{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 9,
  "input_formula": "S6W3",
  "input_spacegroup": "R3m",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -70.67751928550938,
  "input_cartesian_polarization_e_A2": [
    -1.7537669423242372e-09,
    1.1312676794611882e-09,
    -0.0003606181418924574
  ],
  "input_reduced_polarization": [
    -6.481753534320156e-08,
    7.692828453351622e-08,
    -0.0031715516741375608
  ],
  "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": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "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": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "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": 4.540999379571965e-15,
      "parent_symmetrization_rmsd_A": 0.7511220207416279,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -61.245023212990645,
      "reduced_polarization": [
        -1.4063868073395216e-15,
        4.279649792907585e-15,
        -5.721443554561892e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.021618304641012e-17,
        6.293432278500632e-17,
        -6.505510726542857e-17
      ],
      "ranking_score": 0.751122020741637
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "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": 1.1510723481538637e-14,
      "parent_symmetrization_rmsd_A": 0.7511221389828072,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -61.24501908496608,
      "reduced_polarization": [
        -8.905184202483717e-15,
        -7.279179989150185e-15,
        -4.560570949288464e-16
      ],
      "cartesian_polarization_e_A2": [
        -8.941206571791626e-17,
        -1.0704386695531396e-16,
        -5.185552028403726e-17
      ],
      "ranking_score": 0.7511221389828302
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "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": 4.326259136569806e-15,
      "parent_symmetrization_rmsd_A": 0.7511221484108969,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -61.245018667859654,
      "reduced_polarization": [
        -2.226915590437372e-15,
        3.692920126613537e-15,
        -3.459855607873744e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.916765440501014e-17,
        5.4306178896391167e-17,
        -3.933994551316624e-17
      ],
      "ranking_score": 0.7511221484109055
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3m",
      "spacegroup_number": 160,
      "pointgroup": "3m",
      "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": 0.0004236429564976455,
      "parent_symmetrization_rmsd_A": 0.06279279060553619,
      "parent_cell_rmsd_A": 0.25352644549208614,
      "energy_eV": -70.40847269965893,
      "reduced_polarization": [
        1.3056501852758857e-07,
        5.738736249116788e-08,
        -0.00042364293249095105
      ],
      "cartesian_polarization_e_A2": [
        1.747379463624728e-09,
        8.507912315558483e-10,
        -4.828875747192262e-05
      ],
      "ranking_score": 0.627021687891553
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "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": 1.932794466943677e-14,
      "parent_symmetrization_rmsd_A": 0.7511486418770752,
      "parent_cell_rmsd_A": 0.25352644549208614,
      "energy_eV": -61.091645075402475,
      "reduced_polarization": [
        -4.5523608650201865e-15,
        1.742320903363768e-14,
        -7.0197751153158985e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.279150284336757e-16,
        2.5927360445772406e-16,
        -8.001460451050826e-16
      ],
      "ranking_score": 0.8145302532501354
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "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": 1.8490177114082674e-14,
      "parent_symmetrization_rmsd_A": 0.751148760114064,
      "parent_cell_rmsd_A": 0.25352644549208614,
      "energy_eV": -61.09164178434506,
      "reduced_polarization": [
        -1.5202828807315296e-14,
        -1.0480127585492602e-14,
        -9.631052680823023e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.7119044936963318e-16,
        -1.559541072069627e-16,
        -1.0977916080341041e-16
      ],
      "ranking_score": 0.8145303714871225
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3m",
      "spacegroup_number": 160,
      "pointgroup": "3m",
      "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": 0.37126619157269164,
      "parent_symmetrization_rmsd_A": 0.4215847154288491,
      "parent_cell_rmsd_A": 1.4211505543172804,
      "energy_eV": -62.033464582922086,
      "reduced_polarization": [
        3.4015663950067724e-07,
        2.6625155474884136e-07,
        -0.12873380842755966
      ],
      "cartesian_polarization_e_A2": [
        6.15265535660988e-09,
        5.615697261952185e-09,
        -0.015082033824760565
      ],
      "ranking_score": 2.0194047371535526
    },
    {
      "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,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.32269463484278993,
      "parent_symmetrization_rmsd_A": 0.3252465281505266,
      "parent_cell_rmsd_A": 0.30225799133896486,
      "energy_eV": -65.16417656222268,
      "reduced_polarization": [
        -0.03476385896812189,
        0.1792342497256924,
        -0.005712697867611474
      ],
      "cartesian_polarization_e_A2": [
        -0.0019003300322012503,
        0.0026548096336046355,
        -0.0006299354613413577
      ],
      "ranking_score": 1.5462002956708476
    },
    {
      "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": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.40053631988873517,
      "parent_symmetrization_rmsd_A": 0.14086116823407183,
      "parent_cell_rmsd_A": 0.08223649605059417,
      "energy_eV": -68.91423049484122,
      "reduced_polarization": [
        -0.09990116198626693,
        0.0184771254203688,
        -0.0029764418811237593
      ],
      "cartesian_polarization_e_A2": [
        -0.0018243245115963647,
        0.00016562520667509463,
        -0.00032840082063521144
      ],
      "ranking_score": 1.4624929320241908
    },
    {
      "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": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.5497692150303544,
      "parent_symmetrization_rmsd_A": 0.41771959785624785,
      "parent_cell_rmsd_A": 1.3326554974604508,
      "energy_eV": -62.0334072068642,
      "reduced_polarization": [
        -0.007377241139597163,
        0.10272416366849986,
        -0.12004779777534214
      ],
      "cartesian_polarization_e_A2": [
        -0.0009172473387480522,
        0.0014476826831762353,
        -0.013932663553280477
      ],
      "ranking_score": 2.3504219022820694
    },
    {
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.5294536639395837,
      "parent_symmetrization_rmsd_A": 0.42365214945345236,
      "parent_cell_rmsd_A": 1.422242004136729,
      "energy_eV": -61.906583070598955,
      "reduced_polarization": [
        -0.12344617061920961,
        -0.0005470748276700465,
        -0.12780637223772198
      ],
      "cartesian_polarization_e_A2": [
        -0.0019732420620146474,
        -5.0221800362452406e-05,
        -0.014965606755114347
      ],
      "ranking_score": 2.338119978366802
    },
    {
      "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": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.595337031769405,
      "parent_symmetrization_rmsd_A": 0.14501785084108604,
      "parent_cell_rmsd_A": 0.14731993130324006,
      "energy_eV": -68.9410828745851,
      "reduced_polarization": [
        -0.06882097661923588,
        0.08951809038754896,
        -0.00392849504665023
      ],
      "cartesian_polarization_e_A2": [
        -0.001816068083884573,
        0.0012381742485175402,
        -0.0004344968601973623
      ],
      "ranking_score": 1.872521897205706
    },
    {
      "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": 0.6705967666370256,
      "parent_symmetrization_rmsd_A": 0.41914183827944873,
      "parent_cell_rmsd_A": 1.3324488839617739,
      "energy_eV": -61.87890113961294,
      "reduced_polarization": [
        -0.1204052721710908,
        0.09916794994100298,
        -0.11928812249414723
      ],
      "cartesian_polarization_e_A2": [
        -0.0026592101359189935,
        0.00132982138799145,
