Information Restoration, Entropic Barriers, and the Critical Threshold 2/3: A Unified Dynamical Framework for the Riemann Zeta Zeros

We present a unified dynamical framework for the nontrivial zeros of the Riemann zeta function, integrating three perspectives: (i) the de Bruijn–Newman flow and its reduction to a logarithmic Coulomb gas, (ii) a renormalization group information flow from the 2C Theory, and (iii) spectral compression in 2D Dirac systems under strong magnetic fields. Through an iterative discovery process — connecting existing knowledge, identifying new principles at the intersection, then connecting those principles with prior knowledge to discover deeper ones — we identify three structural contributions: (1) The Disorder–Order Paradox: the irregularity of the prime distribution generates the information restoring force (curvature V''(1/2) = π²/8) that confines zeros to the critical line Re(s) = 1/2. (2) The Universal Irreversibility Threshold: the critical value C = 2/3, independently derived in D.S. Theory (holographic ratio β = 3/2), the 2C Theory (RG flow fixed point), and Lowest Landau Level physics (spectral weight threshold for forced Landauer erasure), marks the point at which one-dimensional spectral reduction becomes irreversible. (3) The Entropic Barrier: the information free energy V(σ) possesses a barrier surrounding σ = 1/2 whose height grows with integrated prime density, forbidding zero escape once the critical threshold is exceeded. We formulate one precisely stated open problem: proving that the entropic barrier height diverges as T → ∞, which is equivalent to establishing an L² + entropy → L∞ inequality for the equilibrium measure of the logarithmic gas. The framework connects analytic number theory, information theory, renormalization group methods, and condensed matter physics within a single coherent structure. This paper is a structural framework proposal, not a proof of the Riemann Hypothesis. The iterative discovery methodology is inspired by the WillCore simulation platform.