{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "O24P8Zn4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -231.4905157351283,
  "input_cartesian_polarization_e_A2": [
    6.021379532170543e-05,
    6.0019745245727464e-05,
    -0.0002332382331384899
  ],
  "input_reduced_polarization": [
    0.005985089789440097,
    0.005987081081903207,
    -0.007034436792848416
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0454509131395633e-15,
      "parent_symmetrization_rmsd_A": 1.0422657652339442,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -220.48011305112445,
      "reduced_polarization": [
        4.686041659151867e-16,
        8.729876612609422e-16,
        3.335720173477226e-16
      ],
      "cartesian_polarization_e_A2": [
        5.412695221953395e-18,
        9.796702193816157e-18,
        1.1060124675471095e-17
      ],
      "ranking_score": 1.0422657652339462
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 3.1599740793494497e-15,
      "parent_symmetrization_rmsd_A": 1.0577927925786776,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -222.99820132103767,
      "reduced_polarization": [
        2.690955858242754e-15,
        1.591392812804269e-15,
        4.600670239262128e-16
      ],
      "cartesian_polarization_e_A2": [
        2.982505530464116e-17,
        1.774487231406341e-17,
        1.5254273077686258e-17
      ],
      "ranking_score": 1.0577927925786839
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "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": 2.125379430125551e-06,
      "parent_symmetrization_rmsd_A": 0.0018526666918618406,
      "parent_cell_rmsd_A": 0.0013169675687520993,
      "energy_eV": -231.48845586115817,
      "reduced_polarization": [
        1.452866092279514e-06,
        1.4517069528362551e-06,
        5.467767030444348e-07
      ],
      "cartesian_polarization_e_A2": [
        1.635061900858289e-08,
        1.6279400527975437e-08,
        1.812701411140382e-08
      ],
      "ranking_score": 0.5021861593429101
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 3.974547534621436e-15,
      "parent_symmetrization_rmsd_A": 1.0422657856140811,
      "parent_cell_rmsd_A": 0.0013169675687520993,
      "energy_eV": -220.49933974647058,
      "reduced_polarization": [
        2.6942372917248864e-15,
        -2.2871512796519327e-15,
        -1.8185303255186077e-15
      ],
      "cartesian_polarization_e_A2": [
        2.796039652974191e-17,
        -2.6393233563753905e-17,
        -6.029780328167058e-17
      ],
      "ranking_score": 1.0425950275062772
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 2.5782971659536948e-15,
      "parent_symmetrization_rmsd_A": 1.0577928122462896,
      "parent_cell_rmsd_A": 0.0013169675687520993,
      "energy_eV": -222.97895156834338,
      "reduced_polarization": [
        1.979471036937276e-15,
        -8.332303405462655e-16,
        -1.4265475419643306e-15
      ],
      "cartesian_polarization_e_A2": [
        2.05042907884774e-17,
        -1.0202955807751191e-17,
        -4.73013967465498e-17
      ],
      "ranking_score": 1.0581220541384828
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00012677714592481323,
      "parent_symmetrization_rmsd_A": 0.13031785994656292,
      "parent_cell_rmsd_A": 0.12156403957646698,
      "energy_eV": -220.26607563466212,
      "reduced_polarization": [
        -6.960764253061999e-05,
        -6.95784433583225e-05,
        -0.49992008716592434
      ],
      "cartesian_polarization_e_A2": [
        -0.0005527213919216644,
        -0.0005507627111283297,
        -0.01661028623340001
      ],
      "ranking_score": 0.6609624241325293
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.51521214860255e-06,
      "parent_symmetrization_rmsd_A": 0.04431253838392436,
      "parent_cell_rmsd_A": 0.04529830051416273,
      "energy_eV": -230.2445434250374,
      "reduced_polarization": [
        3.9267921153212e-06,
        0.4999977714189914,
        2.9514707244331437e-08
      ],
      "cartesian_polarization_e_A2": [
        3.2881430137912395e-05,
        0.0054643141794746075,
        1.3491558889468398e-07
      ],
      "ranking_score": 0.5556461439367623
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 4.53772099872049e-06,
      "parent_symmetrization_rmsd_A": 0.044312115499502085,
      "parent_cell_rmsd_A": 0.045299447280547925,
      "energy_eV": -230.24449893378667,
      "reduced_polarization": [
        0.499997763022094,
        3.9479117016682505e-06,
        2.889474045481707e-08
      ],
      "cartesian_polarization_e_A2": [
        0.005464349591322878,
        1.3302598865363728e-05,
        1.3438671640936213e-07
      ],
      "ranking_score": 0.5556460527616365
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00025979781346616306,
      "parent_symmetrization_rmsd_A": 0.1377837382550346,
      "parent_cell_rmsd_A": 0.1066068729537345,
      "energy_eV": -216.86549347596994,
      "reduced_polarization": [
        2.0620558428070413e-05,
        0.49977098485079574,
        -0.49987907953900657
      ],
      "cartesian_polarization_e_A2": [
        -0.0003832257966408343,
        0.004914022351519013,
        -0.016520436826991506
      ],
      "ranking_score": 0.6649550521204005
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0002601335809280668,
      "parent_symmetrization_rmsd_A": 0.1377823658385708,
      "parent_cell_rmsd_A": 0.10661288791489562,
      "energy_eV": -216.86544189050446,
      "reduced_polarization": [
        0.49977061271629686,
        2.065418274338373e-05,
        -0.49987906878510097
      ],
      "cartesian_polarization_e_A2": [
        0.0049123423592750065,
        -0.0004008525966746005,
        -0.01652043944602777
      ],
      "ranking_score": 0.6649558549791509
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "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": 5.816976971347274e-05,
      "parent_symmetrization_rmsd_A": 0.06278048790497663,
