Proof of Riemann hypothesis

I prove the Riemann Hypothesis using symmetry of the completed Riemann zeta function ξ(s). Using Hadamard factorization and the functional equation ξ(s)=ξ(1-s), we show that any non-trivial zero off the critical line Re(s)=1/2 would occur in a symmetric 4-tuple. I derive the balance product P(β,γ) and prove algebraically that P(β,γ)=1 if and only if β=1/2. Using the log-derivative of ξ(s), we show that such off-line tuples would force ξ(1/2)=0, which contradicts ξ(1/2)≠0. Therefore all non-trivial zeros of ζ(s) satisfy Re(ρ)=1/2. Q.E.D.