{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "As4Bi4Ca8O24",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -246.17449818921642,
  "input_cartesian_polarization_e_A2": [
    1.132787951925141e-17,
    9.783596445929172e-18,
    -0.002251075597531765
  ],
  "input_reduced_polarization": [
    7.708213919583858e-16,
    4.954497508177953e-16,
    -0.24643539004979242
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -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": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3154210667877377e-15,
      "parent_symmetrization_rmsd_A": 0.5386385645867909,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -217.13579913411678,
      "reduced_polarization": [
        7.356948464456454e-16,
        9.863225986257262e-16,
        -4.650305444833733e-16
      ],
      "cartesian_polarization_e_A2": [
        1.0811664894635355e-17,
        1.947681324801604e-17,
        -4.247843260588186e-18
      ],
      "ranking_score": 0.5386385645867936
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.149524195281169e-16,
      "parent_symmetrization_rmsd_A": 0.538638564586791,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -217.04609624836363,
      "reduced_polarization": [
        4.674006965924268e-16,
        5.949973912823407e-17,
        -2.077796049819327e-16
      ],
      "cartesian_polarization_e_A2": [
        6.868852932014938e-18,
        1.1749353699499236e-18,
        -1.897972520688338e-18
      ],
      "ranking_score": 0.538638564586792
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.848993216777401e-16,
      "parent_symmetrization_rmsd_A": 0.538638564586791,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -215.25713179123525,
      "reduced_polarization": [
        6.203821745889612e-16,
        2.7919108360171373e-16,
        -7.915413523121248e-17
      ],
      "cartesian_polarization_e_A2": [
        9.117046572592196e-18,
        5.513158274380411e-18,
        -7.2303715073841455e-19
      ],
      "ranking_score": 0.5386385645867924
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00015054883455380017,
      "parent_symmetrization_rmsd_A": 0.015349629114250042,
      "parent_cell_rmsd_A": 0.010836045873482837,
      "energy_eV": -246.09087130181524,
      "reduced_polarization": [
        -2.3882697785089153e-15,
        -3.597956429176629e-15,
        0.00015054883455380017
      ],
      "cartesian_polarization_e_A2": [
        -3.505229795390998e-17,
        -7.096814010096443e-17,
        1.3774865418081231e-06
      ],
      "ranking_score": 0.5183597382517283
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8575867699450527e-15,
      "parent_symmetrization_rmsd_A": 0.5386399984854493,
      "parent_cell_rmsd_A": 0.010836045873482837,
      "energy_eV": -217.54400307119832,
      "reduced_polarization": [
        7.147854642063976e-16,
        2.9773768437402044e-16,
        1.6885089929691627e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0491629878070649e-17,
        5.872602299888846e-18,
        1.5449461435092195e-17
      ],
      "ranking_score": 0.5413490099538236
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.3026619221301153e-15,
      "parent_symmetrization_rmsd_A": 0.657234027815721,
      "parent_cell_rmsd_A": 0.010836045873482837,
      "energy_eV": -231.60381308258061,
      "reduced_polarization": [
        -2.1763374927001563e-15,
        2.2124200238869506e-15,
        -1.1297471078342492e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.194430861647319e-17,
        4.3637952474558654e-17,
        -1.0336921181095021e-17
      ],
      "ranking_score": 0.6599430392840983
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0003537067094538382,
      "parent_symmetrization_rmsd_A": 0.01585631709563427,
      "parent_cell_rmsd_A": 0.01115674534964635,
      "energy_eV": -246.12655079222614,
      "reduced_polarization": [
        9.70056361365632e-16,
        9.05647954075777e-16,
        -0.49964629329054616
      ],
      "cartesian_polarization_e_A2": [
        2.3543736796517614e-17,
        1.184403685505561e-17,
        -0.004556231649353723
      ],
      "ranking_score": 0.5193529168519535
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.213675769098191e-05,
      "parent_symmetrization_rmsd_A": 0.07502146160410192,
      "parent_cell_rmsd_A": 0.049143891201621395,
      "energy_eV": -244.874829899058,
      "reduced_polarization": [
        0.5000149003275359,
        1.3449068537993205e-15,
        -4.996220313247056e-05
      ],
      "cartesian_polarization_e_A2": [
        0.007340180265235875,
        6.103140883452165e-17,
        -6.935390062408041e-05
      ],
      "ranking_score": 0.5874117079198893
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.2234627585840896e-05,
      "parent_symmetrization_rmsd_A": 0.10226537535937738,
      "parent_cell_rmsd_A": 0.05465736318433047,
      "energy_eV": -243.18126336045236,
      "reduced_polarization": [
        2.9795211816800238e-15,
        0.5000327011507054,
        -2.672823431984076e-05
      ],
      "cartesian_polarization_e_A2": [
        2.908427359105862e-17,
        0.009864093763430773,
        -7.733075889991803e-05
      ],
      "ranking_score": 0.6160141854106317
    },
    {
      "candidate_id": "bec_projection_04",
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 5.666317681537759e-05,
      "parent_symmetrization_rmsd_A": 0.07609707127658051,
      "parent_cell_rmsd_A": 0.05029329587153133,
      "energy_eV": -245.00441255148718,