        -0.01383874044779121
      ],
      "ranking_score": 2.5934475925439435
    }
  ],
  "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": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "target_residual": 0.0031715516757328797,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.05047176790503478,
            "max_log_strain_component": 0.010628201439906199,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              0.9987685735739381,
              0.9987685207962116,
              0.9894280783314211
            ],
            "cell_volume_ratio": 0.9869927107909358,
            "cell_rmsd_from_input_A": 0.25352644549208614
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3056501852758857e-07,
              5.738736249116788e-08,
              -0.00042364293249095105
            ],
            "branch_aligned_reduced_polarization": [
              1.3056501852758857e-07,
              5.738736249116788e-08,
              -0.00042364293249095105
            ],
            "target_residual": 0.0004236429564976455,
            "energy_eV": -70.40847269965893
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3m",
        "spacegroup_number": 160,
        "pointgroup": "3m",
        "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": 0.0004236429564976455,
        "parent_symmetrization_rmsd_A": 0.06279279060553619,
        "parent_cell_rmsd_A": 0.25352644549208614,
        "energy_eV": -70.40847269965893,
        "reduced_polarization": [
          1.3056501852758857e-07,
          5.738736249116788e-08,
          -0.00042364293249095105
        ],
        "cartesian_polarization_e_A2": [
          1.747379463624728e-09,
          8.507912315558483e-10,
          -4.828875747192262e-05
        ],
        "ranking_score": 0.627021687891553
      },
      "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": [
          -70.67751928550939,
          -70.67259462723092,
          -70.65944790269825,
          -70.63809491319694,
          -70.6085450845226,
          -70.57080271188326,
          -70.52487084684026,
          -70.4707561065364,
          -70.40847269965892
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.7537669297276314e-09,
            1.1312676861685406e-09,
            -0.00036061814189242164
          ],
          [
            -1.5056993495752226e-09,
            9.97346864982393e-10,
            -0.00031578921863051036
          ],
          [
            -1.2000542012092515e-09,
            8.913575423516795e-10,
            -0.0002720509475939574
          ],
          [
            -8.382334999813543e-10,
            8.135456694519797e-10,
            -0.00022956701597705656
          ],
          [
            -4.2190798686419804e-10,
            7.640818710837903e-10,
            -0.00018863347160614837
          ],
          [
            4.701653926627601e-11,
            7.430698678418864e-10,
            -0.00014963841771873718
          ],
          [
            5.664297130784084e-10,
            7.505490968747941e-10,
            -0.00011300043986239874
          ],
          [
            1.1340383953077184e-09,
            7.864909357465936e-10,
            -7.910964983870875e-05
          ],
          [
            1.7473794532668448e-09,
            8.507912241542589e-10,
            -4.828875747164301e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.6870698915939367e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.687069891593937e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ]
        ],
        "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": [
          [
            -6.481753439535609e-08,
            7.692828496441706e-08,
            -0.0031715516741372407
          ],
          [
            -5.4445380759382545e-08,
            6.789708417720419e-08,
            -0.0027764364249719953
          ],
          [
            -3.984103252863136e-08,
            6.073770197900785e-08,
            -0.002391150391964969
          ],
          [
            -2.1094555824330286e-08,
            5.5460539272189635e-08,
            -0.0020171228656659657
          ],
          [
            1.6870699282023338e-09,
            5.2071481682069987e-08,
            -0.0016569440172516936
          ],
          [
            2.8382675765215026e-08,
            5.057276020181689e-08,
            -0.0013140091800135645
          ],
          [
            5.8858949825157936e-08,
            5.096320676578614e-08,
            -0.0009919770859730392
          ],
          [
            9.297148395592814e-08,
            5.323788410116492e-08,
            -0.0006942520692625465
          ],
          [
            1.305650176863793e-07,
            5.7387361973582074e-08,
            -0.0004236429324884772
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -70.40847269965893,
          -70.34927167985887,
          -70.28117950424537,
          -70.2042999856665,
          -70.11875631541955,
          -70.02468595512212,
          -69.92223546097615,
          -69.81155590524709,
          -69.69279918257666
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.7473794601757979e-09,
            8.507912332295758e-10,
            -4.828875747205358e-05
          ],
          [
            1.882564068288958e-09,
            6.805802098946248e-10,
            -1.167799714476206e-05
          ],
          [
            1.981735835057123e-09,
            4.675315874882572e-10,
            3.353171181780103e-05
          ],
          [
            2.0448267939917063e-09,
            2.133861131549665e-10,
            8.785689021187617e-05
          ],
          [
            2.071677740719146e-09,
            -8.012692378761619e-11,
            0.00015148140774941528
          ],
          [
            2.062044569805685e-09,
            -4.1135019721268216e-10,
            0.0002242467261654419
          ],
          [
            2.0156483939841975e-09,
            -7.78705559481833e-10,
            0.00030566716767389216
          ],
          [
            1.932244897725434e-09,
            -1.1806614913980464e-09,
            0.0003949614609044255
          ],
          [
            1.811697391001718e-09,
            -1.6156759641328923e-09,
            0.0004910921252481821
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.305650183831093e-07,
            5.738736260364307e-08,
            -0.0004236429324921001
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809744e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777028e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.305650183831093e-07,
            5.738736260364307e-08,
            -0.0004236429324921001
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809742e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777027e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.2848388102076357e-07,
          3.878245360679378e-08,
          0.0023221751630304694
        ],
        "actual_opposite_endpoint_branch_residual": 0.001996864507915987
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.6870698915939367e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809744e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777028e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.687069891593937e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809742e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777027e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "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": [
          [
            -6.481753439535609e-08,
            7.692828496441706e-08,
            -0.0031715516741372407
          ],
          [
            -5.4445380759382545e-08,
            6.789708417720419e-08,
            -0.0027764364249719953
          ],
          [
            -3.984103252863136e-08,
            6.073770197900785e-08,
            -0.002391150391964969
          ],
          [
            -2.1094555824330286e-08,
            5.5460539272189635e-08,
            -0.0020171228656659657
          ],
          [
            1.6870699282023338e-09,
            5.2071481682069987e-08,
            -0.0016569440172516936
          ],
          [
            2.8382675765215026e-08,
            5.057276020181689e-08,
