The Chiral Functional Equation

Research Note 36 in the "Geometry of the Critical Line" programme. The pre-gauge eigenvalue equation on the SCT sigma-bubble has real coefficients except for the chiral coupling terms imA(δ)ψ' and imB(δ)ψ, which are purely imaginary and linear in the winding number m. Under m → −m, these terms conjugate, making the (−m)-equation the exact complex conjugate of the (+m)-equation. This immediately implies that the full connection matrix conjugates entry-by-entry: M(−m,λ) = M̄(+m,λ). In particular, M₂₁(−m,λ) = M̄₂₁(+m,λ), mirroring the Riemann functional equation's action as complex conjugation on the critical line. The proof is a single exact symmetry of the differential equation — it requires no Kummer parameter matching, no Gamma-function identities, and no asymptotic approximations.