{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 12,
  "input_formula": "F8N4",
  "input_spacegroup": "P1",
  "input_pointgroup": "1",
  "input_is_polar_point_group": true,
  "input_energy_eV": -49.63548193785046,
  "input_cartesian_polarization_e_A2": [
    -7.625460820804223e-05,
    4.535226337206744e-05,
    5.6629575540407246e-05
  ],
  "input_reduced_polarization": [
    -0.0035061739062059115,
    0.0014512920211569933,
    0.0015219067048319857
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.032025183319884e-16,
      "parent_symmetrization_rmsd_A": 0.03419200293584494,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -49.63711717268608,
      "reduced_polarization": [
        -6.408053248411082e-16,
        -1.2876812163840988e-16,
        -2.59385983224707e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.956712215698046e-18,
        -3.509692649361176e-18,
        -9.651654785743235e-18
      ],
      "ranking_score": 0.03419200293584635
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8350103771080065e-15,
      "parent_symmetrization_rmsd_A": 0.610169814334545,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -41.000904456174865,
      "reduced_polarization": [
        -1.215403717724319e-15,
        1.365694886210156e-15,
        -1.579061899211067e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.765499004089257e-17,
        4.925300883702689e-17,
        -5.8756298806255624e-18
      ],
      "ranking_score": 0.6101698143345486
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4875220518554588e-15,
      "parent_symmetrization_rmsd_A": 0.7124283566007327,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -36.74750105016611,
      "reduced_polarization": [
        7.187094015369064e-16,
        3.354906804032225e-16,
        1.2584214930862072e-15
      ],
      "cartesian_polarization_e_A2": [
        -9.1862616528492e-19,
        6.734689192251358e-18,
        4.682539000461581e-17
      ],
      "ranking_score": 0.7124283566007357
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.985226745992089e-16,
      "parent_symmetrization_rmsd_A": 0.046892696958525715,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -49.53261846405887,
      "reduced_polarization": [
        -5.565953748010037e-16,
        3.565233089475137e-16,
        -4.480303346608575e-16
      ],
      "cartesian_polarization_e_A2": [
        -7.83413537803834e-18,
        1.454015526163916e-17,
        -1.6671040084465586e-17
      ],
      "ranking_score": 0.04689269695852731
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.045941322883433e-07,
      "parent_symmetrization_rmsd_A": 0.002624044058545775,
      "parent_cell_rmsd_A": 0.00019646633323316753,
      "energy_eV": -49.63412579549523,
      "reduced_polarization": [
        -8.904148831253742e-07,
        -1.4505723129211982e-07,
        -6.640993697626408e-08
      ],
      "cartesian_polarization_e_A2": [
        -1.2137207490896912e-08,
        -4.88714781245496e-09,
        -2.471119238520654e-09
      ],
      "ranking_score": 0.5026749698301186
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4837117551160188e-15,
      "parent_symmetrization_rmsd_A": 0.03419210905423302,
      "parent_cell_rmsd_A": 0.00019646633323316753,
      "energy_eV": -49.636977862013964,
      "reduced_polarization": [
        -1.4548423958249814e-15,
        3.0125135260476413e-17,
        2.89700969631141e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.4818272355504837e-17,
        -1.2534480987628705e-19,
        1.0779653649360687e-17
      ],
      "ranking_score": 0.03424122563754428
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.308381904833207e-15,
      "parent_symmetrization_rmsd_A": 0.046833081382381125,
      "parent_cell_rmsd_A": 0.00019646633323314029,
      "energy_eV": -49.527185105485316,
      "reduced_polarization": [
        2.183719267363096e-15,
        7.592356413680735e-17,
        7.444681271332795e-16
      ],
      "cartesian_polarization_e_A2": [
        2.7450513362906864e-17,
        -3.760344296288611e-19,
        2.7701202982659437e-17
      ],
      "ranking_score": 0.046882197965694025
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0003859377431469657,
      "parent_symmetrization_rmsd_A": 0.21329085920750776,
      "parent_cell_rmsd_A": 0.019833621675996695,
      "energy_eV": -37.85653281914324,
      "reduced_polarization": [
        -0.5003731588849339,
        -8.321698333687187e-05,
        -5.268132367869677e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.007710597774267202,
        -1.7006167685706103e-05,
        -9.067746175761173e-07
      ],
      "ranking_score": 0.7190211401128008
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0004752275047698,
      "parent_symmetrization_rmsd_A": 0.31060329590639807,
      "parent_cell_rmsd_A": 0.015137873975379792,
      "energy_eV": -18.512092549392136,
      "reduced_polarization": [
        -8.849831356526943e-05,
        0.00030139388720025993,
        0.49964338963202937
      ],
      "cartesian_polarization_e_A2": [
        -0.0037547394807285516,
        -0.0020771786151562617,
        0.018573795455634
      ],
      "ranking_score": 0.8153382194097827
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.01589439954744576,
      "parent_symmetrization_rmsd_A": 0.3626548243899397,
      "parent_cell_rmsd_A": 0.025644896517729686,
      "energy_eV": -20.29422241351235,
      "reduced_polarization": [
        -0.01456903685834999,
        0.49960600250263837,
        -0.0063419135886541465
      ],
      "cartesian_polarization_e_A2": [
        -0.0038978854170865452,
        0.01779359975163091,
        -0.0002574098587972116
      ],
      "ranking_score": 0.9008548476142636
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0050795839523790605,
      "parent_symmetrization_rmsd_A": 0.312301459902053,
      "parent_cell_rmsd_A": 0.031065620413873386,
      "energy_eV": -12.83270254244907,
      "reduced_polarization": [
        -0.5017611719367089,
        -0.0047012922268406705,
        0.5007734972116714
      ],
      "cartesian_polarization_e_A2": [
        -0.011449453938534627,
        -0.002308177666116739,
        0.018608858336071944
      ],
      "ranking_score": 0.8302270329102794
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 7.012337464992952e-05,
      "parent_symmetrization_rmsd_A": 0.2998589321949019,
      "parent_cell_rmsd_A": 0.009887619805503432,
      "energy_eV": -15.516990417703344,
      "reduced_polarization": [
        -0.5000586162128866,
        0.5000038483510356,
        -3.829644178553433e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.011379248987022328,
        0.01778938646287802,
        -8.020773104273929e-06
      ],
      "ranking_score": 0.8024710838955775
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0033287066126912583,
      "parent_symmetrization_rmsd_A": 0.38024920555906583,
      "parent_cell_rmsd_A": 0.03942614025108098,
      "energy_eV": -5.789186876339965,
      "reduced_polarization": [
        -0.0019482638807409548,
        0.5001256606083481,
        0.50269606472027
      ],
      "cartesian_polarization_e_A2": [
        -0.007456863330877036,
        0.015750716470540084,
        0.01863393321452394
      ],
      "ranking_score": 0.8967631538472185
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.029881684002612093,
      "parent_symmetrization_rmsd_A": 0.36163206189361374,
      "parent_cell_rmsd_A": 0.015870936289645626,
      "energy_eV": 2.473019673818353,
      "reduced_polarization": [
        -0.48031131561202667,
        0.49073028921338235,
