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      [
        1.0,
        0.0
      ]
    ],
    "total_spin_squared_eigenvalues": [
      6,
      2,
      2,
      2,
      0,
      0
    ],
    "exact_checks": {
      "orthogonal_Gram": true,
      "bond_H_eigenstates": true,
      "active_U_eigenstates": true,
      "projector_sum_is_identity": true,
      "full_rank": 6,
      "negative_projector_defects": true
    },
    "actual_regular_B": {
      "roots": [
        0.2886751345948129,
        -0.2886751345948129
      ],
      "raw_coefficient_factor": "2/27",
      "expected_raw_norm_squared": "16/243",
      "raw_norm_squared": 0.06584362139917699
    },
    "energies_with_multiplicity_over_J": [
      4.977931814658079e-16,
      1.0,
      1.0000000000000004,
      1.0000000000000007,
      1.9999999999999996,
      2.999999999999999
    ],
    "expected_energies_with_multiplicity_over_J": [
      0,
      1,
      1,
      1,
      2,
      3
    ],
    "equation_errors": {
      "independent_Pauli_vs_exact_bond_H_frobenius_error": 0.0,
      "full_vs_exact_sector_U_frobenius_error": 0.0,
      "normalized_Gram_frobenius_error": 4.2005566648082894e-16,
      "resolution_of_identity_frobenius_error": 5.102575794795066e-16,
      "H_eigenstate_frobenius_error_over_J": 2.3055512673781017e-16,
      "U_eigenstate_frobenius_error": 0.0,
      "energy_spectrum_max_error_over_J": 8.881784197001252e-16,
      "H_lowering_commutator_frobenius_error_over_J": 0.0,
      "U_lowering_commutator_frobenius_error": 0.0,
      "spin_squared_labels_frobenius_error": 1.2412670766236366e-16,
      "vacuum_twice_lowered_norm_squared_error": 0.0,
      "spin_two_descendant_vector_error": 0.0,
      "m1_one_magnon_highest_weight_error": 0.0,
      "m1_lowered_norm_squared_error": 0.0,
      "m1_normalized_descendant_error": 0.0,
      "m2_one_magnon_highest_weight_error": 0.0,
      "m2_lowered_norm_squared_error": 0.0,
      "m2_normalized_descendant_error": 0.0,
      "m3_one_magnon_highest_weight_error": 0.0,
      "m3_lowered_norm_squared_error": 0.0,
      "m3_normalized_descendant_error": 0.0,
      "B_degree_four_coefficient_frobenius_norm": 0.0,
      "B_degree_three_equals_i_lowering_frobenius_error": 0.0,
      "B_polynomial_evaluation_frobenius_error": 1.0174415683999446e-16,
      "actual_regular_B_coefficient_relative_error": 3.057568955049956e-16,
      "actual_regular_B_phase_aligned_error": 3.3236701876222775e-16,
      "singular_raw_B_vector_norm": 0.0,
      "omit_singular_retained_H_error_over_J": 2.3055512673781017e-16,
      "omit_singular_retained_U_error": 0.0,
      "replace_singular_with_regular_retained_H_error_over_J": 3.2009291313835888e-16,
      "replace_singular_with_regular_retained_U_error": 0.0
    },
    "negative_controls": {
      "omit_singular": {
        "column_count": 5,
        "exact_rank": 5,
        "distinct_energies_over_J": [
          0,
          1,
          2,
          3
        ],
        "retained_H_eigenstate_frobenius_error_over_J": 2.3055512673781017e-16,
        "retained_U_eigenstate_frobenius_error": 0.0,
        "Gram_frobenius_error": 4.2005566648082894e-16,
        "resolution_frobenius_error": 0.9999999999999999,
        "missing_singular_projection_norm": 0.0,
        "exact_projector_defect_verified": true
      },
      "replace_singular_with_regular": {
        "column_count": 6,
        "exact_rank": 5,
        "distinct_energies_over_J": [
          0,
          1,
          2,
          3
        ],
        "retained_H_eigenstate_frobenius_error_over_J": 3.2009291313835888e-16,
        "retained_U_eigenstate_frobenius_error": 0.0,
        "Gram_frobenius_error": 1.4142135623730954,
        "resolution_frobenius_error": 1.4142135623730954,
        "missing_singular_projection_norm": 0.0,
        "exact_projector_defect_verified": true
      }
    },
    "summary": {
      "largest_identity_residual": 8.881784197001252e-16,
      "smallest_completeness_failure_residual": 0.9999999999999999
    }
  }
}