Function surface_is_reducible 

pub fn surface_is_reducible(roots: &[BigInt; 6], p: &BigInt) -> bool

Whether the genus-2 curve with these six Weierstrass points has a reducible Jacobian (splits as a product of elliptic curves) — decided by the Richelot split-test: some (2,2)-splitting has δ = 0. This is exactly the decision the Castryck–Decru per-digit oracle makes — a correct guess yields a splitting abelian surface, a wrong one an indecomposable genus-2 Jacobian.