{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "H10Ba2Ga2",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -45.207654710509765,
  "input_cartesian_polarization_e_A2": [
    3.202622552519969e-18,
    -6.770083294215738e-18,
    0.0005438328653357845
  ],
  "input_reduced_polarization": [
    1.2906273787121548e-16,
    -1.5645931111626163e-16,
    0.023866537976682915
  ],
  "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": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "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": 9.043982732294056e-16,
      "parent_symmetrization_rmsd_A": 0.1996737628805381,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -43.79277684852579,
      "reduced_polarization": [
        5.795927694210781e-17,
        7.499735293304201e-16,
        5.021122027399377e-16
      ],
      "cartesian_polarization_e_A2": [
        1.4382283416904313e-18,
        3.245178075883893e-17,
        1.144133758331021e-17
      ],
      "ranking_score": 0.1996737628805399
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 7.720463809193372e-16,
      "parent_symmetrization_rmsd_A": 0.6662513647981306,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -42.13569565841895,
      "reduced_polarization": [
        -7.192426954037035e-16,
        -2.562046007125602e-16,
        1.144760323071126e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.784762135864225e-17,
        -1.1086118651618166e-17,
        2.608498506263098e-18
      ],
      "ranking_score": 0.6662513647981322
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnnm",
      "spacegroup_number": 58,
      "pointgroup": "mmm",
      "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": 1.6495785594498063e-16,
      "parent_symmetrization_rmsd_A": 0.8290276688872539,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -36.58845547795376,
      "reduced_polarization": [
        2.4968925632669242e-17,
        -1.4989537106377804e-16,
        -6.417962857766866e-17
      ],
      "cartesian_polarization_e_A2": [
        6.1959048492504565e-19,
        -6.486057878428681e-18,
        -1.46242372227088e-18
      ],
      "ranking_score": 0.8290276688872542
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "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": 2.3395739624101077e-06,
      "parent_symmetrization_rmsd_A": 0.012086033725022103,
      "parent_cell_rmsd_A": 0.00233366134048809,
      "energy_eV": -45.20381831805599,
      "reduced_polarization": [
        -1.1571484041320626e-16,
        -1.6059334278357555e-17,
        2.3395739624101077e-06
      ],
      "cartesian_polarization_e_A2": [
        -2.8721427257273576e-18,
        -6.949332364431752e-19,
        5.327751480275884e-08
      ],
      "ranking_score": 0.5126741282080689
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4210785422864587e-15,
      "parent_symmetrization_rmsd_A": 0.19967472229326122,
      "parent_cell_rmsd_A": 0.00233366134048809,
      "energy_eV": -43.800740632587676,
      "reduced_polarization": [
        -1.8055441085802664e-16,
        1.0249834400952182e-15,
        2.185962113159834e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.481514250984031e-18,
        4.435561521495328e-17,
        4.977941741246315e-17
      ],
      "ranking_score": 0.20025813762838807
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "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": 5.260853863231496e-05,
      "parent_symmetrization_rmsd_A": 0.24339422919931017,
      "parent_cell_rmsd_A": 0.04830346165705211,
      "energy_eV": -44.62926072543811,
      "reduced_polarization": [
        -1.3672547736976593e-15,
        2.428102594679527e-15,
        0.4999473914613677
      ],
      "cartesian_polarization_e_A2": [
        -2.56704890950863e-17,
        -1.3165318344526183e-17,
        0.011539262889421361
      ],
      "ranking_score": 0.7555753116908378
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 0.02679530551231782,
      "parent_symmetrization_rmsd_A": 0.5763646450124004,
      "parent_cell_rmsd_A": 0.12376604450111661,
      "energy_eV": -31.908641007181828,
      "reduced_polarization": [
        4.527714835912909e-14,
        -0.5123007039104133,
        0.02380506418405112
      ],
      "cartesian_polarization_e_A2": [
        8.382694079491906e-16,
        -0.02246872345875089,
        0.0001485412423629092
      ],
      "ranking_score": 1.1608967671623152
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "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": 0.00014370496253477945,
      "parent_symmetrization_rmsd_A": 0.2580459913226849,
      "parent_cell_rmsd_A": 0.06681768476393223,
      "energy_eV": -44.2596902654886,
      "reduced_polarization": [
        0.49985661453460273,
        -3.727362487842343e-15,
        9.57729449949389e-06
      ],
      "cartesian_polarization_e_A2": [
        0.012409568478185645,
        -6.460302769881407e-16,
        -0.0002429456441845518
      ],
      "ranking_score": 0.7750378224387375
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 0.04520445607282508,
      "parent_symmetrization_rmsd_A": 0.5829327346805026,
      "parent_cell_rmsd_A": 0.14813292622595833,
      "energy_eV": -32.37679237937391,
      "reduced_polarization": [
        -3.413822122843596e-14,
        -0.47721483927178987,
        0.46095798033618646
      ],
      "cartesian_polarization_e_A2": [
        -3.151798508912102e-16,
        -0.02058009289235422,
        0.010346422012610134
      ],
      "ranking_score": 1.2103748783826425
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "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": 0.00013825766872122984,
      "parent_symmetrization_rmsd_A": 0.38080760332660074,
      "parent_cell_rmsd_A": 0.08594451989342732,
      "energy_eV": -43.442046095829895,
      "reduced_polarization": [
        0.49987271742886835,
        1.0281296798768429e-15,
        0.49994601546474826
      ],
      "cartesian_polarization_e_A2": [
        0.012104817923739911,
        -5.929093302783762e-16,
        0.011296981126794822
      ],
      "ranking_score": 0.9025702486374
    },
    {
      "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": 0.072980435735194,
      "parent_symmetrization_rmsd_A": 0.6257992395802219,
      "parent_cell_rmsd_A": 0.18438017739778828,
      "energy_eV": -34.519728037545335,
      "reduced_polarization": [
        0.4449927687665905,
        -0.45624096072633175,
        0.01963402643317357
      ],
      "cartesian_polarization_e_A2": [
        0.010955210795863434,
        -0.02001661185538738,
        -0.00012324203098662144
      ],
      "ranking_score": 1.317855155400057
    },
    {
      "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": 0.1322245858419687,
      "parent_symmetrization_rmsd_A": 0.631081686192382,
      "parent_cell_rmsd_A": 0.1687383381383774,
      "energy_eV": -33.683397904419515,
      "reduced_polarization": [
        0.4092589690893143,
        -0.4350351523270915,
        0.42908473382139833
      ],
      "cartesian_polarization_e_A2": [
        0.009886751800713585,
        -0.01881726639342358,
        0.009486397744337094
      ],
      "ranking_score": 1.4377154424109138
    }
  ],
  "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": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "target_residual": 0.023866537976682915,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.010674238110257844,
            "max_log_strain_component": 0.0004833131538181325,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0003932207243138,
              1.0002259200442214,
              0.9995168036231703
            ],
            "cell_volume_ratio": 1.0001357340186472,
            "cell_rmsd_from_input_A": 0.00233366134048809
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1571484041320626e-16,
