{
  "status": "PASS",
  "checks_passed": 263,
  "positive_assertions": 263,
  "negative_controls_rejected": 14,
  "scope": "Finite examples and exact symbolic identities. No universal Galois occurrence, automorphic occupancy, or Lean proof checked.",
  "coefficient_domains": [
    "integers",
    "rationals",
    "symbolic polynomials",
    "finite fields F3,F5,F25,F9",
    "Z/(2^n), n <= 4"
  ],
  "bounds": {
    "singular_enumerations": "p=2,3,5 with listed exponents and depths <=5; square-root images at depths <=8 for p=3",
    "trace_kernel_max_modulus": 16,
    "norm_multiplication_pairs": 625,
    "lattice_max_side": 25,
    "quadratic_prime_scan_max": 47
  },
  "versions": {
    "python": "3.13.5",
    "sympy": "1.14.0"
  },
  "checks": [
    {
      "name": "residual_partition_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "positive_depth_preserves_root_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "horizontal_translation_changes_root_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "residual_partition_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "positive_depth_preserves_root_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "horizontal_translation_changes_root_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "residual_partition_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "positive_depth_preserves_root_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "horizontal_translation_changes_root_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quarter_branch_values",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quarter_digits",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quarter_algebraic_identity",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d1_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d1_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d1_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d1_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d2_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q2_d2_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d1_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d1_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d1_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d1_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d2_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q3_d2_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q5_d1_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q5_d1_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q5_d1_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_chart_q5_d1_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "smooth_zeta",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_counts",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_rational_form",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_series",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "empty_weighted_chart",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_direct_count_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_direct_count_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_direct_count_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_direct_count_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "weighted_direct_count_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "sign_first_visibility",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "sign_visibility_depth_two",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e2_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e2_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e2_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_zeta_p2_e2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e3_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e3_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e3_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e3_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p2_e3_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_zeta_p2_e3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e2_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e2_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e2_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_zeta_p3_e2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e3_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e3_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e3_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e3_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p3_e3_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_zeta_p3_e3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p5_e2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p5_e2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p5_e2_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p5_e2_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_direct_p5_e2_m5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_zeta_p5_e2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_square_counts",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_nonzero_child_dies",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_descendants_from_2m_reduce_to_zero_1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_descendants_from_2m_reduce_to_zero_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_descendants_from_2m_reduce_to_zero_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "singular_descendants_from_2m_reduce_to_zero_4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_levels_p2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p2_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p2_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_levels_p3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p3_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p3_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_levels_p5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p5_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p5_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_levels_p7",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p7_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p7_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_levels_p13",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p13_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "root_reduction_p13_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "5_adic_root_path",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negative_path",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "infinite_tail_window_nonempty_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "infinite_tail_window_nonempty_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "infinite_tail_window_nonempty_8",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_condition",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "differential_ranks_mod5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "cohomology_dimensions",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "cohomology_kernel_cardinality",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "cohomology_boundary_cardinality",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_projector_idempotent_0",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "complement_orthogonal_0",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_projector_idempotent_1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "complement_orthogonal_1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_projector_idempotent_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "complement_orthogonal_2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_projector_d0",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "chain_projector_d1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "acyclic_packet_dimensions",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "other_zero_packet_dimensions",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "bad_projector_detected",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "five_sccs",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "minimum_seeds",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "actual_reachability",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "missing_source_unreachable",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negation_preserves_equation_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "translation_fails_m1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negation_preserves_equation_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "translation_fails_m2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negation_preserves_equation_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "translation_fails_m3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negation_preserves_equation_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "translation_fails_m4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "negation_commutes_with_reduction",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "common_polynomial",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "charpoly_reduction_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "charpoly_reduction_7",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "s3_character_determinant",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "s3_trace_vector",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "s3_recovery",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "standard_s3_relations",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "standard_s3_trace_values",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "trace_reduction_kernel_2pow1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "trace_reduction_kernel_2pow2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "trace_reduction_kernel_2pow3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "trace_reduction_kernel_2pow4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "one_digit_loss_witness",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "one_extra_digit_separates",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "adjugate_precision_certificate",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_000",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_001",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_010",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_011",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_100",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