            -0.0013140091800135645
          ],
          [
            5.8858949825157936e-08,
            5.096320676578614e-08,
            -0.0009919770859730392
          ],
          [
            9.297148395592814e-08,
            5.323788410116492e-08,
            -0.0006942520692625465
          ],
          [
            1.305650176863793e-07,
            5.7387361973582074e-08,
            -0.0004236429324884772
          ],
          [
            1.32684148335116e-07,
            4.5848249752289405e-08,
            -0.00010248400415385772
          ],
          [
            1.312799161601319e-07,
            3.139974080745844e-08,
            0.00029435894070040103
          ],
          [
            1.2640861890567123e-07,
            1.4159342698327748e-08,
            0.0007714914527009453
          ],
          [
            1.1812369082875307e-07,
            -5.7536174713490595e-09,
            0.0013306027300350465
          ],
          [
            1.0647278014808137e-07,
            -2.82229928316724e-08,
            0.0019703753911414212
          ],
          [
            9.149910251693427e-08,
            -5.313730644385117e-08,
            0.002686615041257223
          ],
          [
            7.324534623265322e-08,
            -8.038850818348209e-08,
            0.0034725231952844604
          ],
          [
            5.1758814123559205e-08,
            -1.0986893955733379e-07,
            0.004319039646239253
          ]
        ]
      },
      "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": [
        0.0,
        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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375738
            ],
            "target_residual": 0.49682844832587264,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.09497706303477402,
            "max_log_strain_component": 0.02,
            "step_scale": 0.012012559581554417,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.020201340028448,
              1.002321457448798,
              1.0023214405564294
            ],
            "cell_volume_ratio": 1.0249435287880246,
            "cell_rmsd_from_input_A": 0.4919440658456367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.0043396182572283e-07,
              3.11556780887285e-07,
              -0.00997400288320578
            ],
            "branch_aligned_reduced_polarization": [
              4.0043396182572283e-07,
              3.11556780887285e-07,
              -0.009974002883205768
            ],
            "target_residual": 0.4900259971170569,
            "energy_eV": -69.81402225400691,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013389841425590842,
            "step_scale": 0.024442328919229463,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0339535386075789,
              1.003878692803328,
              1.00387861055347
            ],
            "cell_volume_ratio": 1.041989784597192,
            "cell_rmsd_from_input_A": 0.8324667205937334
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.720502196945527e-07,
              6.564319640864668e-07,
              -0.032130729454909406
            ],
            "branch_aligned_reduced_polarization": [
              9.720502196945527e-07,
              6.564319640864668e-07,
              -0.03213072945490941
            ],
            "target_residual": 0.46786927054656086,
            "energy_eV": -68.25563990867431,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005744073545111275,
            "step_scale": 0.058167450139226355,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0399097338111245,
              1.004547439166884,
              1.0045473875238506
            ],
            "cell_volume_ratio": 1.0493890368743912,
            "cell_rmsd_from_input_A": 0.9813649802393716
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.70077082401714e-07,
              4.89670654832152e-07,
              -0.0664595422778887
            ],
            "branch_aligned_reduced_polarization": [
              5.70077082401714e-07,
              4.89670654832152e-07,
              -0.0664595422778887
            ],
            "target_residual": 0.4335404577227627,
            "energy_eV": -65.39872911029445,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0043627334243814845,
            "step_scale": 0.07931192992048518,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.044456493704428,
              1.0050556768066512,
              1.0050556197173186
            ],
            "cell_volume_ratio": 1.055043998887286,
            "cell_rmsd_from_input_A": 1.0956045529847884
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              3.265226651199632e-07,
              3.158437505257271e-07,
              -0.09905168326525743
            ],
            "branch_aligned_reduced_polarization": [
              3.265226651199632e-07,
              3.158437505257271e-07,
              -0.09905168326525743
            ],
            "target_residual": 0.4009483167349999,
            "energy_eV": -62.5264808107506,
            "max_atomic_step_A": 0.047550973944120965,
            "max_log_strain_component": 0.02,
            "step_scale": 0.07322029249628004,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.471994357401023,
            "cell_principal_stretches": [
              1.0573043103526931,
              0.985154385168475,
              0.9851541513767802
            ],
            "cell_volume_ratio": 1.0261444234383073,
            "cell_rmsd_from_input_A": 1.4211505543172804
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              3.4015663950067724e-07,
              2.6625155474884136e-07,
              -0.12873380842755966
            ],
            "branch_aligned_reduced_polarization": [
              3.4015663950067724e-07,
              2.6625155474884136e-07,
              -0.12873380842755966
            ],
            "target_residual": 0.37126619157269164,
            "energy_eV": -62.033464582922086
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3m",
        "spacegroup_number": 160,
        "pointgroup": "3m",
        "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": 0.4995763570675294,
        "parent_symmetrization_rmsd_A": 0.06279279060553619,
        "parent_cell_rmsd_A": 0.25352644549208614,
        "energy_eV": -70.40847269965893,
        "reduced_polarization": [
          1.3056501852758857e-07,
          5.738736249116788e-08,
          -0.00042364293249095105
        ],
        "cartesian_polarization_e_A2": [
          1.747379463624728e-09,
          8.507912315558483e-10,
          -4.828875747192262e-05
        ],
        "ranking_score": 1.6253271161136165
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753534320156e-08,
              7.692828452032785e-08,
              -0.0031715516741375608
            ],
            "target_residual": 0.5000099817121127,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0149149078799619,
            "step_scale": 0.22429142954084513,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.020649914100646,
              0.9977090010941787,
              0.9791380612013046
            ],
            "cell_volume_ratio": 0.9970676518563297,
            "cell_rmsd_from_input_A": 0.06170160516042927
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.03595336895973565,
              0.10615436915639138,
              -0.0034888309930766843
            ],
            "branch_aligned_reduced_polarization": [
              0.03595336895973565,
              0.10615436915639137,
              -0.0034888309930766843
            ],
            "target_residual": 0.3954986695500418,
            "energy_eV": -69.51525563853947,
            "max_atomic_step_A": 0.054454765287008586,
            "max_log_strain_component": 0.02,
            "step_scale": 0.12511862706081836,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0412914473929902,
              0.9971259903261083,
              0.9591741770663543
            ],
            "cell_volume_ratio": 0.9959093641391571,
            "cell_rmsd_from_input_A": 0.09071625960803752
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.013091973072417057,
              0.12538579959095597,
