Polynomial-size black-box identity testing for noncommutative rational formulas

Claims deterministic polynomial-time construction of polynomial-size rational matrix hitting lists for noncommutative rational formulas over $\mathbb Q$, with no bound on inverse nesting or constant heights, each nonzero formula receiving an invertible value. Companions: one rational tuple of dimension at most $2ns^2$ hits every nonzero division-free formula over every characteristic-zero field, and an analogous tuple over $\mathbb F_p$ works in each positive characteristic. It does NOT cover general noncommutative circuits, and the rational result is over $\mathbb Q$ only.

Claims deterministic polynomial-time construction of polynomial-size rational matrix hitting lists for noncommutative rational formulas over $\mathbb Q$, with no bound on inverse nesting or constant heights, each nonzero formula receiving an invertible value. Companions: one rational tuple of dimension at most $2ns^2$ hits every nonzero division-free formula over every characteristic-zero field, and an analogous tuple over $\mathbb F_p$ works in each positive characteristic. It does NOT cover general noncommutative circuits, and the rational result is over $\mathbb Q$ only.