              -1.6059334278357555e-17,
              2.3395739624101077e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.1571484041320626e-16,
              -1.6059334278357555e-17,
              2.3395739624101077e-06
            ],
            "target_residual": 2.3395739624101077e-06,
            "energy_eV": -45.20381831805599
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "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": 9.043982732294056e-16,
        "parent_symmetrization_rmsd_A": 0.1996737628805381,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -43.79277684852579,
        "reduced_polarization": [
          5.795927694210781e-17,
          7.499735293304201e-16,
          5.021122027399377e-16
        ],
        "cartesian_polarization_e_A2": [
          1.4382283416904313e-18,
          3.245178075883893e-17,
          1.144133758331021e-17
        ],
        "ranking_score": 0.1996737628805399
      },
      "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": [
          -45.207654710509765,
          -45.16614802320578,
          -45.02155541691823,
          -44.80528517229942,
          -44.54694196981867,
          -44.27930408747883,
          -44.036967628068055,
          -43.85961104417222,
          -43.79277684852581
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0780123281200854e-17,
            4.4207185211406183e-17,
            0.0005438328653358397
          ],
          [
            -7.976204665086733e-19,
            3.809780713094788e-17,
            0.0020033485274955575
          ],
          [
            9.531334301876156e-19,
            6.838727991748977e-18,
            0.003448327562842846
          ],
          [
            1.5666511248751372e-17,
            -2.249829961651922e-17,
            0.004731151829350343
          ],
          [
            -8.898453885546298e-18,
            -7.756850821256055e-18,
            0.005629016817970875
          ],
          [
            -1.0771868237109806e-17,
            5.148352314992957e-18,
            0.005828752464863252
          ],
          [
            -1.7173525868145011e-18,
            -1.5788280432645067e-17,
            0.00499004799570115
          ],
          [
            -8.124814323491437e-18,
            7.12188736907359e-18,
            0.0029405340967165097
          ],
          [
            1.3417210928876645e-17,
            -1.4621320574579996e-17,
            -8.565787238111271e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.21433698481656e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.5804571731262424e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.585994922772592e-16,
            -1.7926390018897404e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690704e-17,
            -3.648734251633985e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287262e-16,
            0.12904767836655726
          ],
          [
            5.407012374011616e-16,
            -3.3790451982523423e-16,
            -3.75916388010757e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.2143369848165575e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.580457173126243e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.5859949227725925e-16,
            -1.7926390018897406e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690706e-17,
            -3.6487342516339856e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287261997e-16,
            0.12904767836655726
          ],
          [
            5.407012374011617e-16,
            -3.379045198252343e-16,
            -3.885780586188048e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.440892098500626e-16,
            9.992007221626409e-16,
            0.023866537976685365
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            0.08791854402268029
          ],
          [
            0.0,
            1.1102230246251565e-16,
            0.15133259863545778
          ],
          [
            6.661338147750939e-16,
            -4.996003610813204e-16,
            0.2076303622049832
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            0.24703388158517892
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            0.2557994393616676
          ],
          [
            -5.551115123125783e-17,
            -3.885780586188048e-16,
            0.2189922264468841
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            0.12904767836655728
          ],
          [
            5.551115123125783e-16,
            -3.3306690738754696e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -43.79277684852579,
          -43.859611044172205,
          -44.03696762806802,
          -44.27930408747881,
          -44.54694196981868,
          -44.80528517229943,
          -45.02155541691824,
          -45.166148023205785,
          -45.20765471050975
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.475960124668089e-18,
            1.2390367904749714e-17,
            8.048211600248444e-18
          ],
          [
            5.059778110679733e-18,
            -1.767600961480915e-18,
            -0.0029405340967165352
          ],
          [
            -9.01445353304194e-18,
            -1.2459012602282955e-17,
            -0.004990047995701163
          ],
          [
            -8.303339370449875e-18,
            2.9173996451626753e-19,
            -0.005828752464863244
          ],
          [
            3.788252757053436e-20,
            -1.9735350540806334e-18,
            -0.0056290168179708505
          ],
          [
            1.8437034552751402e-19,
            2.5570149831131685e-18,
            -0.0047311518293503
          ],
          [
            -2.935823978849183e-18,
            1.588266689175327e-17,
            -0.003448327562842813
          ],
          [
            -1.7403683393467432e-17,
            -5.1140299662263365e-17,
            -0.0020033485274955462
          ],
          [
            -4.4972753676369004e-18,
            -2.4497576432174816e-17,
            -0.0005438328653358593
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2067614730532917e-16,
            2.8634631844344967e-16,
            3.5320216935236093e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337e-17,
            -0.1290476783665584
          ],
          [
            -3.6327417118567547e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.7422263345410585e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961554e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450694e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733605e-16,
            -5.661487113269036e-16,
            -0.0238665379766862
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2067614730532917e-16,
            2.8634631844344967e-16,
            3.5320216935236093e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337005e-17,
            -0.1290476783665584
          ],
          [
            -3.632741711856755e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.74222633454107e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961547e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450695e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733607e-16,
            -5.661487113269036e-16,
            -0.023866537976686197
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.5158315098961608e-15,
          -1.6974546301079842e-15,
          -0.02386653797668609
        ],
        "actual_opposite_endpoint_branch_residual": 2.042414995280481e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.21433698481656e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.5804571731262424e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.585994922772592e-16,
            -1.7926390018897404e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690704e-17,
            -3.648734251633985e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287262e-16,