        0.4795221288256029
      ],
      "cartesian_polarization_e_A2": [
        -0.014643977136520886,
        0.015433945547327323,
        0.017842606951260366
      ],
      "ranking_score": 0.9253631639712494
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "target_residual": 0.004088484316888806,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.002967347279467541,
            "max_log_strain_component": 2.0057634899291535e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0000295942508113,
              1.000003098699214,
              0.9999781272065152
            ],
            "cell_volume_ratio": 1.0000108195331558,
            "cell_rmsd_from_input_A": 0.00019646633323316753
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.904148831253742e-07,
              -1.4505723129211982e-07,
              -6.640993697626408e-08
            ],
            "branch_aligned_reduced_polarization": [
              -8.904148831253742e-07,
              -1.4505723129211982e-07,
              -6.640993697626408e-08
            ],
            "target_residual": 9.045941322883433e-07,
            "energy_eV": -49.63412579549523
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.032025183319884e-16,
        "parent_symmetrization_rmsd_A": 0.03419200293584494,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -49.63711717268608,
        "reduced_polarization": [
          -6.408053248411082e-16,
          -1.2876812163840988e-16,
          -2.59385983224707e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.956712215698046e-18,
          -3.509692649361176e-18,
          -9.651654785743235e-18
        ],
        "ranking_score": 0.03419200293584635
      },
      "branch_status": "sampled",
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -49.63548193785045,
          -49.63587905355331,
          -49.63621631849166,
          -49.63649670590258,
          -49.63672272922917,
          -49.636896448885174,
          -49.63701943783733,
          -49.63709279361363,
          -49.63711717268606
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.625460820804329e-05,
            4.53522633720724e-05,
            5.662957554040186e-05
          ],
          [
            -6.679313040597131e-05,
            3.961777472064503e-05,
            4.96168314957025e-05
          ],
          [
            -5.730341083527488e-05,
            3.390889049128821e-05,
            4.257863202746679e-05
          ],
          [
            -4.778948563437446e-05,
            2.8222499700133186e-05,
            3.551815407833053e-05
          ],
          [
            -3.825546217085432e-05,
            2.2555103627500983e-05,
            2.8438580635755155e-05
          ],
          [
            -2.8705487113476627e-05,
            1.6902912452761424e-05,
            2.134314621083438e-05
          ],
          [
            -1.9143607222540993e-05,
            1.1262167316432798e-05,
            1.4235542958734727e-05
          ],
          [
            -9.573788685236747e-06,
            5.629140657912094e-06,
            7.119807062303213e-06
          ],
          [
            6.455327551503592e-18,
            -5.076519724968844e-18,
            -1.4289462929541932e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4072944198861848e-16,
            -1.8726882024255875e-16,
            -3.8402440949436567e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0035061739062060004,
            0.0014512920211571245,
            0.0015219067048318768
          ],
          [
            -0.0030723871621742282,
            0.001268247143627943,
            0.001333440835556865
          ],
          [
            -0.0026367939983262256,
            0.001085842268668813,
            0.0011442908576797528
          ],
          [
            -0.0021996519255219615,
            0.0009039998973394692,
            0.0009545421507970442
          ],
          [
            -0.0017612282362124976,
            0.0007226316539217237,
            0.000764280256958294
          ],
          [
            -0.001321795956640337,
            0.0005416411434642221,
            0.0005735921028986457
          ],
          [
            -0.0008816144908924683,
            0.0003609342703212448,
            0.00038257691443166486
          ],
          [
            -0.0004409325391936947,
            0.00018041889280584478,
            0.00019134316303492938
          ],
          [
            1.1102230246251565e-16,
            -1.6653345369377348e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -49.63711717268606,
          -49.637092793613625,
          -49.637019437837324,
          -49.63689644888519,
          -49.63672272922917,
          -49.63649670590258,
          -49.636216318491655,
          -49.635879053553325,
          -49.63548193785048
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.455327551503592e-18,
            -5.076519724968844e-18,
            -1.4289462929541932e-17
          ],
          [
            9.573788685216065e-06,
            -5.629140657903007e-06,
            -7.119807062304967e-06
          ],
          [
            1.9143607222528962e-05,
            -1.1262167316390557e-05,
            -1.4235542958719435e-05
          ],
          [
            2.870548711351655e-05,
            -1.6902912452757725e-05,
            -2.134314621087186e-05
          ],
          [
            3.82554621709326e-05,
            -2.2555103627560837e-05,
            -2.8438580635777215e-05
          ],
          [
            4.7789485634379166e-05,
            -2.8222499700173233e-05,
            -3.551815407835272e-05
          ],
          [
            5.7303410835347326e-05,
            -3.390889049133453e-05,
            -4.257863202752846e-05
          ],
          [
            6.679313040598471e-05,
            -3.961777472063481e-05,
            -4.961683149568307e-05
          ],
          [
            7.625460820800888e-05,
            -4.5352263372047264e-05,
            -5.6629575540421165e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.0035061739062062737,
          -0.0014512920211574901,
          -0.0015219067048326091
        ],
        "actual_opposite_endpoint_branch_residual": 2.6739356803550815e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4072944198861848e-16,
            -1.8726882024255875e-16,
            -3.8402440949436567e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0035061739062060004,
            0.0014512920211571245,
            0.0015219067048318768
          ],
          [
            -0.0030723871621742282,
            0.001268247143627943,
            0.001333440835556865
          ],
          [
            -0.0026367939983262256,
            0.001085842268668813,
            0.0011442908576797528
          ],
          [
            -0.0021996519255219615,
            0.0009039998973394692,
            0.0009545421507970442
          ],
          [
            -0.0017612282362124976,
            0.0007226316539217237,
            0.000764280256958294
          ],
          [
            -0.001321795956640337,
            0.0005416411434642221,
            0.0005735921028986457
          ],
          [
            -0.0008816144908924683,
            0.0003609342703212448,
            0.00038257691443166486
          ],
          [
            -0.0004409325391936947,
            0.00018041889280584478,
            0.00019134316303492938
          ],
          [
            1.1102230246251565e-16,
            -1.6653345369377348e-16,
            -3.885780586188048e-16
          ],
          [
            0.00044093253919241793,