      "reduced_polarization": [
        0.5000129563537274,
        2.073302804379263e-15,
        -0.49994483797950673
      ],
      "cartesian_polarization_e_A2": [
        0.007401833199087666,
        4.448415025534645e-17,
        -0.004628570212063677
      ],
      "ranking_score": 0.5887837215980941
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 5.356242128223261e-05,
      "parent_symmetrization_rmsd_A": 0.10219855830621762,
      "parent_cell_rmsd_A": 0.05521533054363294,
      "energy_eV": -243.58045067254182,
      "reduced_polarization": [
        9.80116120971893e-19,
        0.5000362804303954,
        -0.49996059615064564
      ],
      "cartesian_polarization_e_A2": [
        -9.691279305355724e-18,
        0.00992310452730935,
        -0.004635455251723802
      ],
      "ranking_score": 0.6161095157846903
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.143347521765856e-06,
      "parent_symmetrization_rmsd_A": 0.12477532600697418,
      "parent_cell_rmsd_A": 0.07192778962735828,
      "energy_eV": -241.93318935756503,
      "reduced_polarization": [
        0.5000004224454796,
        0.500001224161464,
        -6.005304929816001e-06
      ],
      "cartesian_polarization_e_A2": [
        0.0073412565086329136,
        0.00986464811970481,
        -0.0001444153424178408
      ],
      "ranking_score": 0.6427695601088572
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.732687686596881e-06,
      "parent_symmetrization_rmsd_A": 0.12539201896380667,
      "parent_cell_rmsd_A": 0.07325852062805413,
      "energy_eV": -242.39832632028703,
      "reduced_polarization": [
        0.5000022991065709,
        0.5000025995551064,
        -0.49999862545295093
      ],
      "cartesian_polarization_e_A2": [
        0.0074026296237027014,
        0.009923420665125717,
        -0.00470401408493799
      ],
      "ranking_score": 0.6437141144961934
    }
  ],
  "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.24643539004979242,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.01953153157609001,
            "max_log_strain_component": 0.0020178794614775916,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.002019916750342,
              0.9991973178223903,
              0.999138692836524
            ],
            "cell_volume_ratio": 1.0003532590417048,
            "cell_rmsd_from_input_A": 0.010836045873482837
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.3882697785089153e-15,
              -3.597956429176629e-15,
              0.00015054883455380017
            ],
            "branch_aligned_reduced_polarization": [
              -2.3882697785089153e-15,
              -3.597956429176629e-15,
              0.00015054883455380017
            ],
            "target_residual": 0.00015054883455380017,
            "energy_eV": -246.09087130181524
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00015054883455380017,
        "parent_symmetrization_rmsd_A": 0.015349629114250042,
        "parent_cell_rmsd_A": 0.010836045873482837,
        "energy_eV": -246.09087130181524,
        "reduced_polarization": [
          -2.3882697785089153e-15,
          -3.597956429176629e-15,
          0.00015054883455380017
        ],
        "cartesian_polarization_e_A2": [
          -3.505229795390998e-17,
          -7.096814010096443e-17,
          1.3774865418081231e-06
        ],
        "ranking_score": 0.5183597382517283
      },
      "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": [
          -246.17449818921642,
          -246.17071570941727,
          -246.1649700086645,
          -246.15729056726417,
          -246.14770618016883,
          -246.1362449604983,
          -246.12293433900456,
          -246.10780108231313,
          -246.09087130181527
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8905041301583052e-17,
            2.465104785798782e-17,
            -0.002251075597531767
          ],
          [
            -2.680501218961069e-17,
            2.1215684707679986e-17,
            -0.001970526830516224
          ],
          [
            -1.2384371462983552e-17,
            -3.773016961459424e-17,
            -0.0016896723919207083
          ],
          [
            -2.129769256426254e-18,
            -1.3103312724834574e-17,
            -0.0014085212846724608
          ],
          [
            -4.617492033395215e-18,
            3.998593032813401e-17,
            -0.0011270823782990218
          ],
          [
            -4.338891695118234e-17,
            -4.55638761666822e-17,
            -0.000845364427475596
          ],
          [
            -1.9936411419037357e-17,
            7.296223232993109e-18,
            -0.0005633760949278596
          ],
          [
            -1.093644589063907e-17,
            -6.281703096136208e-17,
            -0.0002811259555279767
          ],
          [
            -4.776234867546397e-17,
            -7.62534821708644e-17,
            1.3774865418045544e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757507e-16,
            -1.9432887769693967e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840282e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.983340725991733e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455341013
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757506e-16,
            -1.943288776969397e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840278e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.9833407259917333e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455340937
