Function nullstellensatz_basis_size 

pub fn nullstellensatz_basis_size(n: usize, d: usize) -> u128

The width of the degree-d Nullstellensatz system over n variables: the count of multilinear monomials of degree ≤ d, Σ_{k≤d} C(n,k). At d = n this is exactly 2ⁿ — so the degree-n certificate that build_ns_certificate always produces (completeness: no unsatisfiable formula over n variables is “structureless”) lives in an exponentially large space. The certificate’s existence is an information-theoretic fact about the finite cube; it is not an efficient algorithm, and it says nothing about P vs NP — which is a statement about the asymptotic growth of a family of instances, not any fixed finite n (a fixed finite problem is decidable by table lookup, vacuously).