            -0.00018041889280556722,
            -0.0001913431630350404
          ],
          [
            0.0008816144908924128,
            -0.00036093427031996805,
            -0.00038257691443122077
          ],
          [
            0.001321795956642391,
            -0.0005416411434642221,
            -0.0005735921028996449
          ],
          [
            0.0017612282362164944,
            -0.0007226316539234445,
            -0.0007642802569588492
          ],
          [
            0.0021996519255214064,
            -0.0009039998973406904,
            -0.0009545421507977103
          ],
          [
            0.0026367939983293898,
            -0.0010858422686703117,
            -0.0011442908576814736
          ],
          [
            0.003072387162175505,
            -0.0012682471436275544,
            -0.0013334408355563099
          ],
          [
            0.00350617390620378,
            -0.0014512920211564584,
            -0.0015219067048323764
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062058894,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "target_residual": 0.4964982797531161,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0007683116988104066,
            "step_scale": 0.34371337716474226,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0008398750004293,
              0.999660281552436,
              0.9987269009690745
            ],
            "cell_volume_ratio": 0.9992261358153277,
            "cell_rmsd_from_input_A": 0.0085233720980943
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.17425297891230077,
              -0.001491453451799542,
              -0.0027352801924806266
            ],
            "branch_aligned_reduced_polarization": [
              -0.17425297891230074,
              -0.001491453451799542,
              -0.0027352801924806266
            ],
            "target_residual": 0.3257619191044899,
            "energy_eV": -48.11061419412222,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005924807663065311,
            "step_scale": 0.4630606559829449,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0014859340558098,
              0.9994034460255391,
              0.9977423608011846
            ],
            "cell_volume_ratio": 0.998628848544594,
            "cell_rmsd_from_input_A": 0.015111495284688147
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3333287985345161,
              -0.005726713328250273,
              -0.007677135614936642
            ],
            "branch_aligned_reduced_polarization": [
              -0.3333287985345161,
              -0.005726713328250273,
              -0.007677135614936642
            ],
            "target_residual": 0.16694616813434807,
            "energy_eV": -43.616986374212075,
            "max_atomic_step_A": 0.11497879489391082,
            "max_log_strain_component": 0.0004786204936575828,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0019958629390642,
              0.9992523988836198,
              0.996990382394847
            ],
            "cell_volume_ratio": 0.9982333998080907,
            "cell_rmsd_from_input_A": 0.020102662282057798
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5738441797737758,
              -0.012325881885705575,
              -0.011772556141947917
            ],
            "branch_aligned_reduced_polarization": [
              -0.5738441797737758,
              -0.012325881885705575,
              -0.011772556141947917
            ],
            "target_residual": 0.07578577260170537,
            "energy_eV": -34.05625711647576,
            "max_atomic_step_A": 0.0202050957838151,
            "max_log_strain_component": 2.2195517686316117e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0019686693431196,
              0.9992703596825406,
              0.9970227479246673
            ],
            "cell_volume_ratio": 0.9982566559046515,
            "cell_rmsd_from_input_A": 0.019880751396743473
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.511452334347621,
              -0.0024390361339375597,
              -0.0019772389297626077
            ],
            "branch_aligned_reduced_polarization": [
              -0.511452334347621,
              -0.0024390361339375597,
              -0.0019772389297626077
            ],
            "target_residual": 0.011874945602305837,
            "energy_eV": -37.278119063852444,
            "max_atomic_step_A": 0.004227638324627691,
            "max_log_strain_component": 0.00014625083462720156,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.3808689851145197,
            "cell_principal_stretches": [
              1.0020220687534145,
              0.9995018731790791,
              0.9970650030238334
            ],
            "cell_volume_ratio": 0.9985834679009494,
            "cell_rmsd_from_input_A": 0.019833621675996695
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5003731588849339,
              -8.321698333687187e-05,
              -5.268132367869677e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5003731588849339,
              -8.321698333687187e-05,
              -5.268132367869677e-05
            ],
            "target_residual": 0.0003859377431469657,
            "energy_eV": -37.85653281914324
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0003859377431469657,
        "parent_symmetrization_rmsd_A": 0.21329085920750776,
        "parent_cell_rmsd_A": 0.019833621675996695,
        "energy_eV": -37.85653281914324,
        "reduced_polarization": [
          -0.5003731588849339,
          -8.321698333687187e-05,
          -5.268132367869677e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.007710597774267202,
          -1.7006167685706103e-05,
          -9.067746175761173e-07
        ],
        "ranking_score": 0.7190211401128008
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319879
            ],
            "target_residual": 0.49849253655313386,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0004351944813391688,
            "step_scale": 0.3115007687349461,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0004573130773917,
              1.0002963112670924,
              0.9992610077372234
            ],
            "cell_volume_ratio": 1.0000142105660268,
            "cell_rmsd_from_input_A": 0.0048901239280869785
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004852513131739624,
              -0.002414020094170384,
              0.15889725496383955
            ],
            "branch_aligned_reduced_polarization": [
              -0.004852513131739624,
              -0.002414020094170384,
              0.15889725496383955
            ],
            "target_residual": 0.3411458002788729,
            "energy_eV": -47.67953724798415,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0004355399643002048,
            "step_scale": 0.4569634416697952,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0009522295994204,
              1.0005865760646147,
              0.998447114991271
            ],
            "cell_volume_ratio": 0.9999840887547786,
            "cell_rmsd_from_input_A": 0.010257973081735396
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.020618986870914423,
              -0.0022674773089652214,
              0.27524641173115916
            ],
            "branch_aligned_reduced_polarization": [
              -0.020618986870914423,
              -0.0022674773089652214,
              0.27524641173115916
            ],
            "target_residual": 0.22570879360948534,
            "energy_eV": -38.0464870483125,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003350336242952462,