          ]
        ],
        "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": [
          [
            1.3322676295501878e-15,
            1.2212453270876722e-15,
            -0.24643539004979265
          ],
          [
            -1.7763568394002505e-15,
            1.1102230246251565e-15,
            -0.21567756823008355
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            -0.18489908559276869
          ],
          [
            -5.551115123125783e-17,
            -7.216449660063518e-16,
            -0.15410094400243946
          ],
          [
            -2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.12328412990463788
          ],
          [
            -2.886579864025407e-15,
            -2.3314683517128287e-15,
            -0.09244961636981958
          ],
          [
            -1.27675647831893e-15,
            3.3306690738754696e-16,
            -0.06159836561098753
          ],
          [
            -7.216449660063518e-16,
            -3.219646771412954e-15,
            -0.030731329442324096
          ],
          [
            -3.2751579226442118e-15,
            -3.885780586188048e-15,
            0.00015054883455345447
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -246.09087130181527,
          -246.07559637035243,
          -246.0590413406469,
          -246.041219529882,
          -246.0221439193468,
          -246.00182715876355,
          -245.98028157041298,
          -245.95751915306334,
          -245.933551585703
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.299783242524315e-17,
            -3.1328074576714726e-17,
            1.3774865418048705e-06
          ],
          [
            -1.9379813742190526e-17,
            -7.487898512654271e-17,
            0.00027011463586382823
          ],
          [
            -1.532192810188165e-17,
            -1.025763148638443e-16,
            0.0005387093403166603
          ],
          [
            -2.183928921746354e-17,
            -1.8343018070077314e-17,
            0.0008071536230597216
          ],
          [
            -1.0733636480184682e-16,
            -2.279198028703639e-16,
            0.0010754395350363944
          ],
          [
            -1.756652929032132e-17,
            -1.8735478004664333e-16,
            0.0013435591475044588
          ],
          [
            -7.208039670379004e-17,
            -7.139361436054957e-17,
            0.00161150454450504
          ],
          [
            1.6174724500781498e-17,
            -1.1640384197440604e-16,
            0.0018792678152809352
          ],
          [
            -5.83646529869059e-19,
            -1.2228365811863436e-16,
            0.002146841046654497
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.9295920145640313e-15,
            -1.588227059651993e-15,
            0.00015054883455344466
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.91308036075152e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640377e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.9295920145640313e-15,
            -1.588227059651993e-15,
            0.00015054883455344466
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.913080360751522e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640373e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.786531475697735e-15,
          -8.971434327327217e-15,
          0.2467369893684385
        ],
        "actual_opposite_endpoint_branch_residual": 0.011712625332285731
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757507e-16,
            -1.9432887769693967e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840282e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.983340725991733e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455341013
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.91308036075152e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640377e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757506e-16,
            -1.943288776969397e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840278e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.9833407259917333e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455340937
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.913080360751522e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640373e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "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": [
          [
            1.3322676295501878e-15,
            1.2212453270876722e-15,
            -0.24643539004979265
          ],
          [
            -1.7763568394002505e-15,
            1.1102230246251565e-15,
            -0.21567756823008355
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            -0.18489908559276869
          ],
          [
            -5.551115123125783e-17,
            -7.216449660063518e-16,
            -0.15410094400243946
          ],
          [
            -2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.12328412990463788
          ],
          [
            -2.886579864025407e-15,
            -2.3314683517128287e-15,
            -0.09244961636981958
          ],
          [
            -1.27675647831893e-15,
            3.3306690738754696e-16,
            -0.06159836561098753
          ],
          [
            -7.216449660063518e-16,
            -3.219646771412954e-15,
            -0.030731329442324096
          ],
          [
            -3.2751579226442118e-15,
            -3.885780586188048e-15,
            0.00015054883455345447
          ],
          [