              -0.0035199049808971577
            ],
            "branch_aligned_reduced_polarization": [
              0.013091973072417057,
              0.12538579959095597,
              -0.0035199049808971577
            ],
            "target_residual": 0.37485942516910364,
            "energy_eV": -69.3785093162713,
            "max_atomic_step_A": 0.0644794328852084,
            "max_log_strain_component": 0.02,
            "step_scale": 0.16323227477976088,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0639212144468078,
              0.9964414259204593,
              0.9383102308528893
            ],
            "cell_volume_ratio": 0.9947356779655836,
            "cell_rmsd_from_input_A": 0.12076152303038731
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.008252395505981,
              0.14552011530313017,
              -0.003746888542541977
            ],
            "branch_aligned_reduced_polarization": [
              -0.008252395505981,
              0.14552011530313014,
              -0.003746888542541977
            ],
            "target_residual": 0.3545957273572871,
            "energy_eV": -67.94912129700896,
            "max_atomic_step_A": 0.08578101289140869,
            "max_log_strain_component": 0.02,
            "step_scale": 0.21219649512411023,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.092667295240751,
              0.9923499098889336,
              0.9124863214473751
            ],
            "cell_volume_ratio": 0.9894164846552707,
            "cell_rmsd_from_input_A": 0.2239346168429808
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.045242894337341015,
              0.12429218329335298,
              -0.007271896653524879
            ],
            "branch_aligned_reduced_polarization": [
              -0.045242894337341015,
              0.12429218329335301,
              -0.007271896653524879
            ],
            "target_residual": 0.3784919596285168,
            "energy_eV": -65.21603954702596,
            "max_atomic_step_A": 0.0134525472799111,
            "max_log_strain_component": 0.02,
            "step_scale": 0.15525093143766067,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.056323620844071,
            "cell_principal_stretches": [
              1.069267904060761,
              0.9888589984384435,
              0.9185812530380709
            ],
            "cell_volume_ratio": 0.9712666541165375,
            "cell_rmsd_from_input_A": 0.30225799133896486
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.03476385896812189,
              0.1792342497256924,
              -0.005712697867611474
            ],
            "branch_aligned_reduced_polarization": [
              -0.03476385896812189,
              0.1792342497256924,
              -0.005712697867611474
            ],
            "target_residual": 0.32269463484278993,
            "energy_eV": -65.16417656222268
          }
        ],
        "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,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.32269463484278993,
        "parent_symmetrization_rmsd_A": 0.3252465281505266,
        "parent_cell_rmsd_A": 0.30225799133896486,
        "energy_eV": -65.16417656222268,
        "reduced_polarization": [
          -0.03476385896812189,
          0.1792342497256924,
          -0.005712697867611474
        ],
        "cartesian_polarization_e_A2": [
          -0.0019003300322012503,
          0.0026548096336046355,
          -0.0006299354613413577
        ],
        "ranking_score": 1.5462002956708476
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753533904566e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "target_residual": 0.50000999382262,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.07362000099526281,
            "max_log_strain_component": 0.02,
            "step_scale": 0.15542153478980833,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0200798811235698,
              0.9983608553941166,
              0.9799288385659479
            ],
            "cell_volume_ratio": 0.9979671948739663,
            "cell_rmsd_from_input_A": 0.04393036974951004
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.07018122386609259,
              -0.008355124089059097,
              -0.0031409583116698233
            ],
            "branch_aligned_reduced_polarization": [
              -0.0701812238660926,
              -0.008355124089059097,
              -0.0031409583116698233
            ],
            "target_residual": 0.4299114490623729,
            "energy_eV": -70.1595394284515,
            "max_atomic_step_A": 0.021791489370852336,
            "max_log_strain_component": 0.02,
            "step_scale": 0.0754464802303248,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.041051482619332,
              0.9979874668593346,
              0.9598381424161075
            ],
            "cell_volume_ratio": 0.9972299157673767,
            "cell_rmsd_from_input_A": 0.0665935683780487
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.07977486466532584,
              0.0019707464989148584,
              -0.003513711120885344
            ],
            "branch_aligned_reduced_polarization": [
              -0.07977486466532585,
              0.0019707464989148584,
              -0.003513711120885344
            ],
            "target_residual": 0.4202444459771589,
            "energy_eV": -69.57692097942925,
            "max_atomic_step_A": 0.024541933414738152,
            "max_log_strain_component": 0.02,
            "step_scale": 0.08485322256824453,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0625613871279038,
              0.9984337186029667,
              0.9403344955242453
            ],
            "cell_volume_ratio": 0.9975981553117164,
            "cell_rmsd_from_input_A": 0.07441594809095371
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.07376291528390382,
              0.01537375553750512,
              -0.0036778836577835454
            ],
            "branch_aligned_reduced_polarization": [
              -0.07376291528390383,
              0.01537375553750512,
              -0.0036778836577835454
            ],
            "target_residual": 0.4265301062935695,
            "energy_eV": -69.23451985887081,
            "max_atomic_step_A": 0.02193758739155854,
            "max_log_strain_component": 0.02,
            "step_scale": 0.07731699902015171,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0841160493839452,
              0.9991769329561536,
              0.9217468207750068
            ],
            "cell_volume_ratio": 0.9984580470057018,
            "cell_rmsd_from_input_A": 0.08108844766047785
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.04588571992456888,
              0.025004426061100187,
              -0.0037746226549398537
            ],
            "branch_aligned_reduced_polarization": [
              -0.04588571992456886,
              0.025004426061100187,
              -0.0037746226549398537
            ],
            "target_residual": 0.4548178189860852,
            "energy_eV": -68.50692665253936,
            "max_atomic_step_A": 0.012159331059876852,
            "max_log_strain_component": 0.02,
            "step_scale": 0.14519338678004295,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.8176020651901776,
            "cell_principal_stretches": [
              1.0564882821576138,
              0.9985104941955106,
              0.9317902366504162
            ],
            "cell_volume_ratio": 0.9829591590036697,
            "cell_rmsd_from_input_A": 0.08223649605059417
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.09990116198626693,
              0.0184771254203688,
              -0.0029764418811237593
            ],
            "branch_aligned_reduced_polarization": [
              -0.09990116198626692,
              0.0184771254203688,
              -0.0029764418811237593
            ],
            "target_residual": 0.40053631988873517,
            "energy_eV": -68.91423049484122
          }
        ],
        "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": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.40053631988873517,
        "parent_symmetrization_rmsd_A": 0.14086116823407183,
        "parent_cell_rmsd_A": 0.08223649605059417,