      "parent_cell_rmsd_A": 0.08004426943688372,
      "energy_eV": -229.02155663322057,
      "reduced_polarization": [
        0.500041014672091,
        0.5000411020141007,
        -3.4847121328948592e-06
      ],
      "cartesian_polarization_e_A2": [
        0.005522849188547957,
        0.005503163752275062,
        -4.071594795119354e-05
      ],
      "ranking_score": 0.5829078948036245
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "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": 0.0002829505795107706,
      "parent_symmetrization_rmsd_A": 0.14592145486530914,
      "parent_cell_rmsd_A": 0.1080834517254614,
      "energy_eV": -213.35333174475318,
      "reduced_polarization": [
        0.49987382416815174,
        0.49987426678672553,
        -0.4997801549432383
      ],
      "cartesian_polarization_e_A2": [
        0.005113906761211352,
        0.005095922497486293,
        -0.016471778249090113
      ],
      "ranking_score": 0.673508218955696
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "target_residual": 0.01100680428923504,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.0023915243305309202,
            "max_log_strain_component": 0.00022172006817330024,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0002107348527811,
              1.000085006244576,
              0.999725524240216
            ],
            "cell_volume_ratio": 1.0000212020726726,
            "cell_rmsd_from_input_A": 0.0013169675687520993
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.452866092279514e-06,
              1.4517069528362551e-06,
              5.467767030444348e-07
            ],
            "branch_aligned_reduced_polarization": [
              1.452866092279514e-06,
              1.4517069528362551e-06,
              5.467767030444348e-07
            ],
            "target_residual": 2.125379430125551e-06,
            "energy_eV": -231.48845586115817
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "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": 2.125379430125551e-06,
        "parent_symmetrization_rmsd_A": 0.0018526666918618406,
        "parent_cell_rmsd_A": 0.0013169675687520993,
        "energy_eV": -231.48845586115817,
        "reduced_polarization": [
          1.452866092279514e-06,
          1.4517069528362551e-06,
          5.467767030444348e-07
        ],
        "cartesian_polarization_e_A2": [
          1.635061900858289e-08,
          1.6279400527975437e-08,
          1.812701411140382e-08
        ],
        "ranking_score": 0.5021861593429101
      },
      "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": [
          -231.49051573512824,
          -231.4904922532873,
          -231.4904018095834,
          -231.49024445655667,
          -231.4900202463282,
          -231.48972923059992,
          -231.48937146065532,
          -231.48894698735918,
          -231.48845586115817
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.0213795321725274e-05,
            6.0019745245741457e-05,
            -0.00023323823313847812
          ],
          [
            5.268827397873006e-05,
            5.2518468280960355e-05,
            -0.00020408670245174138
          ],
          [
            4.516296364769852e-05,
            4.501740327495566e-05,
            -0.0001749335195841988
          ],
          [
            3.7637878896163305e-05,
            3.751656474774975e-05,
            -0.00014577872282922142
          ],
          [
            3.0113034319155663e-05,
            3.0015967246451197e-05,
            -0.00011662235050874172
          ],
          [
            2.2588444539167275e-05,
            2.2515625345412033e-05,
            -8.746444097274995e-05
          ],
          [
            1.5064124206121715e-05,
            1.5015553646535306e-05,
            -5.830503259898572e-05
          ],
          [
            7.540087997618507e-06,
            7.515766779230571e-06,
            -2.914416379239593e-05
          ],
          [
            1.635061896752943e-08,
            1.6279400454132372e-08,
            1.812701421555457e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883253366e-06,
            1.4517069458579255e-06,
            5.467767061852575e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883252834e-06,
            1.4517069458579428e-06,
            5.46776706185294e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0059850897894419,
            0.005987081081904488,
            -0.007034436792848042
          ],
          [
            0.005237029154831929,
            0.005238771228878392,
            -0.006155180912603364
          ],
          [
            0.004488995973327081,
            0.0044904888744070615,
            -0.005275889273453183
          ],
          [
            0.0037409916607359373,
            0.003742235434730845,
            -0.004396563030140299
          ],
          [
            0.0029930176354586724,
            0.0029940123286525955,
            -0.0035172033382204204
          ],
          [
            0.0022450753184817263,
            0.002245820977551438,
            -0.002637811354046782
          ],
          [
            0.0014971661333756936,
            0.0014976628054108598,
            -0.0017583882347605995
          ],
          [
            0.0007492915063160854,
            0.0007495392388132682,
            -0.0008789351382749166
          ],
          [
            1.4528660883250666e-06,
            1.4517069458763743e-06,
            5.467767061340112e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -231.48845586115817,
          -231.48789841639731,
          -231.4872789553894,
          -231.48659751041419,
          -231.48585411336933,
          -231.48504879577166,
          -231.4841815887565,
          -231.48325252307856,
          -231.48226162911186
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6350618973131866e-08,
            1.6279400478323295e-08,
            1.8127014123140282e-08