            0.12904767836655726
          ],
          [
            5.407012374011616e-16,
            -3.3790451982523423e-16,
            -3.75916388010757e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337e-17,
            -0.1290476783665584
          ],
          [
            -3.6327417118567547e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.7422263345410585e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961554e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450694e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733605e-16,
            -5.661487113269036e-16,
            -0.0238665379766862
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.2143369848165575e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.580457173126243e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.5859949227725925e-16,
            -1.7926390018897406e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690706e-17,
            -3.6487342516339856e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287261997e-16,
            0.12904767836655726
          ],
          [
            5.407012374011617e-16,
            -3.379045198252343e-16,
            -3.885780586188048e-16
          ],
          [
            2.0390439562456072e-16,
            -4.0849959556337005e-17,
            -0.1290476783665584
          ],
          [
            -3.632741711856754e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.74222633454107e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961547e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450695e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733607e-16,
            -5.661487113269036e-16,
            -0.023866537976686197
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            9.992007221626409e-16,
            0.023866537976685365
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            0.08791854402268029
          ],
          [
            0.0,
            1.1102230246251565e-16,
            0.15133259863545778
          ],
          [
            6.661338147750939e-16,
            -4.996003610813204e-16,
            0.2076303622049832
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            0.24703388158517892
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            0.2557994393616676
          ],
          [
            -5.551115123125783e-17,
            -3.885780586188048e-16,
            0.2189922264468841
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            0.12904767836655728
          ],
          [
            5.551115123125783e-16,
            -3.3306690738754696e-16,
            -3.885780586188048e-16
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            -0.1290476783665584
          ],
          [
            -3.885780586188048e-16,
            -2.7755575615628914e-16,
            -0.21899222644688465
          ],
          [
            -3.3306690738754696e-16,
            0.0,
            -0.2557994393616672
          ],
          [
            0.0,
            -5.551115123125783e-17,
            -0.24703388158517775
          ],
          [
            0.0,
            1.1102230246251565e-16,
            -0.20763036220498132
          ],
          [
            -1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.15133259863545628
          ],
          [
            -7.216449660063518e-16,
            -1.1657341758564144e-15,
            -0.08791854402267973
          ],
          [
            -1.6653345369377348e-16,
            -5.551115123125783e-16,
            -0.023866537976686197
          ]
        ]
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682922
            ],
            "target_residual": 0.4761334620233171,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005433416217541642,
            "step_scale": 0.5635144815912461,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0054482039940216,
              0.9974637109910934,
              0.9955900262155182
            ],
            "cell_volume_ratio": 0.9984753424499654,
            "cell_rmsd_from_input_A": 0.026200184575004996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.767972581581235e-16,
              -4.388053728492891e-15,
              0.2898040430196433
            ],
            "branch_aligned_reduced_polarization": [
              -7.767972581581235e-16,
              -4.388053728492891e-15,
              0.2898040430196433
            ],
            "target_residual": 0.2101959569803567,
            "energy_eV": -45.03769133778257,
            "max_atomic_step_A": 0.09217394286336943,
            "max_log_strain_component": 0.004414258440510587,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0098963225645892,
              0.9954078960307456,
              0.9920215629932116
            ],
            "cell_volume_ratio": 0.9972383798520917,
            "cell_rmsd_from_input_A": 0.0474399093005416
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.152491917060328e-15,
              -1.6037532320848916e-15,
              0.492614758973735
            ],
            "branch_aligned_reduced_polarization": [
              -2.152491917060328e-15,
              -1.6037532320848916e-15,
              0.492614758973735
            ],
            "target_residual": 0.007385241026264977,
            "energy_eV": -44.647745092638516,
            "max_atomic_step_A": 0.003603853167548839,
            "max_log_strain_component": 0.0001796496246409266,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.010077766357531,
              0.9953243191306808,
              0.9918766063560246
            ],
            "cell_volume_ratio": 0.9971880709356687,
            "cell_rmsd_from_input_A": 0.04830346165705211
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.3672547736976593e-15,
              2.428102594679527e-15,
              0.4999473914613677
            ],
            "branch_aligned_reduced_polarization": [
              -1.3672547736976593e-15,
              2.428102594679527e-15,
              0.4999473914613677
            ],
            "target_residual": 5.260853863231496e-05,
            "energy_eV": -44.62926072543811
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmn2_1",
        "spacegroup_number": 31,
        "pointgroup": "mm2",
        "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": 5.260853863231496e-05,
        "parent_symmetrization_rmsd_A": 0.24339422919931017,
        "parent_cell_rmsd_A": 0.04830346165705211,
        "energy_eV": -44.62926072543811,
        "reduced_polarization": [
          -1.3672547736976593e-15,
          2.428102594679527e-15,
          0.4999473914613677
        ],
        "cartesian_polarization_e_A2": [
          -2.56704890950863e-17,
          -1.3165318344526183e-17,
          0.011539262889421361
        ],
        "ranking_score": 0.7555753116908378
      },
      "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": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.2906273787121548e-16,
              -1.6653345369377348e-16,
              0.023866537976682915
            ],
            "target_residual": 0.5005692875466815,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003706131036974886,
            "step_scale": 0.2845207009563326,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0036776295589882,
              1.0001118637014865,
              0.9962628759530868
            ],
            "cell_volume_ratio": 1.0000386172629998,
            "cell_rmsd_from_input_A": 0.022009736756981382
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.1607960293994676e-16,
              -0.13979890717410776,
              0.010761447971488872
            ],
            "branch_aligned_reduced_polarization": [
              3.1607960293994676e-16,
              -0.13979890717410776,
              0.010761447971488872
            ],
            "target_residual": 0.3603618126763851,
