{ "status": "PASS", "E6": { "coefficient_systems": 8, "maximal_minors": "all +/-1", "W12_coefficient": 2 }, "E7": { "full_lattice_rank": 28, "determinant": 1, "source_exchange_terms": 87, "source_torus_calibrated_directions": [ 2, 3, 4, 6, 7, 9, 12, 13, 16, 17, 19, 20 ], "mixed_contact_directions_retained": [ 1, 5, 8, 10, 11, 14, 15, 18 ], "boundary_systems": 18, "support_subset_factorizations": 100, "irreducible_factor_cases": 80, "bound_zero": 70, "bound_one": 10, "max_denominator": 13, "max_inequality_rows_used": 16, "max_homogeneity_rows_used": 3 }, "scope": "Exact finite algebra from the saved formulas. No verification of enumerative geometry, full source support bounds, or the eight mixed-contact incidence arguments." }