Singular fiber primes method
The proof route establishing that rs_singular_fiber_primes is complete.
smooth_over_ZZ: the scheme is smooth over $\mathbb Z$, so every fiber is smooth (list[]).direct_integer_critical_certificate: exact hypersurface certificate, with every candidate prime recomputed.direct_equidimensional_jacobian_certificate: exact pure-codimension Jacobian certificate, with every candidate prime recomputed.terminal_three_lines_integer_certificate: an imported three-lines certificate known to be exhaustive.direct_vertical_fiber_jacobian: the only existing fiber was checked directly and is smooth.direct_exceptional_vertical_fiber_jacobian: one additional characteristic-2 calculation of the same kind.smooth_deletion_empty_target: a smooth deletion morphism to a target with no singular fibers.smooth_deletion_sandwich: the known lower bound equals the upper bound given by a smooth deletion's target.simple_core: copied from the simple core.
Full details: docs/realization_scheme_singularity_census.md (Section 18.2).