          ],
          [
            -7.165419669301472e-06,
            -7.143623816124031e-06,
            2.805599931446182e-05
          ],
          [
            -1.4346990336564922e-05,
            -1.4303329247391556e-05,
            5.6093350876457514e-05
          ],
          [
            -2.1528349206189387e-05,
            -2.146282475307829e-05,
            8.413014732326662e-05
          ],
          [
            -2.870948407264708e-05,
            -2.862209816397132e-05,
            0.00011216635427144875
          ],
          [
            -3.58903827008468e-05,
            -3.5781137281525945e-05,
            0.0001402019373290815
          ],
          [
            -4.3071032826561356e-05,
            -4.293992987806616e-05,
            0.0001682368620975594
          ],
          [
            -5.025142215573353e-05,
            -5.0098463696477944e-05,
            0.00019627109417119732
          ],
          [
            -5.743153836531638e-05,
            -5.7256726450278576e-05,
            0.00022430459913790456
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4528660890259512e-06,
            1.4517069482671235e-06,
            5.467767033981883e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4528660890259512e-06,
            1.4517069482671235e-06,
            5.467767033981883e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.005982185073034638,
          -0.005984178686633836,
          0.007035530209943762
        ],
        "actual_opposite_endpoint_branch_residual": 0.00046716643231426146
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883253366e-06,
            1.4517069458579255e-06,
            5.467767061852575e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883252834e-06,
            1.4517069458579428e-06,
            5.46776706185294e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0059850897894419,
            0.005987081081904488,
            -0.007034436792848042
          ],
          [
            0.005237029154831929,
            0.005238771228878392,
            -0.006155180912603364
          ],
          [
            0.004488995973327081,
            0.0044904888744070615,
            -0.005275889273453183
          ],
          [
            0.0037409916607359373,
            0.003742235434730845,
            -0.004396563030140299
          ],
          [
            0.0029930176354586724,
            0.0029940123286525955,
            -0.0035172033382204204
          ],
          [
            0.0022450753184817263,
            0.002245820977551438,
            -0.002637811354046782
          ],
          [
            0.0014971661333756936,
            0.0014976628054108598,
            -0.0017583882347605995
          ],
          [
            0.0007492915063160854,
            0.0007495392388132682,
            -0.0008789351382749166
          ],
          [
            1.4528660883250666e-06,
            1.4517069458763743e-06,
            5.467767061340112e-07
          ],
          [
            -0.0007128202363343439,
            -0.0007131765695552184,
            0.0008461184676881173
          ],
          [
            -0.001427085612998813,
            -0.001427797122952379,
            0.0016916879181795297
          ],
          [
            -0.0021413420810739714,
            -0.002142408769754245,
            0.0025372540910941765
          ],
          [
            -0.0028555884550900412,
            -0.002857010323817355,
            0.0033828159491087195
          ],
          [
            -0.003569823546873574,
            -0.0035716005963066233,
            0.0042283724546022805
          ],
          [
            -0.004284046165590971,
            -0.004286178395717766,
            0.005073922569711509
          ],
          [
            -0.00499825511768448,
            -0.005000742527848934,
            0.005919465256317702
          ],
          [
            -0.005712449206950743,
            -0.0057152917958087635,
            0.006764999476067457
          ]
        ]
      },
      "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": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848431
            ],
            "target_residual": 0.49303824694217496,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.008254819289786209,
            "step_scale": 0.7465296372721377,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0140002323187327,
              0.9938710130041809,
              0.9912931856868163
            ],
            "cell_volume_ratio": 0.9990108374041908,
            "cell_rmsd_from_input_A": 0.08193543211288344
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.009845527859875058,
              0.009845439496689758,
              -0.36374569082788755
            ],
            "branch_aligned_reduced_polarization": [
              0.009845527859875058,
              0.009845439496689758,
              -0.36374569082788755
            ],
            "target_residual": 0.13696387795945383,
            "energy_eV": -226.18344532256998,
            "max_atomic_step_A": 0.049616853962628674,
            "max_log_strain_component": 0.003462990243059462,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0201966025832645,
              0.9910941042406993,
              0.987611298170581
            ],
            "cell_volume_ratio": 0.9985844872983553,
            "cell_rmsd_from_input_A": 0.11942671429270713
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.002522544936673746,
              0.002522640870409207,
              -0.494247133420639
            ],
            "branch_aligned_reduced_polarization": [
              0.002522544936673746,
              0.002522640870409207,
              -0.494247133420639
            ],
            "target_residual": 0.00676922623336865,
            "energy_eV": -220.56786175803649,
            "max_atomic_step_A": 0.002336279652012686,