            "energy_eV": -44.722811315433894,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0033690729017307472,
            "step_scale": 0.33602400158361634,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0071605855580745,
              0.999822676240268,
              0.9930056216469207
            ],
            "cell_volume_ratio": 0.9999387790092095,
            "cell_rmsd_from_input_A": 0.04201178039606186
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.958490434115337e-15,
              -0.25566831094030845,
              0.006271613512945105
            ],
            "branch_aligned_reduced_polarization": [
              -3.958490434115337e-15,
              -0.25566831094030845,
              0.006271613512945105
            ],
            "target_residual": 0.24441216707606342,
            "energy_eV": -43.5224417833703,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0036834787531510953,
            "step_scale": 0.427822074436013,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0109994447216657,
              0.9994794575447987,
              0.9894574995071505
            ],
            "cell_volume_ratio": 0.9998202626263076,
            "cell_rmsd_from_input_A": 0.0639408057130225
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.607734543197912e-15,
              -0.34320258059040076,
              0.014010745134668396
            ],
            "branch_aligned_reduced_polarization": [
              -3.607734543197912e-15,
              -0.34320258059040076,
              0.014010745134668396
            ],
            "target_residual": 0.1574221449248434,
            "energy_eV": -41.63499697449758,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00419274216714841,
            "step_scale": 0.40665206392317893,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0150799203397398,
              0.9999515607513524,
              0.9851753520210786
            ],
            "cell_volume_ratio": 0.9999832770651947,
            "cell_rmsd_from_input_A": 0.08878013047097423
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.5594721256456725e-15,
              -0.40866297997466167,
              0.017710553308468262
            ],
            "branch_aligned_reduced_polarization": [
              -1.5594721256456725e-15,
              -0.40866297997466167,
              0.017710553308468262
            ],
            "target_residual": 0.09303824442454378,
            "energy_eV": -38.916061643341564,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00818763943102485,
            "step_scale": 0.9305597380808219,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.4248278274196715,
            "cell_principal_stretches": [
              1.0099759213978987,
              0.9939255468913033,
              0.974508676727179
            ],
            "cell_volume_ratio": 0.9782516378902422,
            "cell_rmsd_from_input_A": 0.12376604450111661
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              4.527714835912909e-14,
              -0.5123007039104133,
              0.02380506418405112
            ],
            "branch_aligned_reduced_polarization": [
              4.527714835912909e-14,
              -0.5123007039104133,
              0.02380506418405112
            ],
            "target_residual": 0.02679530551231782,
            "energy_eV": -31.908641007181828
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 0.02679530551231782,
        "parent_symmetrization_rmsd_A": 0.5763646450124004,
        "parent_cell_rmsd_A": 0.12376604450111661,
        "energy_eV": -31.908641007181828,
        "reduced_polarization": [
          4.527714835912909e-14,
          -0.5123007039104133,
          0.02380506418405112
        ],
        "cartesian_polarization_e_A2": [
          8.382694079491906e-16,
          -0.02246872345875089,
          0.0001485412423629092
        ],
        "ranking_score": 1.1608967671623152
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "target_residual": 0.5005692875466815,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010130739669749497,
            "step_scale": 0.5535869408507407,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0101599509221102,
              1.0001250600801435,
              0.9898928219766526
            ],
            "cell_volume_ratio": 1.000075138303788,
            "cell_rmsd_from_input_A": 0.034512151739866846
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2732538426773066,
              6.9302530135936034e-15,
              0.011463077459156172
            ],
            "branch_aligned_reduced_polarization": [
              0.2732538426773066,
              6.9302530135936034e-15,
              0.011463077459156172
            ],
            "target_residual": 0.22703572847779316,
            "energy_eV": -44.96230855071883,
            "max_atomic_step_A": 0.10085181565867854,
            "max_log_strain_component": 0.008929226171165719,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.019201218674617,
              1.0002305586163094,
              0.9810702391717493
            ],
            "cell_volume_ratio": 1.000138520770327,
            "cell_rmsd_from_input_A": 0.06494734333787157
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4887866062791081,
              8.732226479576118e-15,
              0.0015528611778482298
            ],
            "branch_aligned_reduced_polarization": [
              0.4887866062791081,
              8.732226479576118e-15,
              0.0015528611778482298
            ],
            "target_residual": 0.011320405318600853,
            "energy_eV": -44.30906396156729,
            "max_atomic_step_A": 0.005458736650502268,
            "max_log_strain_component": 0.000547184479299871,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0197560762882902,
              1.0002486729568079,
              0.9805293426432278
            ],
            "cell_volume_ratio": 1.0001494034166896,
            "cell_rmsd_from_input_A": 0.06681768476393223
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49985661453460273,
              -3.727362487842343e-15,
              9.57729449949389e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49985661453460273,
              -3.727362487842343e-15,
              9.57729449949389e-06
            ],
            "target_residual": 0.00014370496253477945,
            "energy_eV": -44.2596902654886
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "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": 0.00014370496253477945,
        "parent_symmetrization_rmsd_A": 0.2580459913226849,
        "parent_cell_rmsd_A": 0.06681768476393223,
        "energy_eV": -44.2596902654886,
        "reduced_polarization": [
          0.49985661453460273,
          -3.727362487842343e-15,
          9.57729449949389e-06
        ],
        "cartesian_polarization_e_A2": [
          0.012409568478185645,
          -6.460302769881407e-16,
          -0.0002429456441845518
        ],
        "ranking_score": 0.7750378224387375
      },
      "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": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.2906273787121548e-16,
              -1.6653345369377348e-16,
              0.023866537976682922
            ],
            "target_residual": 0.6904368715953033,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003131261699578951,
            "step_scale": 0.24038782351576654,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0041892508611807,
              0.9981163794264187,
              0.997058336569024
            ],
            "cell_volume_ratio": 0.9993493167217568,
            "cell_rmsd_from_input_A": 0.021686123407530768
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.618566589550047e-16,
              -0.11684810872888857,
              0.13217157322021963
            ],