            -1.3322676295501878e-15,
            -3.774758283725532e-15,
            0.029527625246608125
          ],
          [
            -1.1102230246251565e-15,
            -5.162537064506978e-15,
            0.0589013541782043
          ],
          [
            -1.5543122344752192e-15,
            -8.881784197001252e-16,
            0.08827085737001328
          ],
          [
            -7.382983113757291e-15,
            -1.149080830487037e-14,
            0.11763525887265247
          ],
          [
            -1.27675647831893e-15,
            -9.43689570931383e-15,
            0.14699368423225223
          ],
          [
            -4.9404924595819466e-15,
            -3.608224830031759e-15,
            0.1763452596682753
          ],
          [
            1.1102230246251565e-15,
            -5.88418203051333e-15,
            0.20568911124476918
          ],
          [
            -5.551115123125783e-17,
            -6.217248937900877e-15,
            0.2350243640361528
          ]
        ]
      },
      "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.2535646099502076,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.020096566425872386,
            "max_log_strain_component": 0.0020762554374707245,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0008869992610268,
              1.0008265763375945,
              0.997925898489891
            ],
            "cell_volume_ratio": 0.9996366516107018,
            "cell_rmsd_from_input_A": 0.01115674534964635
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.70056361365632e-16,
              9.05647954075777e-16,
              -0.49964629329054616
            ],
            "branch_aligned_reduced_polarization": [
              9.70056361365632e-16,
              9.05647954075777e-16,
              -0.49964629329054616
            ],
            "target_residual": 0.0003537067094538382,
            "energy_eV": -246.12655079222614
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0003537067094538382,
        "parent_symmetrization_rmsd_A": 0.01585631709563427,
        "parent_cell_rmsd_A": 0.01115674534964635,
        "energy_eV": -246.12655079222614,
        "reduced_polarization": [
          9.70056361365632e-16,
          9.05647954075777e-16,
          -0.49964629329054616
        ],
        "cartesian_polarization_e_A2": [
          2.3543736796517614e-17,
          1.184403685505561e-17,
          -0.004556231649353723
        ],
        "ranking_score": 0.5193529168519535
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.5574319702609392,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.07038865890728878,
            "max_log_strain_component": 0.009443211604135329,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0101819276909254,
              0.9991973178223813,
              0.9910659084018136
            ],
            "cell_volume_ratio": 1.0003532590416984,
            "cell_rmsd_from_input_A": 0.04964984813667415
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5041504430214067,
              -6.373652743553697e-15,
              0.01784685072922039
            ],
            "branch_aligned_reduced_polarization": [
              0.5041504430214067,
              -6.373652743553697e-15,
              0.01784685072922039
            ],
            "target_residual": 0.018323107220802305,
            "energy_eV": -244.84021747856082,
            "max_atomic_step_A": 0.0014267233799964375,
            "max_log_strain_component": 0.0001421756992980576,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0100574927333397,
              0.9992538520778655,
              0.9911072612278375
            ],
            "cell_volume_ratio": 1.0003283650391814,
            "cell_rmsd_from_input_A": 0.049143891201621395
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000149003275359,
              1.3449068537993205e-15,
              -4.996220313247056e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000149003275359,
              1.3449068537993205e-15,
              -4.996220313247056e-05
            ],
            "target_residual": 5.213675769098191e-05,
            "energy_eV": -244.874829899058
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.213675769098191e-05,
        "parent_symmetrization_rmsd_A": 0.07502146160410192,
        "parent_cell_rmsd_A": 0.049143891201621395,
        "energy_eV": -244.874829899058,
        "reduced_polarization": [
          0.5000149003275359,
          1.3449068537993205e-15,
          -4.996220313247056e-05
        ],
        "cartesian_polarization_e_A2": [
          0.007340180265235875,
          6.103140883452165e-17,
          -6.935390062408041e-05
        ],
        "ranking_score": 0.5874117079198893
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.708213919583858e-16,
              4.996003610813204e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.5574319702609394,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.11642389602197421,
            "max_log_strain_component": 0.007783653169829019,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0085542286399631,
              0.9991386928365239,
              0.9927236283285829
            ],
            "cell_volume_ratio": 1.0003532590417477,
            "cell_rmsd_from_input_A": 0.054701002801837144
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.139640998281776e-15,
              0.49875632748372717,
              0.023710015062904315
            ],
            "branch_aligned_reduced_polarization": [
