Separating choiceless counting from polynomial time and witnessed choice

Confirms the Blass–Gurevich–Shelah noncapture conjecture: consistency of a linear system over 𝔽₃ defines a polynomial-time query on unordered finite structures that choiceless polynomial time with counting cannot express. A separate result shows that adding witnessed symmetric choice strictly increases expressive power. Both separations hold for the full counting formalism, allowing hereditarily finite sets of arbitrary finite rank.