            "branch_aligned_reduced_polarization": [
              -7.618566589550047e-16,
              -0.11684810872888857,
              0.13217157322021966
            ],
            "target_residual": 0.5311338092532971,
            "energy_eV": -44.796769359160876,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.002946312207296677,
            "step_scale": 0.26214083821867085,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0083022088706386,
              0.996147373621218,
              0.9942759669180437
            ],
            "cell_volume_ratio": 0.998668277628585,
            "cell_rmsd_from_input_A": 0.04270002596454232
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.332563998237489e-15,
              -0.21365750987864465,
              0.22121272646058326
            ],
            "branch_aligned_reduced_polarization": [
              -8.332563998237489e-15,
              -0.21365750987864462,
              0.22121272646058326
            ],
            "target_residual": 0.3996427974284537,
            "energy_eV": -43.72812822418779,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0029906411739610292,
            "step_scale": 0.29826619076087824,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0126752118609432,
              0.9939289719065745,
              0.9914286358558163
            ],
            "cell_volume_ratio": 0.9978999207719944,
            "cell_rmsd_from_input_A": 0.06475355116365013
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.9008943806081584e-15,
              -0.2947389596205934,
              0.2967960178564454
            ],
            "branch_aligned_reduced_polarization": [
              -5.9008943806081584e-15,
              -0.2947389596205934,
              0.2967960178564454
            ],
            "target_residual": 0.28883204991246114,
            "energy_eV": -42.11046318703264,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0032867898723038507,
            "step_scale": 0.360492692675063,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.017546219195925,
              0.9914487692344915,
              0.9882981128276832
            ],
            "cell_volume_ratio": 0.9970395569208209,
            "cell_rmsd_from_input_A": 0.08915698845514447
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.9018365980921195e-15,
              -0.3691952085674141,
              0.36659397548547695
            ],
            "branch_aligned_reduced_polarization": [
              -3.9018365980921195e-15,
              -0.3691952085674141,
              0.36659397548547695
            ],
            "target_residual": 0.18683431386790764,
            "energy_eV": -39.381375874166416,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007729298517590847,
            "step_scale": 0.621029828859684,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.1410201886277047,
            "cell_principal_stretches": [
              1.0206867164407603,
              0.9858926893317416,
              0.9768363979286586
            ],
            "cell_volume_ratio": 0.9829783269535982,
            "cell_rmsd_from_input_A": 0.14813292622595833
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -3.413822122843596e-14,
              -0.47721483927178987,
              0.46095798033618646
            ],
            "branch_aligned_reduced_polarization": [
              -3.413822122843596e-14,
              -0.47721483927178987,
              0.46095798033618646
            ],
            "target_residual": 0.04520445607282508,
            "energy_eV": -32.37679237937391
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 0.04520445607282508,
        "parent_symmetrization_rmsd_A": 0.5829327346805026,
        "parent_cell_rmsd_A": 0.14813292622595833,
        "energy_eV": -32.37679237937391,
        "reduced_polarization": [
          -3.413822122843596e-14,
          -0.47721483927178987,
          0.46095798033618646
        ],
        "cartesian_polarization_e_A2": [
          -3.151798508912102e-16,
          -0.02058009289235422,
          0.010346422012610134
        ],
        "ranking_score": 1.2103748783826425
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              -1.5645931111626163e-16,
              0.023866537976682922
            ],
            "target_residual": 0.6904368715953034,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007231353610911909,
            "step_scale": 0.3951520870315531,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0084047165228442,
              0.9982208087409378,
              0.9923704876628621
            ],
            "cell_volume_ratio": 0.9989306238903917,
            "cell_rmsd_from_input_A": 0.03073104126989545
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19650654203798135,
              -8.393031012657267e-16,
              0.21013697731033124
            ],
            "branch_aligned_reduced_polarization": [
              0.19650654203798135,
              -8.393031012657267e-16,
              0.2101369773103312
            ],
            "target_residual": 0.4196770793700021,
            "energy_eV": -44.977862008095954,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007184448349044898,
            "step_scale": 0.6124017979013326,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0168103135204654,
              0.9964700811258381,
              0.9848567667566562
            ],
            "cell_volume_ratio": 0.9978776128312572,
            "cell_rmsd_from_input_A": 0.06118840000922198
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.37625847805443835,
              2.4233330172742664e-15,
              0.3811069261998921
            ],
            "branch_aligned_reduced_polarization": [
              0.37625847805443835,
              2.4233330172742664e-15,
              0.3811069261998921
            ],
            "target_residual": 0.1716028183073979,
            "energy_eV": -44.277133193245746,
            "max_atomic_step_A": 0.08895745150174193,
            "max_log_strain_component": 0.0055837151771508265,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0233646545580133,
              0.9951368414841613,
              0.9790721614297447
            ],
            "cell_volume_ratio": 0.9970752130776345,
            "cell_rmsd_from_input_A": 0.08471863336531497
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4944549768733233,
              4.758344563422889e-15,
              0.49476913787333615
            ],
            "branch_aligned_reduced_polarization": [
              0.4944549768733233,
              4.758344563422889e-15,
              0.49476913787333615
            ],
            "target_residual": 0.007622939069909044,
            "energy_eV": -43.484383921299646,
            "max_atomic_step_A": 0.00433773330969057,
            "max_log_strain_component": 0.00029418570950673595,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.023708684068861,
              0.9950689786103981,
              0.9787697762157768
            ],
            "cell_volume_ratio": 0.9970343588695493,
            "cell_rmsd_from_input_A": 0.08594451989342732
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49987271742886835,
              1.0281296798768429e-15,
              0.49994601546474826
            ],
            "branch_aligned_reduced_polarization": [
              0.49987271742886835,
              1.0281296798768429e-15,
              0.49994601546474826
            ],
            "target_residual": 0.00013825766872122984,
            "energy_eV": -43.442046095829895
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "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": 0.00013825766872122984,
        "parent_symmetrization_rmsd_A": 0.38080760332660074,
        "parent_cell_rmsd_A": 0.08594451989342732,
        "energy_eV": -43.442046095829895,
        "reduced_polarization": [
