Chapter 22: The Functional Equation in H_

The opening move of the Riemann Hypothesis block. The classical functional equation defines an involution J on the complex plane that exchanges s and 1-s. When we encode the T-effective zeta function in the split-complex codomain H_T = ℤ_{T}[j], this involution acquires a fixed locus—the critical line Re(s) = ½—forced by algebraic structure. The bipolar decomposition ζ_T(s) = e_+ · ζ_B(s) + e_- · ζ_C(s) respects the involution: J exchanges the two idempotent components. The classical symmetry becomes an algebraic constraint.