Function count_instance_linear_marked 

pub fn count_instance_linear_marked(n: usize, q: usize) -> SymmetricInstance

Modular counting with one marked point — the point-stabilizer instrument. Point 0 gets its own sort, so the symmetry drops from Sₙ to Stab(0) ≅ Sₙ₋₁ (adjacent transpositions of the unmarked points only) and the canonical types automatically distinguish “touches the marked point.” The collapsed dual then decides existence of a marked-invariant witness — a strictly larger search space than the fully-invariant one (every Sₙ-invariant functional is Stab(0)-invariant), the first refinement rung between “symmetric” and “arbitrary” on the char-2 gap.