          0.49987271742886835,
          1.0281296798768429e-15,
          0.49994601546474826
        ],
        "cartesian_polarization_e_A2": [
          0.012104817923739911,
          -5.929093302783762e-16,
          0.011296981126794822
        ],
        "ranking_score": 0.9025702486374
      },
      "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": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              -1.6653345369377348e-16,
              0.023866537976682915
            ],
            "target_residual": 0.7075094427885695,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0046321153759523994,
            "step_scale": 0.2531185939263679,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0056842590716109,
              1.00007141398874,
              0.9943110222718073
            ],
            "cell_volume_ratio": 1.0000343550625619,
            "cell_rmsd_from_input_A": 0.025140486724372284
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.12496677498729222,
              -0.12425999925054962,
              0.012895825556485982
            ],
            "branch_aligned_reduced_polarization": [
              0.12496677498729225,
              -0.12425999925054965,
              0.012895825556485982
            ],
            "target_residual": 0.5310336809877624,
            "energy_eV": -44.77453587241369,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0046060869433768425,
            "step_scale": 0.30615871623633223,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0113981693632597,
              0.9998996396550144,
              0.9887816725654676
            ],
            "cell_volume_ratio": 0.9999516079715883,
            "cell_rmsd_from_input_A": 0.04987687416658643
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.23305353564559245,
              -0.23392484167948566,
              0.00796277134260814
            ],
            "branch_aligned_reduced_polarization": [
              0.23305353564559245,
              -0.23392484167948568,
              0.00796277134260814
            ],
            "target_residual": 0.3769878120497537,
            "energy_eV": -43.54863333059999,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005249327739075624,
            "step_scale": 0.36804660399739125,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0178444055108768,
              0.9996671383808566,
              0.9826368268860545
            ],
            "cell_volume_ratio": 0.9998384782243398,
            "cell_rmsd_from_input_A": 0.07717431911291547
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3188236434631986,
              -0.31728660134383935,
              0.013733645830043542
            ],
            "branch_aligned_reduced_polarization": [
              0.3188236434631986,
              -0.31728660134383935,
              0.013733645830043542
            ],
            "target_residual": 0.25767745583232604,
            "energy_eV": -41.67718540162315,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005958859037106648,
            "step_scale": 0.33955729719422256,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0252912850273959,
              0.999940392259523,
              0.9753626359620924
            ],
            "cell_volume_ratio": 0.9999712008162667,
            "cell_rmsd_from_input_A": 0.1099390856081373
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.36666503985861965,
              -0.3721426257542902,
              0.01952666582915376
            ],
            "branch_aligned_reduced_polarization": [
              0.36666503985861965,
              -0.3721426257542902,
              0.01952666582915376
            ],
            "target_residual": 0.18576062667668417,
            "energy_eV": -39.322245774281726,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015836129729274978,
            "step_scale": 0.584460451456414,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.558233338126041,
            "cell_principal_stretches": [
              1.0140437359739587,
              1.0000850484354225,
              0.9518072966583458
            ],
            "cell_volume_ratio": 0.9652563135886226,
            "cell_rmsd_from_input_A": 0.18438017739778828
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4449927687665905,
              -0.45624096072633175,
              0.01963402643317357
            ],
            "branch_aligned_reduced_polarization": [
              0.4449927687665905,
              -0.45624096072633175,
              0.01963402643317357
            ],
            "target_residual": 0.072980435735194,
            "energy_eV": -34.519728037545335
          }
        ],
        "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": 0.072980435735194,
        "parent_symmetrization_rmsd_A": 0.6257992395802219,
        "parent_cell_rmsd_A": 0.18438017739778828,
        "energy_eV": -34.519728037545335,
        "reduced_polarization": [
          0.4449927687665905,
          -0.45624096072633175,
          0.01963402643317357
        ],
        "cartesian_polarization_e_A2": [
          0.010955210795863434,
          -0.02001661185538738,
          -0.00012324203098662144
        ],
        "ranking_score": 1.317855155400057
      },
      "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": [
              1.2906273787121548e-16,
              -1.5645931111626163e-16,
              0.023866537976682915
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              -1.6653345369377348e-16,
              0.023866537976682922
            ],
            "target_residual": 0.8524688109592686,
            "energy_eV": -45.207654710509765,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004035900843073027,
            "step_scale": 0.22053888206851754,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.005615864532629,
              0.9987753798837755,
              0.9950404054889581
            ],
            "cell_volume_ratio": 0.9994030279216041,
            "cell_rmsd_from_input_A": 0.0241810040142076
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.10930530406148772,
              -0.10721107500367134,
              0.12362812197496584
            ],
            "branch_aligned_reduced_polarization": [
              0.10930530406148775,
              -0.10721107500367133,
              0.12362812197496587
            ],
            "target_residual": 0.6697621037371024,
            "energy_eV": -44.823092665596825,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037228109106961778,
            "step_scale": 0.2408966584605236,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0110348602342454,
              0.9974667531623587,
              0.9903777799877534
            ],
            "cell_volume_ratio": 0.9987699039447809,
            "cell_rmsd_from_input_A": 0.04763137222222242
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.1995506893171307,
              -0.19789600320738215,
              0.20746342028017686
            ],
            "branch_aligned_reduced_polarization": [
              0.19955068931713071,
              -0.19789600320738215,
              0.20746342028017684
            ],
            "target_residual": 0.5168309816971675,
            "energy_eV": -43.76829538679154,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0039253862950149885,
            "step_scale": 0.2671552597889264,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0168322562039178,
              0.9959980149921167,
              0.9854763893419833
            ],
            "cell_volume_ratio": 0.9980539345833612,
            "cell_rmsd_from_input_A": 0.07251360316612662
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.2737036655904433,
              -0.2741543376044033,
              0.278663481311792
            ],
            "branch_aligned_reduced_polarization": [
              0.2737036655904433,