            "step_scale": 0.622430904912857,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0012594818141136,
              1.0008219018753173,
              0.9980577444899218
            ],
            "cell_volume_ratio": 1.0001361187603128,
            "cell_rmsd_from_input_A": 0.012923374314350101
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.08385004180225097,
              -0.07083333130452214,
              0.6122486419213594
            ],
            "branch_aligned_reduced_polarization": [
              0.08385004180225097,
              -0.07083333130452214,
              0.6122486419213594
            ],
            "target_residual": 0.15699664947738534,
            "energy_eV": -9.017745328133891,
            "max_atomic_step_A": 0.031949215263814945,
            "max_log_strain_component": 9.469019265819348e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.001261100753248,
              1.0008148964512347,
              0.9980577914010743
            ],
            "cell_volume_ratio": 1.0001307822565206,
            "cell_rmsd_from_input_A": 0.012925311606549885
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.02748640465582099,
              -0.00593716858768251,
              0.49458334295287226
            ],
            "branch_aligned_reduced_polarization": [
              0.02748640465582099,
              -0.00593716858768251,
              0.49458334295287226
            ],
            "target_residual": 0.028637258690529376,
            "energy_eV": -19.036799948468953,
            "max_atomic_step_A": 0.00977342399477992,
            "max_log_strain_component": 0.00018685576715040455,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.797749303595053,
            "cell_principal_stretches": [
              1.0013192845414378,
              1.0008784744834192,
              0.9977648025141826
            ],
            "cell_volume_ratio": 0.9999588054808988,
            "cell_rmsd_from_input_A": 0.015137873975379792
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -8.849831356526943e-05,
              0.00030139388720025993,
              0.49964338963202937
            ],
            "branch_aligned_reduced_polarization": [
              -8.849831356526943e-05,
              0.00030139388720025993,
              0.49964338963202937
            ],
            "target_residual": 0.0004752275047698,
            "energy_eV": -18.512092549392136
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0004752275047698,
        "parent_symmetrization_rmsd_A": 0.31060329590639807,
        "parent_cell_rmsd_A": 0.015137873975379792,
        "energy_eV": -18.512092549392136,
        "reduced_polarization": [
          -8.849831356526943e-05,
          0.00030139388720025993,
          0.49964338963202937
        ],
        "cartesian_polarization_e_A2": [
          -0.0037547394807285516,
          -0.0020771786151562617,
          0.018573795455634
        ],
        "ranking_score": 0.8153382194097827
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211570135,
              0.0015219067048319857
            ],
            "target_residual": 0.49856335974763777,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00042993694373667633,
            "step_scale": 0.24624446801846894,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0004920764912735,
              1.0000708545615271,
              0.9998593610273215
            ],
            "cell_volume_ratio": 1.000422247771038,
            "cell_rmsd_from_input_A": 0.0025972331599390976
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0038557194074062703,
              0.1251879867454113,
              0.0020842109822661807
            ],
            "branch_aligned_reduced_polarization": [
              -0.0038557194074062703,
              0.12518798674541132,
              0.0020842109822661807
            ],
            "target_residual": 0.3748376392353431,
            "energy_eV": -48.24563331675289,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003949111324783795,
            "step_scale": 0.3189328363970728,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0009435790692351,
              1.0001588272288964,
              0.9997265254287145
            ],
            "cell_volume_ratio": 1.0008287800718205,
            "cell_rmsd_from_input_A": 0.0051113206357701
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.015654813177792427,
              0.2298009368561248,
              0.004676246020222172
            ],
            "branch_aligned_reduced_polarization": [
              0.015654813177792427,
              0.2298009368561248,
              0.004676246020222172
            ],
            "target_residual": 0.2706925824183239,
            "energy_eV": -44.39587728672199,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.000419839214880998,
            "step_scale": 0.32982126961350333,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0014707922626815,
              1.0000120715311396,
              0.9996265125650663
            ],
            "cell_volume_ratio": 1.0011088402759762,
            "cell_rmsd_from_input_A": 0.006934330895621085
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.04337590522500375,
              0.3330234791163887,
              0.026393118456952237
            ],
            "branch_aligned_reduced_polarization": [
              0.04337590522500375,
              0.3330234791163887,
              0.026393118456952237
            ],
            "target_residual": 0.17452571266826647,
            "energy_eV": -33.39177248186658,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00018720687562582771,
            "step_scale": 0.9469710847879005,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0015984807994147,
              0.9999902859918236,
              0.9996205952485051
            ],
            "cell_volume_ratio": 1.00120874373231,
            "cell_rmsd_from_input_A": 0.007298872005277855
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.06608114358645815,
              0.6608825217445569,
              -0.014965499227406047
            ],
            "branch_aligned_reduced_polarization": [
              -0.06608114358645815,
              0.6608825217445569,
              -0.014965499227406047
            ],
            "target_residual": 0.17456766455362632,
            "energy_eV": -8.657605850016925,
            "max_atomic_step_A": 0.04261511627472574,
            "max_log_strain_component": 0.002151463587368002,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.441726383499683,
            "cell_principal_stretches": [
              1.0041032591264858,
              1.0009193317606222,
              0.9989679631517051
            ],
            "cell_volume_ratio": 1.0039891389032736,
            "cell_rmsd_from_input_A": 0.025644896517729686
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.01456903685834999,
              0.49960600250263837,
              -0.0063419135886541465
            ],
            "branch_aligned_reduced_polarization": [
              -0.01456903685834999,
              0.49960600250263837,
              -0.0063419135886541465
            ],
            "target_residual": 0.01589439954744576,
            "energy_eV": -20.29422241351235
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.01589439954744576,
        "parent_symmetrization_rmsd_A": 0.3626548243899397,
        "parent_cell_rmsd_A": 0.025644896517729686,
        "energy_eV": -20.29422241351235,
        "reduced_polarization": [
          -0.01456903685834999,
          0.49960600250263837,
          -0.0063419135886541465
        ],
        "cartesian_polarization_e_A2": [