              -2.139640998281776e-15,
              0.49875632748372717,
              0.023710015062904315
            ],
            "target_residual": 0.02374261012632945,
            "energy_eV": -243.1655092585165,
            "max_atomic_step_A": 0.0018787005557050077,
            "max_log_strain_component": 0.0001955933949249911,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0084937999971593,
              0.9992221470054159,
              0.9926662107231882
            ],
            "cell_volume_ratio": 1.0003190121224284,
            "cell_rmsd_from_input_A": 0.05465736318433047
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.9795211816800238e-15,
              0.5000327011507054,
              -2.672823431984076e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.9795211816800238e-15,
              0.5000327011507054,
              -2.672823431984076e-05
            ],
            "target_residual": 4.2234627585840896e-05,
            "energy_eV": -243.18126336045236
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.2234627585840896e-05,
        "parent_symmetrization_rmsd_A": 0.10226537535937738,
        "parent_cell_rmsd_A": 0.05465736318433047,
        "energy_eV": -243.18126336045236,
        "reduced_polarization": [
          2.9795211816800238e-15,
          0.5000327011507054,
          -2.672823431984076e-05
        ],
        "cartesian_polarization_e_A2": [
          2.908427359105862e-17,
          0.009864093763430773,
          -7.733075889991803e-05
        ],
        "ranking_score": 0.6160141854106317
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.5606202024715129,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.07048916164648555,
            "max_log_strain_component": 0.009443211604139364,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0090041784016373,
              1.0008265763375852,
              0.9898978412622925
            ],
            "cell_volume_ratio": 0.999636651610695,
            "cell_rmsd_from_input_A": 0.04967957431618769
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4960343790014,
              -4.2790548951918943e-16,
              -0.4817770612982526
            ],
            "branch_aligned_reduced_polarization": [
              0.4960343790014,
              -4.2790548951918943e-16,
              -0.4817770612982526
            ],
            "target_residual": 0.018649440871837966,
            "energy_eV": -245.0280910632579,
            "max_atomic_step_A": 0.001505139608613313,
            "max_log_strain_component": 0.00015446440589917147,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.009061776390688,
              1.0008880973330516,
              0.9897537353774066
            ],
            "cell_volume_ratio": 0.9996096253421887,
            "cell_rmsd_from_input_A": 0.05029329587153133
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000129563537274,
              2.073302804379263e-15,
              -0.49994483797950673
            ],
            "branch_aligned_reduced_polarization": [
              0.5000129563537274,
              2.073302804379263e-15,
              -0.49994483797950673
            ],
            "target_residual": 5.666317681537759e-05,
            "energy_eV": -245.00441255148718
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 5.666317681537759e-05,
        "parent_symmetrization_rmsd_A": 0.07609707127658051,
        "parent_cell_rmsd_A": 0.05029329587153133,
        "energy_eV": -245.00441255148718,
        "reduced_polarization": [
          0.5000129563537274,
          2.073302804379263e-15,
          -0.49994483797950673
        ],
        "cartesian_polarization_e_A2": [
          0.007401833199087666,
          4.448415025534645e-17,
          -0.004628570212063677
        ],
        "ranking_score": 0.5887837215980941
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.708213919583858e-16,
              4.996003610813204e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.5606202024715131,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.11648731525817711,
            "max_log_strain_component": 0.007783653169826414,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0073194349559575,
              1.0008869992610265,
              0.9914935876006064
            ],
            "cell_volume_ratio": 0.9996366516107442,
            "cell_rmsd_from_input_A": 0.05481290117032426
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.676728293294217e-15,
              0.49879625306871916,
              -0.4737659959998842
            ],
            "branch_aligned_reduced_polarization": [
              1.676728293294217e-15,
              0.49879625306871916,
              -0.4737659959998842
            ],
            "target_residual": 0.026261606435110905,
            "energy_eV": -243.5886265317985,
            "max_atomic_step_A": 0.002078013791867558,
            "max_log_strain_component": 0.000218949258099232,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0073044911495521,
              1.0009805826493805,
              0.9913776052773654
            ],
            "cell_volume_ratio": 0.9995983427977229,
            "cell_rmsd_from_input_A": 0.05521533054363294
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.80116120971893e-19,
              0.5000362804303954,
              -0.49996059615064564
            ],
            "branch_aligned_reduced_polarization": [
              9.80116120971893e-19,
              0.5000362804303954,
              -0.49996059615064564
            ],
