III.T19 — Critical Line Theorem

CONDITIONAL on III.T18 (O3): self-adjointness of H_L (III.T17) forces all eigenvalues real, which via the spectral correspondence (III.T18) forces all non-trivial zeros of ζ_τ to lie on Re(s) = ½. The K5 off-diagonal exclusion is the mechanism: off-critical-line zeros would require imaginary spectral coupling, which K5 forbids.