Function decide_invariant_witness_for_all_scales 

pub fn decide_invariant_witness_for_all_scales(
    make: &dyn Fn(usize) -> SymmetricInstance,
    window: &[usize],
    degree: usize,
    max_count_degree: usize,
) -> ForAllVerdict

Decide the invariant-witness question at every scale by one finite computation. Build the labeled entry counts at each window scale (consecutive scales, all post-onset so every label is realizable throughout), fit each entry as a degree-≤ max_count_degree integer polynomial (the finite-difference certificate — window points beyond the fitting prefix are exact verifications), read off the Lucas period, and solve the fitted system once per residue class. Every window scale is differentially validated: the fitted verdict must equal invariant_witness_exists_direct’s, and positive verdicts lift to check_ns_lower_bound_polys-passing witnesses. A true residue is a machine-decided NS-degree > degree lower bound for every scale in that class from onset on — including scales no explicit basis can represent.