Function ns_lower_bound_witness_on_basis_gfp 

pub fn ns_lower_bound_witness_on_basis_gfp(
    f: NsField,
    num_vars: usize,
    gens: &[GfpPoly],
    degree: usize,
    in_basis: &dyn Fn(Mono) -> bool,
) -> Option<Vec<(Mono, u64)>>

ns_lower_bound_witness_polys_gfp restricted to a sub-basis: the functional L is sought only on monomials passing in_basis (L = 0 elsewhere), while the constraints ⟨L, m·g⟩ = 0 still range over all admitted generator products — so any Some is a fully valid, check_ns_lower_bound_polys_gfp-verifiable witness, and None means only “no witness on this sub-basis”. The structure probe of the GF(2) engine, carried to every characteristic: which candidate supports hold a family’s lower bound, field by field. Degree-bounded enumeration — num_vars ≤ 63.