        "energy_eV": -68.91423049484122,
        "reduced_polarization": [
          -0.09990116198626693,
          0.0184771254203688,
          -0.0029764418811237593
        ],
        "cartesian_polarization_e_A2": [
          -0.0018243245115963647,
          0.00016562520667509463,
          -0.00032840082063521144
        ],
        "ranking_score": 1.4624929320241908
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753534320156e-08,
              7.692828452032785e-08,
              -0.0031715516741375738
            ],
            "target_residual": 0.704867668529072,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.09519231698085244,
            "max_log_strain_component": 0.02,
            "step_scale": 0.012012558432879137,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0202027065548944,
              1.0034249052411384,
              1.0012178578132127
            ],
            "cell_volume_ratio": 1.0249435213028952,
            "cell_rmsd_from_input_A": 0.4919433990042838
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.683966002630849e-05,
              0.004714056350210129,
              -0.009968507539681976
            ],
            "branch_aligned_reduced_polarization": [
              -5.683966002630849e-05,
              0.004714056350210105,
              -0.009968507539681981
            ],
            "target_residual": 0.6967345497466712,
            "energy_eV": -69.81076066662798,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.013409072399551174,
            "step_scale": 0.02434518136482934,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0339832665282633,
              1.007761791089335,
              1.000005388663393
            ],
            "cell_volume_ratio": 1.042014443667754,
            "cell_rmsd_from_input_A": 0.8329715509237192
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00174128584571912,
              0.014959809954996557,
              -0.031999684646752784
            ],
            "branch_aligned_reduced_polarization": [
              -0.00174128584571912,
              0.014959809954996572,
              -0.03199968464675279
            ],
            "target_residual": 0.6740113598493933,
            "energy_eV": -68.23949091659527,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005670666432769118,
            "step_scale": 0.05677728316883313,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0398948630461378,
              1.0128844504979326,
              0.9962267019734515
            ],
            "cell_volume_ratio": 1.0493189472624884,
            "cell_rmsd_from_input_A": 0.9800134713219816
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0052197041312242835,
              0.053128030112786086,
              -0.06545198542051062
            ],
            "branch_aligned_reduced_polarization": [
              -0.0052197041312242835,
              0.05312803011278611,
              -0.06545198542051062
            ],
            "target_residual": 0.6233408215070408,
            "energy_eV": -65.35330456597887,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.004228112824696779,
            "step_scale": 0.07706137080115814,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0443445343378042,
              1.0169072254226426,
              0.9932175837183744
            ],
            "cell_volume_ratio": 1.0547985665150645,
            "cell_rmsd_from_input_A": 1.0907719732079801
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.00765874953982163,
              0.08390810204930127,
              -0.09724740062604549
            ],
            "branch_aligned_reduced_polarization": [
              -0.00765874953982163,
              0.08390810204930127,
              -0.09724740062604548
            ],
            "target_residual": 0.5791379630858312,
            "energy_eV": -62.4482661491949,
            "max_atomic_step_A": 0.03684211595159126,
            "max_log_strain_component": 0.02,
            "step_scale": 0.05554919280262827,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.321973600991197,
            "cell_principal_stretches": [
              1.0538380295832486,
              1.0069346569768884,
              0.9728097315711512
            ],
            "cell_volume_ratio": 1.0322931892984368,
            "cell_rmsd_from_input_A": 1.3326554974604508
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.007377241139597163,
              0.10272416366849986,
              -0.12004779777534214
            ],
            "branch_aligned_reduced_polarization": [
              -0.007377241139597163,
              0.10272416366849985,
              -0.12004779777534214
            ],
            "target_residual": 0.5497692150303544,
            "energy_eV": -62.0334072068642
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3m",
        "spacegroup_number": 160,
        "pointgroup": "3m",
        "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": 0.7068072432803028,
        "parent_symmetrization_rmsd_A": 0.06279279060553619,
        "parent_cell_rmsd_A": 0.25352644549208614,
        "energy_eV": -70.40847269965893,
        "reduced_polarization": [
          1.3056501852758857e-07,
          5.738736249116788e-08,
          -0.00042364293249095105
        ],
        "cartesian_polarization_e_A2": [
          1.747379463624728e-09,
          8.507912315558483e-10,
          -4.828875747192262e-05
        ],
        "ranking_score": 2.0397888885391633
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753533904566e-08,
              7.692828453351622e-08,
              -0.0031715516741375738
            ],
            "target_residual": 0.7048676771198683,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.09514540939284105,
            "max_log_strain_component": 0.02,
            "step_scale": 0.012012558771068889,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0202024238979732,
              1.0038714512214553,
              1.0007727752694993
            ],
            "cell_volume_ratio": 1.0249435272237768,
            "cell_rmsd_from_input_A": 0.49194309412241777
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004987210742726404,
              -5.6146600729351565e-05,
              -0.009969196010060312
            ],
            "branch_aligned_reduced_polarization": [
              -0.0049872107427264,
              -5.6146600729351565e-05,
              -0.0099691960100603
            ],
            "target_residual": 0.6965399152523375,
            "energy_eV": -69.81100413554185,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01339338296348933,
            "step_scale": 0.02436488623168897,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0339650056164187,
              1.0092012985601972,
              0.998577353144946
            ],
            "cell_volume_ratio": 1.0419943244632923,
            "cell_rmsd_from_input_A": 0.8325667981652799
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.017623405675127712,
              0.0003656262396081908,
              -0.03202656910532374
            ],
            "branch_aligned_reduced_polarization": [
              -0.017623405675127712,
              0.0003656262396081908,
              -0.032026569105323754
            ],
            "target_residual": 0.6720762192328663,
            "energy_eV": -68.2409661141818,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006146379146257203,
            "step_scale": 0.05709872513529986,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0398681176724232,
              1.0160732764865585,
              0.9931030195027672
            ],
            "cell_volume_ratio": 1.0492949785727046,
            "cell_rmsd_from_input_A": 0.9795300720446096
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.06115565345720776,
              0.0012597114741603034,
              -0.06574276937710148
            ],
            "branch_aligned_reduced_polarization": [
              -0.06115565345720775,
              0.0012597114741603034,
              -0.0657427693771015
            ],
            "target_residual": 0.6173858515659698,
            "energy_eV": -65.35412490986424,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004847823078989347,