              -0.2741543376044033,
              0.278663481311792
            ],
            "target_residual": 0.3888523481928883,
            "energy_eV": -42.17179855799674,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004610889325950949,
            "step_scale": 0.30925785035390074,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.4088386601375564,
            "cell_principal_stretches": [
              1.0235652301427893,
              0.9943435211163977,
              0.9798225618605365
            ],
            "cell_volume_ratio": 0.9972393537487145,
            "cell_rmsd_from_input_A": 0.10102561197812857
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.3348733008109067,
              -0.34085106444972374,
              0.34316991872608166
            ],
            "branch_aligned_reduced_polarization": [
              0.3348733008109067,
              -0.34085106444972374,
              0.34316991872608166
            ],
            "target_residual": 0.27783247625908514,
            "energy_eV": -39.77360928275888,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010436022187149207,
            "step_scale": 0.4879556520043007,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.1731047081629327,
            "cell_principal_stretches": [
              1.0236843338683246,
              0.9923610296134979,
              0.961040661566901
            ],
            "cell_volume_ratio": 0.9762870330539357,
            "cell_rmsd_from_input_A": 0.1687383381383774
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4092589690893143,
              -0.4350351523270915,
              0.42908473382139833
            ],
            "branch_aligned_reduced_polarization": [
              0.4092589690893143,
              -0.4350351523270915,
              0.42908473382139833
            ],
            "target_residual": 0.1322245858419687,
            "energy_eV": -33.683397904419515
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.1322245858419687,
        "parent_symmetrization_rmsd_A": 0.631081686192382,
        "parent_cell_rmsd_A": 0.1687383381383774,
        "energy_eV": -33.683397904419515,
        "reduced_polarization": [
          0.4092589690893143,
          -0.4350351523270915,
          0.42908473382139833
        ],
        "cartesian_polarization_e_A2": [
          0.009886751800713585,
          -0.01881726639342358,
          0.009486397744337094
        ],
        "ranking_score": 1.4377154424109138
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13
        ],
        "endpoint_rmsd_A": 0.1996737628805381,
        "minimum_distance_A_by_image": [
          1.572656817931774,
          1.5526618131484136,
          1.5351221601211662,
          1.5201228530762119,
          1.5077397095844423,
          1.498037608584887,
          1.4910688860932624,
          1.4868719752822728,
          1.485470370000002
        ],
        "minimum_distance_A": 1.485470370000002,
        "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": [
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924,
          202.16838745766924
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.407012374011616e-16,
        -3.3790451982523423e-16,
        -3.75916388010757e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -45.207654710509765,
          -45.16614802320578,
          -45.02155541691823,
          -44.80528517229942,
          -44.54694196981867,
          -44.27930408747883,
          -44.036967628068055,
          -43.85961104417222,
          -43.79277684852581
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0780123281200854e-17,
            4.4207185211406183e-17,
            0.0005438328653358397
          ],
          [
            -7.976204665086733e-19,
            3.809780713094788e-17,
            0.0020033485274955575
          ],
          [
            9.531334301876156e-19,
            6.838727991748977e-18,
            0.003448327562842846
          ],
          [
            1.5666511248751372e-17,
            -2.249829961651922e-17,
            0.004731151829350343
          ],
          [
            -8.898453885546298e-18,
            -7.756850821256055e-18,
            0.005629016817970875
          ],
          [
            -1.0771868237109806e-17,
            5.148352314992957e-18,
            0.005828752464863252
          ],
          [
            -1.7173525868145011e-18,
            -1.5788280432645067e-17,
            0.00499004799570115
          ],
          [
            -8.124814323491437e-18,
            7.12188736907359e-18,
            0.0029405340967165097
          ],
          [
            1.3417210928876645e-17,
            -1.4621320574579996e-17,
            -8.565787238111271e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.21433698481656e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.5804571731262424e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.585994922772592e-16,
            -1.7926390018897404e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690704e-17,
            -3.648734251633985e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287262e-16,
            0.12904767836655726
          ],
          [
            5.407012374011616e-16,
            -3.3790451982523423e-16,
            -3.75916388010757e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.2143369848165575e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.580457173126243e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.5859949227725925e-16,
            -1.7926390018897406e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690706e-17,
            -3.6487342516339856e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287261997e-16,
            0.12904767836655726
          ],
          [
            5.407012374011617e-16,
            -3.379045198252343e-16,
            -3.885780586188048e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.440892098500626e-16,
            9.992007221626409e-16,
            0.023866537976685365
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            0.08791854402268029
          ],
          [
            0.0,
            1.1102230246251565e-16,
            0.15133259863545778
          ],
          [
            6.661338147750939e-16,
            -4.996003610813204e-16,
            0.2076303622049832
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            0.24703388158517892
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            0.2557994393616676
          ],
          [
            -5.551115123125783e-17,
            -3.885780586188048e-16,
            0.2189922264468841
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            0.12904767836655728
          ],
          [
            5.551115123125783e-16,
            -3.3306690738754696e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -43.79277684852579,
          -43.859611044172205,
          -44.03696762806802,
          -44.27930408747881,
          -44.54694196981868,
          -44.80528517229943,
          -45.02155541691824,
          -45.166148023205785,
          -45.20765471050975
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.475960124668089e-18,
            1.2390367904749714e-17,
            8.048211600248444e-18
          ],
          [
            5.059778110679733e-18,
            -1.767600961480915e-18,
            -0.0029405340967165352
          ],
          [
            -9.01445353304194e-18,
            -1.2459012602282955e-17,
            -0.004990047995701163
          ],
          [
            -8.303339370449875e-18,
            2.9173996451626753e-19,
            -0.005828752464863244
          ],
          [
            3.788252757053436e-20,
            -1.9735350540806334e-18,
            -0.0056290168179708505
          ],
          [
            1.8437034552751402e-19,
            2.5570149831131685e-18,
            -0.0047311518293503