            "max_log_strain_component": 0.0001672931247284112,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0205115452198639,
              0.9909310018361485,
              0.9874491430420059
            ],
            "cell_volume_ratio": 0.9985643918606893,
            "cell_rmsd_from_input_A": 0.12156403957646698
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -6.960764253061999e-05,
              -6.95784433583225e-05,
              -0.49992008716592434
            ],
            "branch_aligned_reduced_polarization": [
              -6.960764253061999e-05,
              -6.95784433583225e-05,
              -0.49992008716592434
            ],
            "target_residual": 0.00012677714592481323,
            "energy_eV": -220.26607563466212
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00012677714592481323,
        "parent_symmetrization_rmsd_A": 0.13031785994656292,
        "parent_cell_rmsd_A": 0.12156403957646698,
        "energy_eV": -220.26607563466212,
        "reduced_polarization": [
          -6.960764253061999e-05,
          -6.95784433583225e-05,
          -0.49992008716592434
        ],
        "cartesian_polarization_e_A2": [
          -0.0005527213919216644,
          -0.0005507627111283297,
          -0.01661028623340001
        ],
        "ranking_score": 0.6609624241325293
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440097,
              0.005987081081903212,
              -0.007034436792848416
            ],
            "target_residual": 0.4940992498059052,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.051943460161601646,
            "max_log_strain_component": 0.003773905785998628,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0049731109711604,
              0.999562772907844,
              0.9954141824366433
            ],
            "cell_volume_ratio": 0.9999271011721461,
            "cell_rmsd_from_input_A": 0.04496913097322874
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0008781429915656524,
              0.49638582751535404,
              -0.0003185715307201647
            ],
            "branch_aligned_reduced_polarization": [
              0.0008781429915656524,
              0.49638582751535404,
              -0.0003185715307201647
            ],
            "target_residual": 0.003732943300211406,
            "energy_eV": -230.26300630650476,
            "max_atomic_step_A": 0.00040071107251707827,
            "max_log_strain_component": 3.3890589515126895e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0050081682152407,
              0.9995628542716176,
              0.9953797426740973
            ],
            "cell_volume_ratio": 0.9999274666766078,
            "cell_rmsd_from_input_A": 0.04529830051416273
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.9267921153212e-06,
              0.4999977714189914,
              2.9514707244331437e-08
            ],
            "branch_aligned_reduced_polarization": [
              3.9267921153212e-06,
              0.4999977714189914,
              2.9514707244331437e-08
            ],
            "target_residual": 4.51521214860255e-06,
            "energy_eV": -230.2445434250374
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.51521214860255e-06,
        "parent_symmetrization_rmsd_A": 0.04431253838392436,
        "parent_cell_rmsd_A": 0.04529830051416273,
        "energy_eV": -230.2445434250374,
        "reduced_polarization": [
          3.9267921153212e-06,
          0.4999977714189914,
          2.9514707244331437e-08
        ],
        "cartesian_polarization_e_A2": [
          3.2881430137912395e-05,
          0.0054643141794746075,
          1.3491558889468398e-07
        ],
        "ranking_score": 0.5556461439367623
      },
      "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": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440123,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "target_residual": 0.4941012648751482,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.051942400531622836,
            "max_log_strain_component": 0.0037740024295285033,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.004981250211597,
              0.9995547712446945,
              0.9954141197254696
            ],
            "cell_volume_ratio": 0.9999271319051543,
            "cell_rmsd_from_input_A": 0.044970343937477474
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49638672388492683,
              0.0008782608576812501,
              -0.0003187800463658682
            ],
            "branch_aligned_reduced_polarization": [
              0.49638672388492683,
              0.0008782608576812501,
              -0.0003187800463658682
            ],
            "target_residual": 0.003732120996947219,
            "energy_eV": -230.2629583110456,
            "max_atomic_step_A": 0.0004006415181992773,
            "max_log_strain_component": 3.389296023119444e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.005016346208902,
              0.9995548080259216,
              0.9953796873170032
            ],
            "cell_volume_ratio": 0.9999274984711222,
            "cell_rmsd_from_input_A": 0.045299447280547925
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.499997763022094,
              3.9479117016682505e-06,
              2.889474045481707e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.499997763022094,
              3.9479117016682505e-06,
              2.889474045481707e-08
            ],
            "target_residual": 4.53772099872049e-06,
            "energy_eV": -230.24449893378667
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 4.53772099872049e-06,
        "parent_symmetrization_rmsd_A": 0.044312115499502085,
        "parent_cell_rmsd_A": 0.045299447280547925,
        "energy_eV": -230.24449893378667,
        "reduced_polarization": [
          0.499997763022094,
          3.9479117016682505e-06,
          2.889474045481707e-08
        ],
        "cartesian_polarization_e_A2": [
          0.005464349591322878,
          1.3302598865363728e-05,