            "step_scale": 0.07805622946688004,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0443148538248466,
              1.0214848174558633,
              0.9887786601623855
            ],
            "cell_volume_ratio": 1.0547813837165718,
            "cell_rmsd_from_input_A": 1.0904194921728398
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.09921914238569135,
              0.0007758009714507484,
              -0.09793813532514681
            ],
            "branch_aligned_reduced_polarization": [
              -0.09921914238569135,
              0.0007758009714507484,
              -0.09793813532514684
            ],
            "target_residual": 0.5676967859016184,
            "energy_eV": -62.44351200997506,
            "max_atomic_step_A": 0.04863535690072979,
            "max_log_strain_component": 0.02,
            "step_scale": 0.0739232456671584,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.190380483407482,
            "cell_principal_stretches": [
              1.057447142009715,
              1.0096169715935128,
              0.9613504121750048
            ],
            "cell_volume_ratio": 1.0263536403200242,
            "cell_rmsd_from_input_A": 1.422242004136729
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.12344617061920961,
              -0.0005470748276700465,
              -0.12780637223772198
            ],
            "branch_aligned_reduced_polarization": [
              -0.1234461706192096,
              -0.0005470748276700465,
              -0.12780637223772195
            ],
            "target_residual": 0.5294536639395837,
            "energy_eV": -61.906583070598955
          }
        ],
        "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": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.6383203754141703,
        "parent_symmetrization_rmsd_A": 0.14086116823407183,
        "parent_cell_rmsd_A": 0.08223649605059417,
        "energy_eV": -68.91423049484122,
        "reduced_polarization": [
          -0.09990116198626693,
          0.0184771254203688,
          -0.0029764418811237593
        ],
        "cartesian_polarization_e_A2": [
          -0.0018243245115963647,
          0.00016562520667509463,
          -0.00032840082063521144
        ],
        "ranking_score": 1.9380610430750609
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753533904566e-08,
              7.692828452032785e-08,
              -0.0031715516741375608
            ],
            "target_residual": 0.7071137935256333,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.08852266665901973,
            "max_log_strain_component": 0.02,
            "step_scale": 0.10361436061939394,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0212065070156429,
              0.9991217875658814,
              0.9787658815480559
            ],
            "cell_volume_ratio": 0.9986442943567257,
            "cell_rmsd_from_input_A": 0.034284015791244835
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.02825767936249839,
              0.03924830656073808,
              -0.0033422611189808465
            ],
            "branch_aligned_reduced_polarization": [
              -0.0282576793624984,
              0.03924830656073808,
              -0.0033422611189808465
            ],
            "target_residual": 0.6594271080240715,
            "energy_eV": -69.92844746553118,
            "max_atomic_step_A": 0.019917268409603842,
            "max_log_strain_component": 0.02,
            "step_scale": 0.03527018139746485,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0427270103591828,
              0.9994795448847642,
              0.9584170793938727
            ],
            "cell_volume_ratio": 0.9988472500107789,
            "cell_rmsd_from_input_A": 0.04780785761910192
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.037442358287891525,
              0.05504059928374077,
              -0.0037420578549050435
            ],
            "branch_aligned_reduced_polarization": [
              -0.03744235828789155,
              0.055040599283740776,
              -0.0037420578549050435
            ],
            "target_residual": 0.6418430050947267,
            "energy_eV": -69.8532921564102,
            "max_atomic_step_A": 0.02766738026509223,
            "max_log_strain_component": 0.02,
            "step_scale": 0.041737091027887564,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0646894070929964,
              1.000763602059426,
              0.9387237143593118
            ],
            "cell_volume_ratio": 1.0002123763288415,
            "cell_rmsd_from_input_A": 0.062154474715292146
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.04352729750317942,
              0.06744027405684468,
              -0.0039373755767010635
            ],
            "branch_aligned_reduced_polarization": [
              -0.04352729750317941,
              0.06744027405684466,
              -0.0039373755767010635
            ],
            "target_residual": 0.6288805511058523,
            "energy_eV": -69.32986359122056,
            "max_atomic_step_A": 0.03651329557428934,
            "max_log_strain_component": 0.02,
            "step_scale": 0.05547321006266601,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0876843576639244,
              1.002846730403534,
              0.919093042410733
            ],
            "cell_volume_ratio": 1.0025289538150695,
            "cell_rmsd_from_input_A": 0.09634852162510109
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.061136859489287286,
              0.0647735649314492,
              -0.0038799090076548108
            ],
            "branch_aligned_reduced_polarization": [
              -0.061136859489287265,
              0.0647735649314492,
              -0.0038799090076548108
            ],
            "target_residual": 0.6180921934269294,
            "energy_eV": -68.74544029597459,
            "max_atomic_step_A": 0.04294623778824995,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.06278694682372533,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.3679672940767267,
            "cell_principal_stretches": [
              1.0552154707756813,
              1.006022826957316,
              0.92618058985293
            ],
            "cell_volume_ratio": 0.9832063169117408,
            "cell_rmsd_from_input_A": 0.14731993130324006
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.06882097661923588,
              0.08951809038754896,
              -0.00392849504665023
            ],
            "branch_aligned_reduced_polarization": [
              -0.06882097661923586,
              0.08951809038754899,
              -0.00392849504665023
            ],
            "target_residual": 0.595337031769405,
            "energy_eV": -68.9410828745851
          }
        ],
        "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": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.595337031769405,
        "parent_symmetrization_rmsd_A": 0.14501785084108604,
        "parent_cell_rmsd_A": 0.14731993130324006,
        "energy_eV": -68.9410828745851,
        "reduced_polarization": [
          -0.06882097661923588,
          0.08951809038754896,
          -0.00392849504665023
        ],
        "cartesian_polarization_e_A2": [
          -0.001816068083884573,
          0.0012381742485175402,
          -0.0004344968601973623
        ],
        "ranking_score": 1.872521897205706
      },
      "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": [
              -6.481753534320156e-08,
              7.692828453351622e-08,
              -0.0031715516741375608
            ],
            "branch_aligned_reduced_polarization": [
              -6.481753533904566e-08,
              7.692828452032785e-08,
              -0.0031715516741375738
            ],
            "target_residual": 0.8641981053670937,
            "energy_eV": -70.67751928550938,
            "max_atomic_step_A": 0.09552796112106529,
            "max_log_strain_component": 0.02,
            "step_scale": 0.012012557622393765,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0202044333589175,
              1.004777787100709,
              0.9998680753047806
            ],
            "cell_volume_ratio": 1.024943519738648,
            "cell_rmsd_from_input_A": 0.4919458691582814