_101",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_110",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_111",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "progressive_positive_ranks",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "empty_joint_packet",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "each_pair_occupied",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "trace_mod5_boundary",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "jordan_boundary",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "nonzero_sequence_converges_mod_p",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "signed_norm_residue_counterexample",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "two_nonsquare_in_F5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "field_norm_zero_fiber",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "field_norm_fiber_counts",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "determinant_norm",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "norm_multiplicativity_625_pairs",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "matrix_multiplication_625_pairs",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "nonscalar_unit_witness",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quotient_unit_permutation",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "character_sum_zero",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "character_action_25_points",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "unit_orbits_three_eights",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "unit_orbits_alternating",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "scalar_quadratic_exception",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "degree_three_sufficient",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "coprimality_not_necessary",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k0_d6",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k1_d6",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k2_d6",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "exact_scalar_criterion_k3_d6",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "crt_solution",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "crt_avoidance",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "crt_units",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L1",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L2",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L6",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L7",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L8",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L9",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L10",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L11",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L12",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L13",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L14",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L15",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L16",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L17",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L18",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L19",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L20",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L21",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L22",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L23",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L24",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "lattice_boundary_L25",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "complete_lattice_tiles_zero",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "boundary_area_at_12",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_envelope_difference",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_bound_h-1/4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_bound_h-1/8",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_bound_h0",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_bound_h1/8",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_bound_h1/4",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_derivative_at_one",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "repeated_identity_trace_rows_rank_one",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_5",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_7",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_11",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_13",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_17",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_19",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_23",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_29",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_31",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_37",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_41",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_43",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "quadratic_factorization_prime_47",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "matrix_root_exists_over_F3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "scalar_root_absent_over_F3",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "extension_roots_over_F9",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "companion_charpoly",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "adding_F_to_G_reduces_source_rank",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "every_smooth_parent_has_nine_children",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_sum_identity",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "joint_packet_pairwise_annihilation",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "norm_basis_change_invariance_all25",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "boundary_sum_at_12",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "zero_bulk_at_12",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "mellin_logarithmic_moment",
      "status": "PASS",
      "scope": "exact worked example"
    },
    {
      "name": "fourth_power_representation_over_Q",
      "status": "PASS",
      "scope": "exact worked example"
    }
  ],
  "negative_controls": [
    {
      "name": "arbitrary_residues_not_a_branch",
      "status": "REJECTED",
      "expected_reason": "Second residue must reduce to first.",
      "actual_exception": "ValueError"
    },
    {
      "name": "growing_counts_do_not_mean_all_nodes_lift",
      "status": "REJECTED",
      "expected_reason": "The depth-two node 3 has no child.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "residual_root_does_not_ensure_deep_root",
      "status": "REJECTED",
      "expected_reason": "x^2+1 has a root mod 2 but no root mod 4.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "degreewise_projectors_need_chain_condition",
      "status": "REJECTED",
      "expected_reason": "Degreewise idempotence does not imply differential compatibility.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "one_seed_cannot_cover_three_sources",
      "status": "REJECTED",
      "expected_reason": "A seed outside a source component cannot reach it.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "trace_solution_not_integral",
      "status": "REJECTED",
      "expected_reason": "Rational solution is not an integral multiplicity vector.",
      "actual_exception": "ValueError"
    },
    {
      "name": "negative_multiplicity",
      "status": "REJECTED",
      "expected_reason": "Representations do not have negative multiplicities.",
      "actual_exception": "ValueError"
    },
    {
      "name": "capacity_failure",
      "status": "REJECTED",
      "expected_reason": "Target multiplicity exceeds known carrier capacity.",
      "actual_exception": "ValueError"
    },
    {
      "name": "equal_precision_trace_recovery",
      "status": "REJECTED",
      "expected_reason": "Distinct multiplicities modulo 8 can give the same traces modulo 8.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "pairwise_occupancy_does_not_imply_joint",
      "status": "REJECTED",
      "expected_reason": "The selected triple 011 is absent although each pair occurs.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "lagrange_formula_without_semisimplicity",
      "status": "REJECTED",
      "expected_reason": "The sole-eigenvalue Lagrange product is I, not the ordinary eigenspace projector.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "absolute_norm_is_residue_function_over_Q",
      "status": "REJECTED",
      "expected_reason": "Opposite real signs can change absolute-norm residues.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "nontrivial_scalar_character_alone_insufficient",
      "status": "REJECTED",
      "expected_reason": "A nontrivial quadratic character is trivial on every scalar square.",
      "actual_exception": "AssertionError"
    },
    {
      "name": "no_scalar_root_does_not_mean_no_representation",
      "status": "REJECTED",
      "expected_reason": "A 2 by 2 companion matrix realizes the equation over F3.",
      "actual_exception": "AssertionError"
    }
  ],
  "limits": [
    "Exact finite results do not assert an infinite arithmetic existence theorem.",
    "The finite-tail counterexample and Mellin analytic argument have their stated prose proofs, not proofs inferred from sampling.",
    "No fresh Lean compilation."
  ],
  "data": {
    "quarter_residues": [
      4,
      19,
      94,
      469,
      2344,
      11719
    ],
    "weighted_counts": [
      1,
      2,
      8,
      32,
      256,
      2048,
      16384
    ],
    "norm_fiber_counts": [
      1,
      6,
      6,
      6,
      6
    ],
    "lattice_side_12_sum": 1,
    "source_components": [
      [
        "A",
        "B"
      ],
      [
        "C"
      ],
      [
        "D",
        "E"
      ],
      [
        "F"
      ],
      [
        "G"
      ]
    ],
    "minimum_seed_sets": [
      [
        "A",
        "D",
        "G"
      ],
      [
        "A",
        "E",
        "G"
      ],
      [
        "B",
        "D",
        "G"
      ],
      [
        "B",
        "E",
        "G"
      ]
    ]
  },
  "source_sha256": {
    "source/models.py": "47727d61f486819929352395a1bf840dc443e68c075e855517d07e6877705149",
    "checks/verify_examples.py": "d2ba2641bd3d130fa8b258d579677563a06063badf4f4315d8d7aa893e3806a5"
  }
}