            "target_residual": 5.356242128223261e-05,
            "energy_eV": -243.58045067254182
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 5.356242128223261e-05,
        "parent_symmetrization_rmsd_A": 0.10219855830621762,
        "parent_cell_rmsd_A": 0.05521533054363294,
        "energy_eV": -243.58045067254182,
        "reduced_polarization": [
          9.80116120971893e-19,
          0.5000362804303954,
          -0.49996059615064564
        ],
        "cartesian_polarization_e_A2": [
          -9.691279305355724e-18,
          0.00992310452730935,
          -0.004635455251723802
        ],
        "ranking_score": 0.6161095157846903
      },
      "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              4.996003610813204e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.7488193383380213,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00838411173436582,
            "step_scale": 0.8878453735687224,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.01152860540904,
              0.9992662651203907,
              0.9896389798320454
            ],
            "cell_volume_ratio": 1.0003136331935552,
            "cell_rmsd_from_input_A": 0.06488362599990774
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.45114811729008636,
              0.4451865898228084,
              0.005947981065268158
            ],
            "branch_aligned_reduced_polarization": [
              0.45114811729008636,
              0.4451865898228084,
              0.005947981065268158
            ],
            "target_residual": 0.07366406761989865,
            "energy_eV": -242.76880720730523,
            "max_atomic_step_A": 0.014387960840137652,
            "max_log_strain_component": 0.0008733680908866552,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.012691925703568,
              0.9993156894960645,
              0.9884322250277816
            ],
            "cell_volume_ratio": 1.0002923540874054,
            "cell_rmsd_from_input_A": 0.07196850430526537
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5003528320489125,
              0.5002130022893762,
              0.0012461371984788386
            ],
            "branch_aligned_reduced_polarization": [
              0.5003528320489125,
              0.5002130022893762,
              0.0012461371984788386
            ],
            "target_residual": 0.0013125236559589817,
            "energy_eV": -241.92721181902684,
            "max_atomic_step_A": 0.00010588775843505574,
            "max_log_strain_component": 9.798227864253555e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.012682061045929,
              0.999319697471077,
              0.9884361939294679
            ],
            "cell_volume_ratio": 1.000290638568611,
            "cell_rmsd_from_input_A": 0.07192778962735828
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000004224454796,
              0.500001224161464,
              -6.005304929816001e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000004224454796,
              0.500001224161464,
              -6.005304929816001e-06
            ],
            "target_residual": 6.143347521765856e-06,
            "energy_eV": -241.93318935756503
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.143347521765856e-06,
        "parent_symmetrization_rmsd_A": 0.12477532600697418,
        "parent_cell_rmsd_A": 0.07192778962735828,
        "energy_eV": -241.93318935756503,
        "reduced_polarization": [
          0.5000004224454796,
          0.500001224161464,
          -6.005304929816001e-06
        ],
        "cartesian_polarization_e_A2": [
          0.0073412565086329136,
          0.00986464811970481,
          -0.0001444153424178408
        ],
        "ranking_score": 0.6427695601088572
      },
      "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": [
              7.708213919583858e-16,
              4.954497508177953e-16,
              -0.24643539004979242
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              4.996003610813204e-16,
              -0.24643539004979242
            ],
            "target_residual": 0.7511957211134789,
            "energy_eV": -246.17449818921642,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008380724171462737,
            "step_scale": 0.8874866436102431,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0104542940572,
              1.0007552175103138,
              0.9885881313056232
            ],
            "cell_volume_ratio": 0.9996775265651924,
            "cell_rmsd_from_input_A": 0.0649060248980324
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4442474869668269,
              0.4446960715074611,
              -0.43599474768025603
            ],
            "branch_aligned_reduced_polarization": [
              0.4442474869668269,
              0.4446960715074611,
              -0.43599474768025603
            ],
            "target_residual": 0.10130912861502699,
            "energy_eV": -243.18636483096017,
            "max_atomic_step_A": 0.015851617912403696,
            "max_log_strain_component": 0.001044671470789314,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0116764370438762,
              1.0010051993314564,
              0.9870419323755868
            ],
            "cell_volume_ratio": 0.9995708243051489,
            "cell_rmsd_from_input_A": 0.07324915715983354
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49995394241335184,
              0.5001691779125423,
              -0.4982355599637743
            ],
