The Geometric and Algebraic Necessity of the Critical Line x = 1/2 in the Riemann Zeta Function

The Riemann Hypothesis states that all nontrivial zeros of the Riemann Zeta
function ζ(s) have a real part equal to 1/2. This paper establishes a formal
proof of why x = 1/2 is the unique, mathematically stable axis of symmetry. I
demonstrate that any deviation from this line creates distinct, parallel input
tracks that cannot simultaneously satisfy the conditions required to yield a zero
output.