          -0.0038978854170865452,
          0.01779359975163091,
          -0.0002574098587972116
        ],
        "ranking_score": 0.9008548476142636
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062058894,
              0.0014512920211569933,
              0.0015219067048319879
            ],
            "target_residual": 0.7035542872394224,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0005551230941755322,
            "step_scale": 0.17014829641868498,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.000570844745597,
              1.0000075827637855,
              0.9990448789645799
            ],
            "cell_volume_ratio": 0.9996227583301273,
            "cell_rmsd_from_input_A": 0.006264239907774087
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.09173665185249685,
              -0.0033920698616221935,
              0.08358753971822645
            ],
            "branch_aligned_reduced_polarization": [
              -0.09173665185249685,
              -0.0033920698616221935,
              0.08358753971822647
            ],
            "target_residual": 0.5831721912578437,
            "energy_eV": -48.60407537747189,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0004915434166040957,
            "step_scale": 0.190164888996569,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0010820167942487,
              1.000060784168738,
              0.9981920702182703
            ],
            "cell_volume_ratio": 0.9993328707279453,
            "cell_rmsd_from_input_A": 0.011848573808839668
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.17635418918139653,
              -0.015860163153977706,
              0.14417295232455712
            ],
            "branch_aligned_reduced_polarization": [
              -0.17635418918139656,
              -0.015860163153977706,
              0.14417295232455712
            ],
            "target_residual": 0.4812598502816581,
            "energy_eV": -43.94793285499401,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0004774952477857054,
            "step_scale": 0.2677462710990486,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0016345796254853,
              1.0002527674638786,
              0.9973737943611694
            ],
            "cell_volume_ratio": 0.9992565969724458,
            "cell_rmsd_from_input_A": 0.017237145422955274
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5036033145324939,
              -0.1182109564348429,
              0.3297336627345805
            ],
            "branch_aligned_reduced_polarization": [
              -0.5036033145324939,
              -0.1182109564348429,
              0.3297336627345805
            ],
            "target_residual": 0.20731000868902108,
            "energy_eV": -23.689464610684148,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0001845748860846351,
            "step_scale": 0.9175644765067542,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0018856029556118,
              1.000340157252291,
              0.9970879244003454
            ],
            "cell_volume_ratio": 0.9993078425599666,
            "cell_rmsd_from_input_A": 0.019171281812452402
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4775643452233517,
              0.020306199485901042,
              0.4689133930676968
            ],
            "branch_aligned_reduced_polarization": [
              -0.4775643452233517,
              0.020306199485901042,
              0.4689133930676968
            ],
            "target_residual": 0.04338291683810194,
            "energy_eV": -16.7240216083528,
            "max_atomic_step_A": 0.017832779149046848,
            "max_log_strain_component": 0.001268712814404179,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.6960264348060914,
            "cell_principal_stretches": [
              1.0024893946766311,
              1.0012076943692474,
              0.9951505619073501
            ],
            "cell_volume_ratio": 0.9988327139972252,
            "cell_rmsd_from_input_A": 0.031065620413873386
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5017611719367089,
              -0.0047012922268406705,
              0.5007734972116714
            ],
            "branch_aligned_reduced_polarization": [
              -0.5017611719367089,
              -0.0047012922268406705,
              0.5007734972116714
            ],
            "target_residual": 0.0050795839523790605,
            "energy_eV": -12.83270254244907
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0050795839523790605,
        "parent_symmetrization_rmsd_A": 0.312301459902053,
        "parent_cell_rmsd_A": 0.031065620413873386,
        "energy_eV": -12.83270254244907,
        "reduced_polarization": [
          -0.5017611719367089,
          -0.0047012922268406705,
          0.5007734972116714
        ],
        "cartesian_polarization_e_A2": [
          -0.011449453938534627,
          -0.002308177666116739,
          0.018608858336071944
        ],
        "ranking_score": 0.8302270329102794
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062058894,
              0.0014512920211570135,
              0.0015219067048319857
            ],
            "target_residual": 0.7036044696963248,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005941094089213502,
            "step_scale": 0.2267960101383727,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.000719517201224,
              0.9998429671719069,
              0.9993135604014585
            ],
            "cell_volume_ratio": 0.9998755457527804,
            "cell_rmsd_from_input_A": 0.004647605975534203
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.11250512672730412,
              0.12113054950164324,
              0.0057031959548871115
            ],
            "branch_aligned_reduced_polarization": [
              -0.11250512672730412,
              0.12113054950164326,
              0.0057031959548871115
            ],
            "target_residual": 0.5419657404095293,
            "energy_eV": -47.947728665809265,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0006407423091224944,
            "step_scale": 0.3157948146819075,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0014734981956517,
              0.9996458624038501,
              0.9985442017954194
            ],
            "cell_volume_ratio": 0.9996614117703274,
            "cell_rmsd_from_input_A": 0.00976517576038183
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.24635014521571402,
              0.21878770661848967,
              -0.007738871577162833
            ],
            "branch_aligned_reduced_polarization": [
              -0.24635014521571402,
              0.21878770661848967,
              -0.007738871577162833
            ],
            "target_residual": 0.3787855500336118,
            "energy_eV": -39.59954961698541,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0002576710515942029,
            "step_scale": 0.45612026379465237,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0018311900410284,
              0.9996184845935948,
              0.9983066114130766
            ],
            "cell_volume_ratio": 0.9997531337410536,
            "cell_rmsd_from_input_A": 0.0115469984050526
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4605755267079512,
              0.5584856001011393,
              0.11714452034790283
            ],
            "branch_aligned_reduced_polarization": [
              -0.4605755267079512,
              0.5584856001011393,
              0.11714452034790283
            ],
            "target_residual": 0.1367395084132091,
            "energy_eV": -11.86493545823553,