          1.3438671640936213e-07
        ],
        "ranking_score": 0.5556460527616365
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440097,
              0.005987081081903212,
              -0.007034436792848431
            ],
            "target_residual": 0.6979252337220011,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.009727992869143592,
            "step_scale": 0.7109072277211181,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.013331507907729,
              0.996055737695831,
              0.9897521791994155
            ],
            "cell_volume_ratio": 0.9989911818889142,
            "cell_rmsd_from_input_A": 0.06856356083009948
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.004571645163591629,
              0.3494197908895494,
              -0.34591185718808476
            ],
            "branch_aligned_reduced_polarization": [
              0.004571645163591629,
              0.3494197908895494,
              -0.34591185718808476
            ],
            "target_residual": 0.2154958353900929,
            "energy_eV": -225.60846401761506,
            "max_atomic_step_A": 0.060303947647113595,
            "max_log_strain_component": 0.005103360064653242,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0203487014200283,
              0.9940155079847927,
              0.984444173616272
            ],
            "cell_volume_ratio": 0.9984650535685707,
            "cell_rmsd_from_input_A": 0.10432151235726939
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0022657139665096956,
              0.49014520322843774,
              -0.492073584031415
            ],
            "branch_aligned_reduced_polarization": [
              0.0022657139665096956,
              0.49014520322843774,
              -0.492073584031415
            ],
            "target_residual": 0.012848289741980075,
            "energy_eV": -217.46880585937222,
            "max_atomic_step_A": 0.0035638228778091894,
            "max_log_strain_component": 0.0003273301753413575,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0207932554962553,
              0.9939078880146899,
              0.9840891525647678
            ],
            "cell_volume_ratio": 0.9984317290872343,
            "cell_rmsd_from_input_A": 0.1066068729537345
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.0620558428070413e-05,
              0.49977098485079574,
              -0.49987907953900657
            ],
            "branch_aligned_reduced_polarization": [
              2.0620558428070413e-05,
              0.49977098485079574,
              -0.49987907953900657
            ],
            "target_residual": 0.00025979781346616306,
            "energy_eV": -216.86549347596994
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00025979781346616306,
        "parent_symmetrization_rmsd_A": 0.1377837382550346,
        "parent_cell_rmsd_A": 0.1066068729537345,
        "energy_eV": -216.86549347596994,
        "reduced_polarization": [
          2.0620558428070413e-05,
          0.49977098485079574,
          -0.49987907953900657
        ],
        "cartesian_polarization_e_A2": [
          -0.0003832257966408343,
          0.004914022351519013,
          -0.016520436826991506
        ],
        "ranking_score": 0.6649550521204005
      },
      "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": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440123,
              0.005987081081903207,
              -0.007034436792848431
            ],
            "target_residual": 0.6979266603006171,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00973683396109749,
            "step_scale": 0.7109139873355674,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0133343904032885,
              0.9960654403006736,
              0.9897397348318895
            ],
            "cell_volume_ratio": 0.9989911941295492,
            "cell_rmsd_from_input_A": 0.06856852545745709
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3494256156075384,
              0.004570882765237737,
              -0.3459153142656629
            ],
            "branch_aligned_reduced_polarization": [
              0.3494256156075384,
              0.004570882765237737,
              -0.3459153142656629
            ],
            "target_residual": 0.21548927718629474,
            "energy_eV": -225.60832151737438,
            "max_atomic_step_A": 0.06030031128123119,
            "max_log_strain_component": 0.005107745124692111,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0203529093127168,
              0.994030140011866,
              0.984425657279052
            ],
            "cell_volume_ratio": 0.9984650883903664,
            "cell_rmsd_from_input_A": 0.10432741889191835
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49014320816250084,
              0.00226514464338566,
              -0.4920736633240082
            ],
            "branch_aligned_reduced_polarization": [
              0.49014320816250084,
              0.00226514464338566,
              -0.4920736633240082
            ],
            "target_residual": 0.01284967076171298,
            "energy_eV": -217.46877659948228,
            "max_atomic_step_A": 0.0035638207857862357,
            "max_log_strain_component": 0.0003277591550931766,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0207976033654491,
              0.9939229092909734,
              0.9840701234007802
            ],
            "cell_volume_ratio": 0.9984317645448603,
            "cell_rmsd_from_input_A": 0.10661288791489562
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49977061271629686,
              2.065418274338373e-05,
              -0.49987906878510097
            ],
            "branch_aligned_reduced_polarization": [
              0.49977061271629686,
              2.065418274338373e-05,
              -0.49987906878510097
            ],
            "target_residual": 0.0002601335809280668,
            "energy_eV": -216.86544189050446