          ],
          [
            -2.935823978849183e-18,
            1.588266689175327e-17,
            -0.003448327562842813
          ],
          [
            -1.7403683393467432e-17,
            -5.1140299662263365e-17,
            -0.0020033485274955462
          ],
          [
            -4.4972753676369004e-18,
            -2.4497576432174816e-17,
            -0.0005438328653358593
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2067614730532917e-16,
            2.8634631844344967e-16,
            3.5320216935236093e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337e-17,
            -0.1290476783665584
          ],
          [
            -3.6327417118567547e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.7422263345410585e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961554e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450694e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733605e-16,
            -5.661487113269036e-16,
            -0.0238665379766862
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2067614730532917e-16,
            2.8634631844344967e-16,
            3.5320216935236093e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337005e-17,
            -0.1290476783665584
          ],
          [
            -3.632741711856755e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.74222633454107e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961547e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450695e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733607e-16,
            -5.661487113269036e-16,
            -0.023866537976686197
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.5158315098961608e-15,
          -1.6974546301079842e-15,
          -0.02386653797668609
        ],
        "actual_opposite_endpoint_branch_residual": 2.042414995280481e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.21433698481656e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.5804571731262424e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.585994922772592e-16,
            -1.7926390018897404e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690704e-17,
            -3.648734251633985e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287262e-16,
            0.12904767836655726
          ],
          [
            5.407012374011616e-16,
            -3.3790451982523423e-16,
            -3.75916388010757e-16
          ],
          [
            2.0390439562456074e-16,
            -4.0849959556337e-17,
            -0.1290476783665584
          ],
          [
            -3.6327417118567547e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.7422263345410585e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961554e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450694e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733605e-16,
            -5.661487113269036e-16,
            -0.0238665379766862
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.3442903509383754e-16,
            1.0216455904575156e-15,
            0.023866537976685337
          ],
          [
            -3.2143369848165575e-17,
            8.804554389812443e-16,
            0.08791854402268026
          ],
          [
            3.8410398989978914e-17,
            1.580457173126243e-16,
            0.15133259863545775
          ],
          [
            6.313459677173243e-16,
            -5.199446308578428e-16,
            0.20763036220498324
          ],
          [
            -3.5859949227725925e-16,
            -1.7926390018897406e-16,
            0.24703388158517886
          ],
          [
            -4.340963644234209e-16,
            1.1898046472719516e-16,
            0.2557994393616676
          ],
          [
            -6.920772682690706e-17,
            -3.6487342516339856e-16,
            0.2189922264468841
          ],
          [
            -3.274225307818362e-16,
            1.6458964287261997e-16,
            0.12904767836655726
          ],
          [
            5.407012374011617e-16,
            -3.379045198252343e-16,
            -3.885780586188048e-16
          ],
          [
            2.0390439562456072e-16,
            -4.0849959556337005e-17,
            -0.1290476783665584
          ],
          [
            -3.632741711856754e-16,
            -2.879327246398123e-16,
            -0.21899222644688468
          ],
          [
            -3.346169256757689e-16,
            6.74222633454107e-18,
            -0.2557994393616672
          ],
          [
            1.526630954961547e-18,
            -4.5609178145424814e-17,
            -0.24703388158517775
          ],
          [
            7.4299550402278e-18,
            5.909363081450695e-17,
            -0.20763036220498135
          ],
          [
            -1.183110011887292e-16,
            3.67054733683397e-16,
            -0.15133259863545628
          ],
          [
            -7.013524044653114e-16,
            -1.1818726162901386e-15,
            -0.08791854402267976
          ],
          [
            -1.8123605338733607e-16,
            -5.661487113269036e-16,
            -0.023866537976686197
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            9.992007221626409e-16,
            0.023866537976685365
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            0.08791854402268029
          ],
          [
            0.0,
            1.1102230246251565e-16,
            0.15133259863545778
          ],
          [
            6.661338147750939e-16,
            -4.996003610813204e-16,
            0.2076303622049832
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            0.24703388158517892
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            0.2557994393616676
          ],
          [
            -5.551115123125783e-17,
            -3.885780586188048e-16,
            0.2189922264468841
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            0.12904767836655728
          ],
          [
            5.551115123125783e-16,
            -3.3306690738754696e-16,
            -3.885780586188048e-16
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            -0.1290476783665584
          ],
          [
            -3.885780586188048e-16,
            -2.7755575615628914e-16,
            -0.21899222644688465
          ],
          [
            -3.3306690738754696e-16,
            0.0,
            -0.2557994393616672
          ],
          [
            0.0,
            -5.551115123125783e-17,
            -0.24703388158517775
          ],
          [
            0.0,
            1.1102230246251565e-16,
            -0.20763036220498132
          ],
          [
            -1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.15133259863545628
          ],
          [
            -7.216449660063518e-16,
            -1.1657341758564144e-15,
            -0.08791854402267973
          ],
          [
            -1.6653345369377348e-16,
            -5.551115123125783e-16,
            -0.023866537976686197
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "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": 9.043982732294056e-16,
        "parent_symmetrization_rmsd_A": 0.1996737628805381,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -43.79277684852579,
        "reduced_polarization": [
          5.795927694210781e-17,
          7.499735293304201e-16,
          5.021122027399377e-16
        ],
        "cartesian_polarization_e_A2": [
          1.4382283416904313e-18,
          3.245178075883893e-17,
          1.144133758331021e-17
        ],
        "ranking_score": 0.1996737628805399
      }
    }
  ],
  "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": 114,
      "full_response": 32,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 139,
      "full_response": 57,
      "energy_polarization": 82
    },
    "elapsed_seconds": 338.36270536499796
  }
}