The Geometry of the Critical Line: Further Developments (Papers 9–10)

Papers 9 and 10 in The Geometry of the Critical Line programme. This record contains two further papers in the programme, completing the analytic and geometric bridge between the cover equation and the SCT 5-manifold. Paper 9: The Analytic Vortex and the Lambert Spectrum promotes the cover equation Φ + exp(iπ − 1/Φ) = 0 from a discrete root condition to a continuous complex function C(z) = z − exp(−1/z). Its antiderivative contains the Exponential Integral Ei(−1/z), introducing an essential singularity at z = 0. Picard's Great Theorem formalises the "Left Modality" (phase collapse) as a theorem-level analytic obstruction. The scaled constraint Cα(z) = z − exp(−α/z) yields a countable Lambert spectrum zₖ(α) =…