Paper XIII: The Tautology of Symmetry: A Mathematical, Physical, and Numerical Refutation of Off-Critical Zeros in the Riemann Hypothesis

The Riemann Hypothesis asserts that all non-trivial zeros of the Zeta function lie on the critical line Re(s) = 0.5. A central defense of the hypothesis in modern mathematics is that the Functional Equation (the symmetry condition) permits deviations, meaning a zero at Re(s) = 0.4 could be mirrored by a zero at Re(s) = 0.6. This paper demonstrates, through rigorous mathematical analysis, physical interpretation, and 10,000-point numerical simulation, that this defense is a logical and physical fallacy. We prove that the symmetry condition, when interpreted as a boundary constraint on a standing wave (as required by the Hilbert-Pólya framework), strictly forbids off-critical zeros. The Functional Equation is shown to be a tautological mirror—it reflects relationships, not existence. Three independent C-language simulations verify that zero magnitude is achieved exclusively at the critical line, and that any deviation produces a persistent non-zero oscillation. We conclude that the Riemann Hypothesis requires no new proof; it requires a correct physical interpretation.