Spectral-Norm Backward Error for Prescribed Dominant Right Singular Subspaces: The Fixed-Vector Case and Multidirectional Obstructions

This record archives the manuscript "Spectral-Norm Backward Error for Prescribed Dominant Right Singular Subspaces: The Fixed-Vector Case and Multidirectional Obstructions" (B. M. Lindsey) together with a self-verifying reproducibility archive for its certified base instance. For a fixed real matrix A and a prescribed unit vector z, the paper studies the smallest spectral-norm perturbation E for which z becomes the strictly dominant (top, strict-gap) right singular vector of A+E, with the left singular frame left free. Unlike the classical prescribed-pair backward-error problems (Kahan-Parlett-Jiang; Sun; Wang-Wu; Chandrasekaran-Ipsen), only the right subspace is prescribed and a top-of-spectrum dominance constraint is imposed. The central phenomenon is multidirectionality: the exact backward error can strictly exceed the supremum over all single competing directions of the two-plane compression bound, so no single direction witnesses the true cost; this holds on a nonempty open set of instances. It is certified at an explicit base instance A0=diag(5,4,1), z0=(1,1,3)/sqrt(11) by an exact-rational strictly-feasible semidefinite dual (positive-definiteness proved over Q) giving gamma >= 1.923057, paired with an outward-rounded interval upper bound Delta2 <= 1.829974, hence a certified strict separation >= 0.093. The load-bearing results are proved analytically; the archive's computations are the certificate reproduction (exact-rational + interval, self-verifying). This is the extended program paper of the FG-1 A->B->C singular-subspace/Grassmannian line. The manuscript contains an AI-use disclosure in accordance with the venue's policy.