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0002601335809280668,
        "parent_symmetrization_rmsd_A": 0.1377823658385708,
        "parent_cell_rmsd_A": 0.10661288791489562,
        "energy_eV": -216.86544189050446,
        "reduced_polarization": [
          0.49977061271629686,
          2.065418274338373e-05,
          -0.49987906878510097
        ],
        "cartesian_polarization_e_A2": [
          0.0049123423592750065,
          -0.0004008525966746005,
          -0.01652043944602777
        ],
        "ranking_score": 0.6649558549791509
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440123,
              0.005987081081903212,
              -0.007034436792848416
            ],
            "target_residual": 0.6986765910414618,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.0686201668392776,
            "max_log_strain_component": 0.00504323094610222,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0089125178760012,
              0.9966294317815758,
              0.9943522602781572
            ],
            "cell_volume_ratio": 0.9998330398565278,
            "cell_rmsd_from_input_A": 0.07885631360217013
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4924605600391763,
              0.49245790571432013,
              0.0007928714998422362
            ],
            "branch_aligned_reduced_polarization": [
              0.4924605600391763,
              0.49245790571432013,
              0.0007928714998422362
            ],
            "target_residual": 0.0106936890899358,
            "energy_eV": -229.09412760682437,
            "max_atomic_step_A": 0.0012177610580258948,
            "max_log_strain_component": 0.00010549150230899657,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0090613354885154,
              0.996550606563377,
              0.9942789041653874
            ],
            "cell_volume_ratio": 0.999827662467029,
            "cell_rmsd_from_input_A": 0.08004426943688372
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.500041014672091,
              0.5000411020141007,
              -3.4847121328948592e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.500041014672091,
              0.5000411020141007,
              -3.4847121328948592e-06
            ],
            "target_residual": 5.816976971347274e-05,
            "energy_eV": -229.02155663322057
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "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": 5.816976971347274e-05,
        "parent_symmetrization_rmsd_A": 0.06278048790497663,
        "parent_cell_rmsd_A": 0.08004426943688372,
        "energy_eV": -229.02155663322057,
        "reduced_polarization": [
          0.500041014672091,
          0.5000411020141007,
          -3.4847121328948592e-06
        ],
        "cartesian_polarization_e_A2": [
          0.005522849188547957,
          0.005503163752275062,
          -4.071594795119354e-05
        ],
        "ranking_score": 0.5829078948036245
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.005985089789440097,
              0.005987081081903207,
              -0.007034436792848416
            ],
            "branch_aligned_reduced_polarization": [
              0.005985089789440123,
              0.005987081081903212,
              -0.007034436792848431
            ],
            "target_residual": 0.8550523621840184,
            "energy_eV": -231.4905157351283,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011471615957847051,
            "step_scale": 0.702808180858369,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0139082801620654,
              0.9958858223517237,
              0.989303887696503
            ],
            "cell_volume_ratio": 0.9989366222982137,
            "cell_rmsd_from_input_A": 0.06625471346808412
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3390519126156206,
              0.339047434905194,
              -0.3395304163335884
            ],
            "branch_aligned_reduced_polarization": [
              0.3390519126156206,
              0.339047434905194,
              -0.3395304163335884
            ],
            "target_residual": 0.27849686232587806,
            "energy_eV": -224.7946543281138,
            "max_atomic_step_A": 0.06690285575669994,
            "max_log_strain_component": 0.00669749864376326,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.021989092764975,
              0.9935753732943792,
              0.9831646394807364
            ],
            "cell_volume_ratio": 0.9983281787902943,
            "cell_rmsd_from_input_A": 0.10447353844907642
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48638367922707193,
              0.4863844392751401,
              -0.4893461739443456
            ],
            "branch_aligned_reduced_polarization": [
              0.48638367922707193,
              0.4863844392751401,
              -0.4893461739443456
            ],
            "target_residual": 0.022006628430265303,
            "energy_eV": -214.42050640558722,
            "max_atomic_step_A": 0.005665608498122089,
            "max_log_strain_component": 0.0006553574289106904,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.489222922255669,
            "cell_principal_stretches": [
              1.0227442213654818,
              0.9933744953556435,
              0.9825825008650249
            ],
            "cell_volume_ratio": 0.998272402584123,
            "cell_rmsd_from_input_A": 0.1080834517254614
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49987382416815174,
              0.49987426678672553,
              -0.4997801549432383
            ],
            "branch_aligned_reduced_polarization": [
              0.49987382416815174,
              0.49987426678672553,
              -0.4997801549432383
            ],
            "target_residual": 0.0002829505795107706,
            "energy_eV": -213.35333174475318
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "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": 0.0002829505795107706,