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004930650196079617,
              0.004591377160321158,
              -0.009959512411992165
            ],
            "branch_aligned_reduced_polarization": [
              -0.004930650196079633,
              0.004591377160321153,
              -0.009959512411992166
            ],
            "target_residual": 0.8547883037189244,
            "energy_eV": -69.80465094887978,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.013413294699379455,
            "step_scale": 0.02418205781241236,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.033999138103233,
              1.0127739756624101,
              0.9950462904805162
            ],
            "cell_volume_ratio": 1.0420198565732508,
            "cell_rmsd_from_input_A": 0.8331207262037958
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.01947535706176782,
              0.015450923951221803,
              -0.031802630036845726
            ],
            "branch_aligned_reduced_polarization": [
              -0.01947535706176784,
              0.015450923951221829,
              -0.03180263003684575
            ],
            "target_residual": 0.8275871656877328,
            "energy_eV": -68.20992786621316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008910204169339775,
            "step_scale": 0.054673828342606465,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0397273806546854,
              1.023034647975852,
              0.9862750505112168
            ],
            "cell_volume_ratio": 1.0490782199106086,
            "cell_rmsd_from_input_A": 0.9753301860156138
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.06449142041432161,
              0.0534488855783877,
              -0.06420652677740639
            ],
            "branch_aligned_reduced_polarization": [
              -0.0644914204143216,
              0.05344888557838767,
              -0.0642065267774064
            ],
            "target_residual": 0.7609149571320901,
            "energy_eV": -65.31431913459022,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006232401080169461,
            "step_scale": 0.07513345768010272,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5484959722388478,
            "cell_principal_stretches": [
              1.0439485940406117,
              1.0303951615873785,
              0.9801036337174225
            ],
            "cell_volume_ratio": 1.0542774653141411,
            "cell_rmsd_from_input_A": 1.0805247604767017
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.10110726882533189,
              0.08220407000357881,
              -0.09573890110012541
            ],
            "branch_aligned_reduced_polarization": [
              -0.10110726882533189,
              0.08220407000357882,
              -0.0957389011001254
            ],
            "target_residual": 0.7050502721007167,
            "energy_eV": -62.408593907236124,
            "max_atomic_step_A": 0.039545857351832,
            "max_log_strain_component": 0.02,
            "step_scale": 0.05766593892555355,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.952294157268036,
            "cell_principal_stretches": [
              1.053892531255275,
              1.0255750517060993,
              0.9551941459746809
            ],
            "cell_volume_ratio": 1.0324176641874916,
            "cell_rmsd_from_input_A": 1.3324488839617739
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.1204052721710908,
              0.09916794994100298,
              -0.11928812249414723
            ],
            "branch_aligned_reduced_polarization": [
              -0.12040527217109082,
              0.09916794994100298,
              -0.11928812249414722
            ],
            "target_residual": 0.6705967666370256,
            "energy_eV": -61.87890113961294
          }
        ],
        "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": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.774917857807752,
        "parent_symmetrization_rmsd_A": 0.14501785084108604,
        "parent_cell_rmsd_A": 0.14731993130324006,
        "energy_eV": -68.9410828745851,
        "reduced_polarization": [
          -0.06882097661923588,
          0.08951809038754896,
          -0.00392849504665023
        ],
        "cartesian_polarization_e_A2": [
          -0.001816068083884573,
          0.0012381742485175402,
          -0.0004344968601973623
        ],
        "ranking_score": 2.2316835492824003
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_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
        ],
        "endpoint_rmsd_A": 0.06279279060553619,
        "minimum_distance_A_by_image": [
          2.418895498939845,
          2.4117671232809132,
          2.404681259815998,
          2.397638137397186,
          2.390637762541972,
          2.383680141286609,
          2.376765279170736,
          2.3698931812218778,
          2.363063851939845
        ],
        "minimum_distance_A": 2.363063851939845,
        "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": [
          187.6714117788081,
          187.36452404783003,
          187.05813815183362,
          186.75225327019788,
          186.4468685836445,
          186.14198327423475,
          185.83759652536708,
          185.53370752177565,
          185.23031544952767
        ],
        "cell_deformation_log_strain_norm": 0.010770114070726753
      },
      "parent_reduced_polarization": [
        1.3056501767609578e-07,
        5.738736199377926e-08,
        -0.00042364293248849805
      ],
      "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": [
          -70.67751928550939,
          -70.67259462723092,
          -70.65944790269825,
          -70.63809491319694,
          -70.6085450845226,
          -70.57080271188326,
          -70.52487084684026,
          -70.4707561065364,
          -70.40847269965892
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.7537669297276314e-09,
            1.1312676861685406e-09,
            -0.00036061814189242164
          ],
          [
            -1.5056993495752226e-09,
            9.97346864982393e-10,
            -0.00031578921863051036
          ],
          [
            -1.2000542012092515e-09,
            8.913575423516795e-10,
            -0.0002720509475939574
          ],
          [
            -8.382334999813543e-10,
            8.135456694519797e-10,
            -0.00022956701597705656
          ],
          [
            -4.2190798686419804e-10,
            7.640818710837903e-10,
            -0.00018863347160614837
          ],
          [
            4.701653926627601e-11,
            7.430698678418864e-10,
            -0.00014963841771873718
          ],
          [
            5.664297130784084e-10,
            7.505490968747941e-10,
            -0.00011300043986239874
          ],
          [
            1.1340383953077184e-09,
            7.864909357465936e-10,
            -7.910964983870875e-05
          ],
          [
            1.7473794532668448e-09,
            8.507912241542589e-10,
            -4.828875747164301e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.6870698915939367e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.687069891593937e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ]
        ],
        "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": [
          [
            -6.481753439535609e-08,
            7.692828496441706e-08,
            -0.0031715516741372407
          ],
          [
            -5.4445380759382545e-08,
            6.789708417720419e-08,
            -0.0027764364249719953
          ],
          [
            -3.984103252863136e-08,
            6.073770197900785e-08,
            -0.002391150391964969
          ],
          [
            -2.1094555824330286e-08,
            5.5460539272189635e-08,
            -0.0020171228656659657
          ],
          [
            1.6870699282023338e-09,
            5.2071481682069987e-08,
            -0.0016569440172516936
          ],
          [
            2.8382675765215026e-08,
            5.057276020181689e-08,
            -0.0013140091800135645
          ],
          [
            5.8858949825157936e-08,
            5.096320676578614e-08,
