Scalar Perturbation Obstruction in Saturating Bounce Cosmology: Frobenius Analysis, Five-Route Completion Audit, and Parameter Triangle

This preprint studies scalar perturbations in a minimal saturating bounce cosmology with effective Friedmann dynamics of the form: H² = (8π/3)ρeff(1 − ρeff/ρsat). The tensor sector remains regular through the bounce, while the scalar sector exhibits a structural obstruction associated with divergence of the Mukhanov–Sasaki pump field at H = 0. The paper presents:- a Frobenius analysis of the scalar perturbation equation,- a class-level symplectic obstruction theorem for single-field effective bounces,- a five-route completion audit,- and a post-bounce parameter-triangle analysis. The work explicitly does not claim a complete trans-bounce scalar perturbation theory or a UV-complete theory of quantum gravity.