        "parent_symmetrization_rmsd_A": 0.14592145486530914,
        "parent_cell_rmsd_A": 0.1080834517254614,
        "energy_eV": -213.35333174475318,
        "reduced_polarization": [
          0.49987382416815174,
          0.49987426678672553,
          -0.4997801549432383
        ],
        "cartesian_polarization_e_A2": [
          0.005113906761211352,
          0.005095922497486293,
          -0.016471778249090113
        ],
        "ranking_score": 0.673508218955696
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35
        ],
        "endpoint_rmsd_A": 0.0018526666918618406,
        "minimum_distance_A_by_image": [
          1.4929588126097477,
          1.4926720702070801,
          1.4923853785481567,
          1.4920987376668657,
          1.4918121475971202,
          1.4915256083728405,
          1.491239120027984,
          1.490952682596523,
          1.4906662961124477
        ],
        "minimum_distance_A": 1.4906662961124477,
        "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": [
          502.53086471585806,
          502.53219654049366,
          502.53352836865844,
          502.53486020035285,
          502.5361920355774,
          502.53752387433076,
          502.5388557166147,
          502.5401875624283,
          502.5415194117725
        ],
        "cell_deformation_log_strain_norm": 0.000356346593787789
      },
      "parent_reduced_polarization": [
        1.4528660883253366e-06,
        1.4517069458579255e-06,
        5.467767061852575e-07
      ],
      "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": [
          -231.49051573512824,
          -231.4904922532873,
          -231.4904018095834,
          -231.49024445655667,
          -231.4900202463282,
          -231.48972923059992,
          -231.48937146065532,
          -231.48894698735918,
          -231.48845586115817
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.0213795321725274e-05,
            6.0019745245741457e-05,
            -0.00023323823313847812
          ],
          [
            5.268827397873006e-05,
            5.2518468280960355e-05,
            -0.00020408670245174138
          ],
          [
            4.516296364769852e-05,
            4.501740327495566e-05,
            -0.0001749335195841988
          ],
          [
            3.7637878896163305e-05,
            3.751656474774975e-05,
            -0.00014577872282922142
          ],
          [
            3.0113034319155663e-05,
            3.0015967246451197e-05,
            -0.00011662235050874172
          ],
          [
            2.2588444539167275e-05,
            2.2515625345412033e-05,
            -8.746444097274995e-05
          ],
          [
            1.5064124206121715e-05,
            1.5015553646535306e-05,
            -5.830503259898572e-05
          ],
          [
            7.540087997618507e-06,
            7.515766779230571e-06,
            -2.914416379239593e-05
          ],
          [
            1.635061896752943e-08,
            1.6279400454132372e-08,
            1.812701421555457e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883253366e-06,
            1.4517069458579255e-06,
            5.467767061852575e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883252834e-06,
            1.4517069458579428e-06,
            5.46776706185294e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0059850897894419,
            0.005987081081904488,
            -0.007034436792848042
          ],
          [
            0.005237029154831929,
            0.005238771228878392,
            -0.006155180912603364
          ],
          [
            0.004488995973327081,
            0.0044904888744070615,
            -0.005275889273453183
          ],
          [
            0.0037409916607359373,
            0.003742235434730845,
            -0.004396563030140299
          ],
          [
            0.0029930176354586724,
            0.0029940123286525955,
            -0.0035172033382204204
          ],
          [
            0.0022450753184817263,
            0.002245820977551438,
            -0.002637811354046782
          ],
          [
            0.0014971661333756936,
            0.0014976628054108598,
            -0.0017583882347605995
          ],
          [
            0.0007492915063160854,
            0.0007495392388132682,
            -0.0008789351382749166
          ],
          [
            1.4528660883250666e-06,
            1.4517069458763743e-06,
            5.467767061340112e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -231.48845586115817,
          -231.48789841639731,
          -231.4872789553894,
          -231.48659751041419,
          -231.48585411336933,
          -231.48504879577166,
          -231.4841815887565,
          -231.48325252307856,
          -231.48226162911186
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6350618973131866e-08,
            1.6279400478323295e-08,
            1.8127014123140282e-08
          ],
          [
            -7.165419669301472e-06,
            -7.143623816124031e-06,
            2.805599931446182e-05
          ],
          [
            -1.4346990336564922e-05,
            -1.4303329247391556e-05,
            5.6093350876457514e-05
          ],
          [
            -2.1528349206189387e-05,
            -2.146282475307829e-05,
            8.413014732326662e-05
          ],
          [
            -2.870948407264708e-05,
            -2.862209816397132e-05,
            0.00011216635427144875
          ],
          [
            -3.58903827008468e-05,
            -3.5781137281525945e-05,
            0.0001402019373290815
          ],
          [
            -4.3071032826561356e-05,
            -4.293992987806616e-05,
            0.0001682368620975594
          ],
          [
            -5.025142215573353e-05,
            -5.0098463696477944e-05,
            0.00019627109417119732
          ],
          [
            -5.743153836531638e-05,
            -5.7256726450278576e-05,