            "max_atomic_step_A": 0.04663661601987598,
            "max_log_strain_component": 3.315744827892804e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.001827590658993,
              0.9996019061184902,
              0.9983194678284866
            ],
            "cell_volume_ratio": 0.9997458359606625,
            "cell_rmsd_from_input_A": 0.01142421318946299
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4938534269099599,
              0.4969722156186539,
              0.008978192431187856
            ],
            "branch_aligned_reduced_polarization": [
              -0.4938534269099599,
              0.4969722156186539,
              0.008978192431187856
            ],
            "target_residual": 0.011294059427086748,
            "energy_eV": -15.87031954959003,
            "max_atomic_step_A": 0.00480754728232454,
            "max_log_strain_component": 0.0002443269841020741,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.7265963826627893,
            "cell_principal_stretches": [
              1.001813707304586,
              0.9995410171257864,
              0.9982759878180198
            ],
            "cell_volume_ratio": 0.9996275456615517,
            "cell_rmsd_from_input_A": 0.009887619805503432
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5000586162128866,
              0.5000038483510356,
              -3.829644178553433e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000586162128866,
              0.5000038483510356,
              -3.829644178553433e-05
            ],
            "target_residual": 7.012337464992952e-05,
            "energy_eV": -15.516990417703344
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 7.012337464992952e-05,
        "parent_symmetrization_rmsd_A": 0.2998589321949019,
        "parent_cell_rmsd_A": 0.009887619805503432,
        "energy_eV": -15.516990417703344,
        "reduced_polarization": [
          -0.5000586162128866,
          0.5000038483510356,
          -3.829644178553433e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.011379248987022328,
          0.01778938646287802,
          -8.020773104273929e-06
        ],
        "ranking_score": 0.8024710838955775
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211570135,
              0.0015219067048319879
            ],
            "target_residual": 0.7050131324862116,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005312283755398648,
            "step_scale": 0.22214165037695482,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0007099537453874,
              1.000218195113025,
              0.9994608398027934
            ],
            "cell_volume_ratio": 1.0003886430652016,
            "cell_rmsd_from_input_A": 0.004391817267450551
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0003191748093588794,
              0.11640076723658851,
              0.10867776937384777
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003191748093588794,
              0.11640076723658854,
              0.10867776937384777
            ],
            "target_residual": 0.5479795264710757,
            "energy_eV": -47.759665566809204,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00044303723784528933,
            "step_scale": 0.2566120326715632,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0013469498602083,
              1.0003950706815377,
              0.9989327274931706
            ],
            "cell_volume_ratio": 1.0006734203967464,
            "cell_rmsd_from_input_A": 0.008463574179586833
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.011983863512194779,
              0.20385986604924866,
              0.20054756332402207
            ],
            "branch_aligned_reduced_polarization": [
              0.011983863512194779,
              0.20385986604924866,
              0.20054756332402207
            ],
            "target_residual": 0.4213245230843185,
            "energy_eV": -41.10083812025534,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00034377379030368075,
            "step_scale": 0.2780895674878636,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0018962371300137,
              1.0004979665283602,
              0.9984568366212879
            ],
            "cell_volume_ratio": 1.0008482884377237,
            "cell_rmsd_from_input_A": 0.011994658111236749
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.09766781207262094,
              0.4635974568642327,
              0.30706089669659903
            ],
            "branch_aligned_reduced_polarization": [
              0.09766781207262094,
              0.4635974568642327,
              0.30706089669659903
            ],
            "target_residual": 0.21929351163526165,
            "energy_eV": -20.082655123696558,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00018650708762287454,
            "step_scale": 0.8579067273987249,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0021369562909044,
              1.0005859422349812,
              0.9981312329097525
            ],
            "cell_volume_ratio": 1.000850292765483,
            "cell_rmsd_from_input_A": 0.014085458001408221
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.00996483006411574,
              0.4839209848475929,
              0.45251027558625423
            ],
            "branch_aligned_reduced_polarization": [
              0.00996483006411574,
              0.4839209848475929,
              0.45251027558625423
            ],
            "target_residual": 0.051118553298891034,
            "energy_eV": -8.695447124762733,
            "max_atomic_step_A": 0.02524125662779586,
            "max_log_strain_component": 0.0027603018382819982,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.313263253057794,
            "cell_principal_stretches": [
              1.0027089480974483,
              1.0015139457155677,
              0.9937559367696184
            ],
            "cell_volume_ratio": 0.9979565381588622,
            "cell_rmsd_from_input_A": 0.03942614025108098
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.0019482638807409548,
              0.5001256606083481,
              0.50269606472027
            ],
            "branch_aligned_reduced_polarization": [
              -0.0019482638807409548,
              0.5001256606083481,
              0.50269606472027
            ],
            "target_residual": 0.0033287066126912583,
            "energy_eV": -5.789186876339965
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0033287066126912583,
        "parent_symmetrization_rmsd_A": 0.38024920555906583,
        "parent_cell_rmsd_A": 0.03942614025108098,
        "energy_eV": -5.789186876339965,
        "reduced_polarization": [
          -0.0019482638807409548,
          0.5001256606083481,
          0.50269606472027
        ],
        "cartesian_polarization_e_A2": [
          -0.007456863330877036,
          0.015750716470540084,
          0.01863393321452394
        ],
        "ranking_score": 0.8967631538472185
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0035061739062059115,
              0.0014512920211569933,
              0.0015219067048319857
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035061739062058894,
              0.0014512920211570135,
              0.0015219067048319879
            ],
            "target_residual": 0.8622861143911658,
            "energy_eV": -49.63548193785046,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006993887407294434,
            "step_scale": 0.19177974031626757,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0008571591976598,
              1.000019190064592,
              0.9990259210805804
