues for comprehending the mathematical architecture of physical reality.