The Square-Root Symmetry: A Structural Framework for the Riemann Zeta Function

We formalize a structural perspective on the Riemann zeta function, highlighting a natural balance between the "inside" (integer counting) and "outside" (density/reflection) perspectives of the number system. Using divisor pairings, information measures, and the functional equation, we show that s = 1/2 is a unique symmetry axis where information is balanced. While this framework does not prove the Riemann Hypothesis, it provides rigorous structural context explaining why the critical line is distinguished and suggests constraints that might govern the location of zeros. We position this work as establishing formal groundwork for future approaches, particularly those drawing on spectral theory, information theory, or geometric constraints