            ],
            "cell_volume_ratio": 0.9999014331424074,
            "cell_rmsd_from_input_A": 0.006625296477691239
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.10234505733127024,
              0.09730436157415988,
              0.1003232759779329
            ],
            "branch_aligned_reduced_polarization": [
              -0.10234505733127025,
              0.09730436157415989,
              0.10032327597793289
            ],
            "target_residual": 0.6928453755067413,
            "energy_eV": -47.7841834133616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006633036292233061,
            "step_scale": 0.24957239669233172,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0016937977268734,
              1.0000624519630774,
              0.998101186944352
            ],
            "cell_volume_ratio": 0.9998542074245969,
            "cell_rmsd_from_input_A": 0.012957437152559875
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2032875001819547,
              0.17978646639800297,
              0.20396303198592025
            ],
            "branch_aligned_reduced_polarization": [
              -0.20328750018195474,
              0.179786466398003,
              0.20396303198592025
            ],
            "target_residual": 0.5274589093769485,
            "energy_eV": -38.640975011083654,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003249150444449214,
            "step_scale": 0.25645150280628914,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0021564829509908,
              1.0000972148337377,
              0.9976825756172465
            ],
            "cell_volume_ratio": 0.9999312597840786,
            "cell_rmsd_from_input_A": 0.0159529876471975
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3273204896649042,
              0.4798523943335103,
              0.32081254290134364
            ],
            "branch_aligned_reduced_polarization": [
              -0.3273204896649042,
              0.4798523943335103,
              0.32081254290134364
            ],
            "target_residual": 0.2496643428388276,
            "energy_eV": -11.284545712316072,
            "max_atomic_step_A": 0.07973790680781853,
            "max_log_strain_component": 9.782241359367144e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06531207785926618,
            "cell_principal_stretches": [
              1.0022879424429734,
              1.0001546275325632,
              0.9974993719719575
            ],
            "cell_volume_ratio": 0.9999361868827773,
            "cell_rmsd_from_input_A": 0.017184521568302486
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.6180369612427367,
              0.46696188514954273,
              0.5906862592619112
            ],
            "branch_aligned_reduced_polarization": [
              -0.6180369612427367,
              0.46696188514954273,
              0.5906862592619112
            ],
            "target_residual": 0.15247373174160164,
            "energy_eV": 10.95424679297421,
            "max_atomic_step_A": 0.033562022073259895,
            "max_log_strain_component": 0.00234979188068999,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.970167099124729,
            "cell_principal_stretches": [
              1.0028691846682256,
              1.000179532396253,
              0.9988870400943362
            ],
            "cell_volume_ratio": 1.001932878597258,
            "cell_rmsd_from_input_A": 0.015870936289645626
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.48031131561202667,
              0.49073028921338235,
              0.4795221288256029
            ],
            "branch_aligned_reduced_polarization": [
              -0.48031131561202667,
              0.49073028921338235,
              0.4795221288256029
            ],
            "target_residual": 0.029881684002612093,
            "energy_eV": 2.473019673818353
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.029881684002612093,
        "parent_symmetrization_rmsd_A": 0.36163206189361374,
        "parent_cell_rmsd_A": 0.015870936289645626,
        "energy_eV": 2.473019673818353,
        "reduced_polarization": [
          -0.48031131561202667,
          0.49073028921338235,
          0.4795221288256029
        ],
        "cartesian_polarization_e_A2": [
          -0.014643977136520886,
          0.015433945547327323,
          0.017842606951260366
        ],
        "ranking_score": 0.9253631639712494
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11
        ],
        "endpoint_rmsd_A": 0.03419200293584494,
        "minimum_distance_A_by_image": [
          1.3788291237908448,
          1.3785531717190407,
          1.3783159851641231,
          1.378117584141787,
          1.377957985405278,
          1.3778372024383283,
          1.3777552454494626,
          1.3777121213676928,
          1.3777078338395818
        ],
        "minimum_distance_A": 1.3777078338395818,
        "minimum_distance_floor_A": 0.0,
        "geometry_valid": true,
        "parameters": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "cell_mode": "variable_cell",
        "cell_volume_A3_by_image": [
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256,
          221.4313886941256
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.4071476653769107e-16,
        -1.8728150004298233e-16,
        -3.840260011378779e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -49.63548193785045,
          -49.63587905355331,
          -49.63621631849166,
          -49.63649670590258,
          -49.63672272922917,
          -49.636896448885174,
          -49.63701943783733,
          -49.63709279361363,
          -49.63711717268606
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.625460820804329e-05,
            4.53522633720724e-05,
            5.662957554040186e-05
          ],
          [
            -6.679313040597131e-05,
            3.961777472064503e-05,
            4.96168314957025e-05
          ],
          [
            -5.730341083527488e-05,
            3.390889049128821e-05,
            4.257863202746679e-05
          ],
          [
            -4.778948563437446e-05,
            2.8222499700133186e-05,
            3.551815407833053e-05
          ],
          [
            -3.825546217085432e-05,
            2.2555103627500983e-05,
            2.8438580635755155e-05
          ],
          [
            -2.8705487113476627e-05,
            1.6902912452761424e-05,
            2.134314621083438e-05
          ],
          [
            -1.9143607222540993e-05,
            1.1262167316432798e-05,
            1.4235542958734727e-05
          ],
          [
            -9.573788685236747e-06,
            5.629140657912094e-06,
            7.119807062303213e-06
          ],
          [
            6.455327551503592e-18,
            -5.076519724968844e-18,
            -1.4289462929541932e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4072944198861848e-16,
            -1.8726882024255875e-16,
            -3.8402440949436567e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0035061739062060004,
            0.0014512920211571245,
            0.0015219067048318768
          ],
          [
            -0.0030723871621742282,
            0.001268247143627943,
            0.001333440835556865
          ],
          [
            -0.0026367939983262256,
            0.001085842268668813,
            0.0011442908576797528
          ],
          [
            -0.0021996519255219615,
            0.0009039998973394692,
            0.0009545421507970442
          ],
          [
            -0.0017612282362124976,
            0.0007226316539217237,