            0.00022430459913790456
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4528660890259512e-06,
            1.4517069482671235e-06,
            5.467767033981883e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4528660890259512e-06,
            1.4517069482671235e-06,
            5.467767033981883e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.005982185073034638,
          -0.005984178686633836,
          0.007035530209943762
        ],
        "actual_opposite_endpoint_branch_residual": 0.00046716643231426146
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883253366e-06,
            1.4517069458579255e-06,
            5.467767061852575e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0059850897894418815,
            0.005987081081904462,
            -0.007034436792848061
          ],
          [
            0.005237029154831952,
            0.005238771228878356,
            -0.006155180912603386
          ],
          [
            0.004488995973327048,
            0.004490488874407113,
            -0.005275889273453165
          ],
          [
            0.0037409916607359654,
            0.003742235434730879,
            -0.004396563030140285
          ],
          [
            0.0029930176354586277,
            0.0029940123286525643,
            -0.0035172033382204243
          ],
          [
            0.0022450753184817375,
            0.0022458209775514174,
            -0.0026378113540467605
          ],
          [
            0.0014971661333756997,
            0.0014976628054108184,
            -0.0017583882347606038
          ],
          [
            0.0007492915063160644,
            0.0007495392388132908,
            -0.0008789351382749114
          ],
          [
            1.4528660883252834e-06,
            1.4517069458579428e-06,
            5.46776706185294e-07
          ],
          [
            -0.0007128202363343198,
            -0.0007131765695552395,
            0.0008461184676881511
          ],
          [
            -0.001427085612998824,
            -0.0014277971229523533,
            0.0016916879181795364
          ],
          [
            -0.0021413420810739965,
            -0.0021424087697542215,
            0.0025372540910942173
          ],
          [
            -0.00285558845509003,
            -0.002857010323817356,
            0.0033828159491086935
          ],
          [
            -0.003569823546873573,
            -0.0035716005963066138,
            0.004228372454602326
          ],
          [
            -0.004284046165590993,
            -0.004286178395717763,
            0.005073922569711532
          ],
          [
            -0.004998255117684484,
            -0.005000742527848928,
            0.005919465256317714
          ],
          [
            -0.005712449206950753,
            -0.005715291795808759,
            0.006764999476067489
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0059850897894419,
            0.005987081081904488,
            -0.007034436792848042
          ],
          [
            0.005237029154831929,
            0.005238771228878392,
            -0.006155180912603364
          ],
          [
            0.004488995973327081,
            0.0044904888744070615,
            -0.005275889273453183
          ],
          [
            0.0037409916607359373,
            0.003742235434730845,
            -0.004396563030140299
          ],
          [
            0.0029930176354586724,
            0.0029940123286525955,
            -0.0035172033382204204
          ],
          [
            0.0022450753184817263,
            0.002245820977551438,
            -0.002637811354046782
          ],
          [
            0.0014971661333756936,
            0.0014976628054108598,
            -0.0017583882347605995
          ],
          [
            0.0007492915063160854,
            0.0007495392388132682,
            -0.0008789351382749166
          ],
          [
            1.4528660883250666e-06,
            1.4517069458763743e-06,
            5.467767061340112e-07
          ],
          [
            -0.0007128202363343439,
            -0.0007131765695552184,
            0.0008461184676881173
          ],
          [
            -0.001427085612998813,
            -0.001427797122952379,
            0.0016916879181795297
          ],
          [
            -0.0021413420810739714,
            -0.002142408769754245,
            0.0025372540910941765
          ],
          [
            -0.0028555884550900412,
            -0.002857010323817355,
            0.0033828159491087195
          ],
          [
            -0.003569823546873574,
            -0.0035716005963066233,
            0.0042283724546022805
          ],
          [
            -0.004284046165590971,
            -0.004286178395717766,
            0.005073922569711509
          ],
          [
            -0.00499825511768448,
            -0.005000742527848934,
            0.005919465256317702
          ],
          [
            -0.005712449206950743,
            -0.0057152917958087635,
            0.006764999476067457
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "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": 2.125379430125551e-06,
        "parent_symmetrization_rmsd_A": 0.0018526666918618406,
        "parent_cell_rmsd_A": 0.0013169675687520993,
        "energy_eV": -231.48845586115817,
        "reduced_polarization": [
          1.452866092279514e-06,
          1.4517069528362551e-06,
          5.467767030444348e-07
        ],
        "cartesian_polarization_e_A2": [
          1.635061900858289e-08,
          1.6279400527975437e-08,
          1.812701411140382e-08
        ],
        "ranking_score": 0.5021861593429101
      }
    }
  ],
  "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": 54,
      "full_response": 20,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 79,
      "full_response": 45,
      "energy_polarization": 34
    },
    "elapsed_seconds": 770.0621223720373
  }
}