            -0.0009919770859730392
          ],
          [
            9.297148395592814e-08,
            5.323788410116492e-08,
            -0.0006942520692625465
          ],
          [
            1.305650176863793e-07,
            5.7387361973582074e-08,
            -0.0004236429324884772
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -70.40847269965893,
          -70.34927167985887,
          -70.28117950424537,
          -70.2042999856665,
          -70.11875631541955,
          -70.02468595512212,
          -69.92223546097615,
          -69.81155590524709,
          -69.69279918257666
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.7473794601757979e-09,
            8.507912332295758e-10,
            -4.828875747205358e-05
          ],
          [
            1.882564068288958e-09,
            6.805802098946248e-10,
            -1.167799714476206e-05
          ],
          [
            1.981735835057123e-09,
            4.675315874882572e-10,
            3.353171181780103e-05
          ],
          [
            2.0448267939917063e-09,
            2.133861131549665e-10,
            8.785689021187617e-05
          ],
          [
            2.071677740719146e-09,
            -8.012692378761619e-11,
            0.00015148140774941528
          ],
          [
            2.062044569805685e-09,
            -4.1135019721268216e-10,
            0.0002242467261654419
          ],
          [
            2.0156483939841975e-09,
            -7.78705559481833e-10,
            0.00030566716767389216
          ],
          [
            1.932244897725434e-09,
            -1.1806614913980464e-09,
            0.0003949614609044255
          ],
          [
            1.811697391001718e-09,
            -1.6156759641328923e-09,
            0.0004910921252481821
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.305650183831093e-07,
            5.738736260364307e-08,
            -0.0004236429324921001
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809744e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777028e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.305650183831093e-07,
            5.738736260364307e-08,
            -0.0004236429324921001
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809742e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777027e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.2848388102076357e-07,
          3.878245360679378e-08,
          0.0023221751630304694
        ],
        "actual_opposite_endpoint_branch_residual": 0.001996864507915987
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.6870698915939367e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809744e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777028e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.481753437331461e-08,
            7.692828498962853e-08,
            -0.0031715516741372468
          ],
          [
            -5.444538075527842e-08,
            6.78970841778224e-08,
            -0.002776436424972002
          ],
          [
            -3.9841032517871374e-08,
            6.07377020299822e-08,
            -0.0023911503919649894
          ],
          [
            -2.109455580567067e-08,
            5.5460539220451784e-08,
            -0.0020171228656659665
          ],
          [
            1.687069891593937e-09,
            5.2071481726549824e-08,
            -0.0016569440172516763
          ],
          [
            2.8382675715032718e-08,
            5.0572760226017284e-08,
            -0.0013140091800135673
          ],
          [
            5.8858949874940305e-08,
            5.096320675656281e-08,
            -0.0009919770859730124
          ],
          [
            9.297148399763589e-08,
            5.323788409497041e-08,
            -0.0006942520692625713
          ],
          [
            1.3056501767609578e-07,
            5.738736199377926e-08,
            -0.00042364293248849805
          ],
          [
            1.3268414830583065e-07,
            4.5848249800850406e-08,
            -0.00010248400415387371
          ],
          [
            1.3127991613682722e-07,
            3.139974082590049e-08,
            0.0002943589407003947
          ],
          [
            1.264086189433599e-07,
            1.4159342661809742e-08,
            0.0007714914527009944
          ],
          [
            1.1812369078271425e-07,
            -5.753617488777027e-09,
            0.0013306027300350786
          ],
          [
            1.0647278019375222e-07,
            -2.822299284576355e-08,
            0.001970375391141452
          ],
          [
            9.149910251112645e-08,
            -5.31373064590077e-08,
            0.002686615041257278
          ],
          [
            7.324534627668928e-08,
            -8.038850819916791e-08,
            0.0034725231952844504
          ],
          [
            5.175881411947302e-08,
            -1.0986893954397863e-07,
            0.004319039646239222
          ]
        ],
        "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": [
          [
            -6.481753439535609e-08,
            7.692828496441706e-08,
            -0.0031715516741372407
          ],
          [
            -5.4445380759382545e-08,
            6.789708417720419e-08,
            -0.0027764364249719953
          ],
          [
            -3.984103252863136e-08,
            6.073770197900785e-08,
            -0.002391150391964969
          ],
          [
            -2.1094555824330286e-08,
            5.5460539272189635e-08,
            -0.0020171228656659657
          ],
          [
            1.6870699282023338e-09,
            5.2071481682069987e-08,
            -0.0016569440172516936
          ],
          [
            2.8382675765215026e-08,
            5.057276020181689e-08,
            -0.0013140091800135645
          ],
          [
            5.8858949825157936e-08,
            5.096320676578614e-08,
            -0.0009919770859730392
          ],
          [
            9.297148395592814e-08,
            5.323788410116492e-08,
            -0.0006942520692625465
          ],
          [
            1.305650176863793e-07,
            5.7387361973582074e-08,
            -0.0004236429324884772
          ],
          [
            1.32684148335116e-07,
            4.5848249752289405e-08,
            -0.00010248400415385772
          ],
          [
            1.312799161601319e-07,
            3.139974080745844e-08,
            0.00029435894070040103
          ],
          [
            1.2640861890567123e-07,
            1.4159342698327748e-08,
            0.0007714914527009453
          ],
          [
            1.1812369082875307e-07,
            -5.7536174713490595e-09,
            0.0013306027300350465
          ],
          [
            1.0647278014808137e-07,
            -2.82229928316724e-08,
            0.0019703753911414212
          ],
          [
            9.149910251693427e-08,
            -5.313730644385117e-08,
            0.002686615041257223
          ],
          [
            7.324534623265322e-08,
            -8.038850818348209e-08,
            0.0034725231952844604
          ],
          [
            5.1758814123559205e-08,
            -1.0986893955733379e-07,
            0.004319039646239253
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3m",
        "spacegroup_number": 160,
        "pointgroup": "3m",
        "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": 0.0004236429564976455,
        "parent_symmetrization_rmsd_A": 0.06279279060553619,
        "parent_cell_rmsd_A": 0.25352644549208614,
        "energy_eV": -70.40847269965893,
        "reduced_polarization": [
          1.3056501852758857e-07,
          5.738736249116788e-08,
          -0.00042364293249095105
        ],
        "cartesian_polarization_e_A2": [
          1.747379463624728e-09,
          8.507912315558483e-10,
          -4.828875747192262e-05
        ],
        "ranking_score": 0.627021687891553
      }
    }
  ],
  "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": 156,
      "full_response": 37,
      "energy_polarization": 119
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 181,
      "full_response": 62,
      "energy_polarization": 119
    },
    "elapsed_seconds": 215.48835780803347
  }
}