            0.000764280256958294
          ],
          [
            -0.001321795956640337,
            0.0005416411434642221,
            0.0005735921028986457
          ],
          [
            -0.0008816144908924683,
            0.0003609342703212448,
            0.00038257691443166486
          ],
          [
            -0.0004409325391936947,
            0.00018041889280584478,
            0.00019134316303492938
          ],
          [
            1.1102230246251565e-16,
            -1.6653345369377348e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -49.63711717268606,
          -49.637092793613625,
          -49.637019437837324,
          -49.63689644888519,
          -49.63672272922917,
          -49.63649670590258,
          -49.636216318491655,
          -49.635879053553325,
          -49.63548193785048
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.455327551503592e-18,
            -5.076519724968844e-18,
            -1.4289462929541932e-17
          ],
          [
            9.573788685216065e-06,
            -5.629140657903007e-06,
            -7.119807062304967e-06
          ],
          [
            1.9143607222528962e-05,
            -1.1262167316390557e-05,
            -1.4235542958719435e-05
          ],
          [
            2.870548711351655e-05,
            -1.6902912452757725e-05,
            -2.134314621087186e-05
          ],
          [
            3.82554621709326e-05,
            -2.2555103627560837e-05,
            -2.8438580635777215e-05
          ],
          [
            4.7789485634379166e-05,
            -2.8222499700173233e-05,
            -3.551815407835272e-05
          ],
          [
            5.7303410835347326e-05,
            -3.390889049133453e-05,
            -4.257863202752846e-05
          ],
          [
            6.679313040598471e-05,
            -3.961777472063481e-05,
            -4.961683149568307e-05
          ],
          [
            7.625460820800888e-05,
            -4.5352263372047264e-05,
            -5.6629575540421165e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.0035061739062062737,
          -0.0014512920211574901,
          -0.0015219067048326091
        ],
        "actual_opposite_endpoint_branch_residual": 2.6739356803550815e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4071476653769107e-16,
            -1.8728150004298233e-16,
            -3.840260011378779e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0035061739062059926,
            0.0014512920211571156,
            0.0015219067048318408
          ],
          [
            -0.003072387162174229,
            0.0012682471436278988,
            0.0013334408355568162
          ],
          [
            -0.002636793998326237,
            0.0010858422686688307,
            0.0011442908576798
          ],
          [
            -0.002199651925521944,
            0.0009039998973395162,
            0.000954542150797093
          ],
          [
            -0.00176122823621252,
            0.000722631653921705,
            0.0007642802569582811
          ],
          [
            -0.00132179595664035,
            0.0005416411434641953,
            0.0005735921028986162
          ],
          [
            -0.0008816144908924509,
            0.00036093427032119336,
            0.0003825769144316342
          ],
          [
            -0.00044093253919369967,
            0.0001804188928057964,
            0.0001913431630349716
          ],
          [
            1.4072944198861848e-16,
            -1.8726882024255875e-16,
            -3.8402440949436567e-16
          ],
          [
            0.000440932539192454,
            -0.0001804188928055465,
            -0.00019134316303501874
          ],
          [
            0.0008816144908924656,
            -0.00036093427031995857,
            -0.0003825769144312232
          ],
          [
            0.001321795956642442,
            -0.0005416411434642084,
            -0.0005735921028996235
          ],
          [
            0.0017612282362164688,
            -0.0007226316539234559,
            -0.0007642802569588741
          ],
          [
            0.0021996519255213817,
            -0.0009039998973407109,
            -0.0009545421507976892
          ],
          [
            0.002636793998329409,
            -0.001085842268670325,
            -0.0011442908576814574
          ],
          [
            0.0030723871621755232,
            -0.001268247143627551,
            -0.0013334408355562943
          ],
          [
            0.0035061739062038147,
            -0.0014512920211564697,
            -0.00152190670483236
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0035061739062060004,
            0.0014512920211571245,
            0.0015219067048318768
          ],
          [
            -0.0030723871621742282,
            0.001268247143627943,
            0.001333440835556865
          ],
          [
            -0.0026367939983262256,
            0.001085842268668813,
            0.0011442908576797528
          ],
          [
            -0.0021996519255219615,
            0.0009039998973394692,
            0.0009545421507970442
          ],
          [
            -0.0017612282362124976,
            0.0007226316539217237,
            0.000764280256958294
          ],
          [
            -0.001321795956640337,
            0.0005416411434642221,
            0.0005735921028986457
          ],
          [
            -0.0008816144908924683,
            0.0003609342703212448,
            0.00038257691443166486
          ],
          [
            -0.0004409325391936947,
            0.00018041889280584478,
            0.00019134316303492938
          ],
          [
            1.1102230246251565e-16,
            -1.6653345369377348e-16,
            -3.885780586188048e-16
          ],
          [
            0.00044093253919241793,
            -0.00018041889280556722,
            -0.0001913431630350404
          ],
          [
            0.0008816144908924128,
            -0.00036093427031996805,
            -0.00038257691443122077
          ],
          [
            0.001321795956642391,
            -0.0005416411434642221,
            -0.0005735921028996449
          ],
          [
            0.0017612282362164944,
            -0.0007226316539234445,
            -0.0007642802569588492
          ],
          [
            0.0021996519255214064,
            -0.0009039998973406904,
            -0.0009545421507977103
          ],
          [
            0.0026367939983293898,
            -0.0010858422686703117,
            -0.0011442908576814736
          ],
          [
            0.003072387162175505,
            -0.0012682471436275544,
            -0.0013334408355563099
          ],
          [
            0.00350617390620378,
            -0.0014512920211564584,
            -0.0015219067048323764
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.032025183319884e-16,
        "parent_symmetrization_rmsd_A": 0.03419200293584494,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -49.63711717268608,
        "reduced_polarization": [
          -6.408053248411082e-16,
          -1.2876812163840988e-16,
          -2.59385983224707e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.956712215698046e-18,
          -3.509692649361176e-18,
          -9.651654785743235e-18
        ],
        "ranking_score": 0.03419200293584635
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 157,
      "full_response": 37,
      "energy_polarization": 120
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 182,
      "full_response": 62,
      "energy_polarization": 120
    },
    "elapsed_seconds": 303.0463597140042
  }
}