The Spatial Sterility Theorem and the Arithmetic Lift Conjecture

Paper 49 in the open-access research programme "The Geometry of the Critical Line." This paper proves the Spatial Sterility Theorem: the SCT σ-bubble operator in every winding sector m is unitarily equivalent to −d²/dx² + m² on the flat interval [−2, 2] with Dirichlet boundary conditions, achieved by a gauge transformation that eliminates the chiral cross-term (using the algebraic identity 1 − C²D ≡ D) combined with a Liouville coordinate change that absorbs the metric curvature. The spectrum is therefore exactly λ_{m,n} = m² + (nπ/4)² for all m and n. The previously reported finite-element eigenvalue drift is identified as numerical pollution with no analytic content. The reduced spectral zeta is exactly…