            "branch_aligned_reduced_polarization": [
              0.49995394241335184,
              0.5001691779125423,
              -0.4982355599637743
            ],
            "target_residual": 0.0017731303135461497,
            "energy_eV": -242.39638374397353,
            "max_atomic_step_A": 0.00014276159871430056,
            "max_log_strain_component": 1.4698706403003652e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.8313834303761314,
            "cell_principal_stretches": [
              1.0116736401461954,
              1.001011209191798,
              0.9870361957501367
            ],
            "cell_volume_ratio": 0.9995682526454648,
            "cell_rmsd_from_input_A": 0.07325852062805413
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000022991065709,
              0.5000025995551064,
              -0.49999862545295093
            ],
            "branch_aligned_reduced_polarization": [
              0.5000022991065709,
              0.5000025995551064,
              -0.49999862545295093
            ],
            "target_residual": 3.732687686596881e-06,
            "energy_eV": -242.39832632028703
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.732687686596881e-06,
        "parent_symmetrization_rmsd_A": 0.12539201896380667,
        "parent_cell_rmsd_A": 0.07325852062805413,
        "energy_eV": -242.39832632028703,
        "reduced_polarization": [
          0.5000022991065709,
          0.5000025995551064,
          -0.49999862545295093
        ],
        "cartesian_polarization_e_A2": [
          0.0074026296237027014,
          0.009923420665125717,
          -0.00470401408493799
        ],
        "ranking_score": 0.6437141144961934
      },
      "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,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.015349629114250042,
        "minimum_distance_A_by_image": [
          1.7233331446297602,
          1.7270486917142251,
          1.726379405084197,
          1.7252307509330151,
          1.7240845992229479,
          1.722940960469024,
          1.721799845209081,
          1.7206612640037093,
          1.7195252274361603
        ],
        "minimum_distance_A": 1.7195252274361603,
        "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": [
          614.1997121400038,
          614.2268293995021,
          614.253947856242,
          614.2810675102779,
          614.3081883616605,
          614.3353104104439,
          614.3624336566819,
          614.3895581004253,
          614.4166837417296
        ],
        "cell_deformation_log_strain_norm": 0.002336480952768951
      },
      "parent_reduced_polarization": [
        -3.2541942926858802e-15,
        -3.865920345113247e-15,
        0.00015054883455341013
      ],
      "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": [
          -246.17449818921642,
          -246.17071570941727,
          -246.1649700086645,
          -246.15729056726417,
          -246.14770618016883,
          -246.1362449604983,
          -246.12293433900456,
          -246.10780108231313,
          -246.09087130181527
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8905041301583052e-17,
            2.465104785798782e-17,
            -0.002251075597531767
          ],
          [
            -2.680501218961069e-17,
            2.1215684707679986e-17,
            -0.001970526830516224
          ],
          [
            -1.2384371462983552e-17,
            -3.773016961459424e-17,
            -0.0016896723919207083
          ],
          [
            -2.129769256426254e-18,
            -1.3103312724834574e-17,
            -0.0014085212846724608
          ],
          [
            -4.617492033395215e-18,
            3.998593032813401e-17,
            -0.0011270823782990218
          ],
          [
            -4.338891695118234e-17,
            -4.55638761666822e-17,
            -0.000845364427475596
          ],
          [
            -1.9936411419037357e-17,
            7.296223232993109e-18,
            -0.0005633760949278596
          ],
          [
            -1.093644589063907e-17,
            -6.281703096136208e-17,
            -0.0002811259555279767
          ],
          [
            -4.776234867546397e-17,
            -7.62534821708644e-17,
            1.3774865418045544e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757507e-16,
            -1.9432887769693967e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840282e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.983340725991733e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455341013
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757506e-16,
            -1.943288776969397e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840278e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.9833407259917333e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455340937
          ]
        ],
        "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": [
          [
            1.3322676295501878e-15,
            1.2212453270876722e-15,
            -0.24643539004979265
          ],
          [
            -1.7763568394002505e-15,
            1.1102230246251565e-15,
            -0.21567756823008355
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            -0.18489908559276869
          ],
          [
            -5.551115123125783e-17,
            -7.216449660063518e-16,
            -0.15410094400243946
          ],
          [
            -2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.12328412990463788
          ],
          [
