Obstructions and Necessary Conditions for the Arithmetic Lift

Research Note 50 in the "Geometry of the Critical Line" programme. This note identifies what any successful arithmetic packaging functional cannot be and what structural features it must possess, following the rigidity and open packaging problem established in Paper 50. Three no-go results are proved. First, on the Gaussian heat family, no functional acting purely on the angular/Hecke sector can yield the Weil distribution; the σ-sector must participate (factorization obstruction). Second, no spectral diagonal lift can produce the Weil prime term (diagonal no-go). Third, the ordering τ_{1/2} ∘ D ∘ E is impossible for any derivation vanishing on the fixed-point subalgebra (post-expectation derivation vanishes).…