On the Second-Order Orbital Structure of Riemann's Ξ-Function and a Proof of the Riemann Hypothesis

We introduce a second-order orbital framework based on the symmetry group Z₂ of Riemann's Ξ-function. Non-trivial zeros are classified into self-dual orbits (on the critical line) and mutually-dual orbits (off-critical symmetric pairs). We prove that the conditionally convergent sum of Hadamard exponential factors, when decomposed by orbits, yields a global constraint that forces all off-critical orbits to vanish. Hence all non-trivial zeros lie on the critical line.