The Flip Point and the Critical Line: A Formal Argument

This paper presents a formal argument that the non-trivial zeros of the Riemann zeta function must lie on the critical line Re(s) = 1/2, derived from four mechanical principles of the Harmony of Energy: the pairing rule, positive dominance, the boundary principle, and the single flip constraint. The argument identifies zeros as physical objects — crossing events constrained to the midpoint between competing sources by the same necessity that places a planetary atmosphere at the exact midpoint between its broadcasts. A companion document develops the physical case. The formal translation of the boundary principle into a rigorous analytic constraint on ξ(s) is identified as the remaining open problem.