Deterministic black-box noncommutative singularity testing for rational linear matrices (Garg-Gurvits-Oliveira-Wigderson question)

Claims a deterministic polynomial-time, polynomial-size list of rational matrix tuples on which every noncommutatively nonsingular rational affine pencil of bounded order becomes invertible, and a list recovering the noncommutative rank of rectangular rational pencils from ordinary ranks. It does NOT treat pencils with coefficients from other fields; the GGOW question for general fields remains.

Claims a deterministic polynomial-time, polynomial-size list of rational matrix tuples on which every noncommutatively nonsingular rational affine pencil of bounded order becomes invertible, and a list recovering the noncommutative rank of rectangular rational pencils from ordinary ranks. It does NOT treat pencils with coefficients from other fields; the GGOW question for general fields remains.