Function structural_factor 

pub fn structural_factor(
    n: &BigInt,
    budget: StructuralBudget,
) -> Option<StructuralWitness>

Run the whole structural arsenal against n within budget, returning the first certified factorization found, or None — the number-theoretic incompressible residue (a sound modulus has no structural shortcut, so only the general sub-exponential algorithms, out of scope here, remain).