Function ns_lower_bound_witness_polys_on_basis 

pub fn ns_lower_bound_witness_polys_on_basis(
    num_vars: usize,
    gens: &[Poly],
    degree: usize,
    in_basis: &dyn Fn(Mono) -> bool,
) -> Option<Vec<Mono>>

ns_lower_bound_witness_polys 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 generators — so any Some is a fully valid, check_ns_lower_bound_polys-verifiable witness, and None means only “no witness on this sub-basis”. The structure probe: which candidate supports carry a family’s lower bound (for pigeonhole this is how the hole-injective support was found and the classical partial-matching support was ruled out over GF(2)). Degree-bounded enumeration — num_vars ≤ 63.