            -2.886579864025407e-15,
            -2.3314683517128287e-15,
            -0.09244961636981958
          ],
          [
            -1.27675647831893e-15,
            3.3306690738754696e-16,
            -0.06159836561098753
          ],
          [
            -7.216449660063518e-16,
            -3.219646771412954e-15,
            -0.030731329442324096
          ],
          [
            -3.2751579226442118e-15,
            -3.885780586188048e-15,
            0.00015054883455345447
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -246.09087130181527,
          -246.07559637035243,
          -246.0590413406469,
          -246.041219529882,
          -246.0221439193468,
          -246.00182715876355,
          -245.98028157041298,
          -245.95751915306334,
          -245.933551585703
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.299783242524315e-17,
            -3.1328074576714726e-17,
            1.3774865418048705e-06
          ],
          [
            -1.9379813742190526e-17,
            -7.487898512654271e-17,
            0.00027011463586382823
          ],
          [
            -1.532192810188165e-17,
            -1.025763148638443e-16,
            0.0005387093403166603
          ],
          [
            -2.183928921746354e-17,
            -1.8343018070077314e-17,
            0.0008071536230597216
          ],
          [
            -1.0733636480184682e-16,
            -2.279198028703639e-16,
            0.0010754395350363944
          ],
          [
            -1.756652929032132e-17,
            -1.8735478004664333e-16,
            0.0013435591475044588
          ],
          [
            -7.208039670379004e-17,
            -7.139361436054957e-17,
            0.00161150454450504
          ],
          [
            1.6174724500781498e-17,
            -1.1640384197440604e-16,
            0.0018792678152809352
          ],
          [
            -5.83646529869059e-19,
            -1.2228365811863436e-16,
            0.002146841046654497
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.9295920145640313e-15,
            -1.588227059651993e-15,
            0.00015054883455344466
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.91308036075152e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640377e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.9295920145640313e-15,
            -1.588227059651993e-15,
            0.00015054883455344466
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.913080360751522e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640373e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.786531475697735e-15,
          -8.971434327327217e-15,
          0.2467369893684385
        ],
        "actual_opposite_endpoint_branch_residual": 0.011712625332285731
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757507e-16,
            -1.9432887769693967e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840282e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.983340725991733e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455341013
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.91308036075152e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640377e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.286419954092169e-15,
            1.2483502959404494e-15,
            -0.24643539004979265
          ],
          [
            -1.7906390840198573e-15,
            1.0558476849863699e-15,
            -0.21567756823008358
          ],
          [
            -7.853088411757506e-16,
            -1.943288776969397e-15,
            -0.18489908559276869
          ],
          [
            -7.289383449840278e-17,
            -7.039228080259398e-16,
            -0.15410094400243948
          ],
          [
            -2.3747698041201324e-16,
            1.9833407259917333e-15,
            -0.12328412990463787
          ],
          [
            -2.882589382402846e-15,
            -2.34914330565969e-15,
            -0.09244961636981956
          ],
          [
            -1.30016952422911e-15,
            3.3775486624776804e-16,
            -0.0615983656109875
          ],
          [
            -7.114055940163574e-16,
            -3.202987941578197e-15,
            -0.030731329442324096
          ],
          [
            -3.2541942926858802e-15,
            -3.865920345113247e-15,
            0.00015054883455340937
          ],
          [
            -1.3523857760821202e-15,
            -3.777845812595209e-15,
            0.02952762524660812
          ],
          [
            -1.098695575999778e-15,
            -5.168410037295588e-15,
            0.05890135417820435
          ],
          [
            -1.5560669870670252e-15,
            -8.913080360751522e-16,
            0.08827085737001322
          ],
          [
            -7.381684194841614e-15,
            -1.1507936255227062e-14,
            0.11763525887265243
          ],
          [
            -1.2646539630640373e-15,
            -9.453698160303092e-15,
            0.14699368423225223
          ],
          [
            -4.961292810455122e-15,
            -3.585913806663903e-15,
            0.17634525966827527
          ],
          [
            1.0687335687693167e-15,
            -5.877820162468497e-15,
            0.20568911124476916
          ],
          [
            -3.9715043737954575e-17,
            -6.192549772346207e-15,
            0.23502436403615276
          ]
        ],
        "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": [
          [
            1.3322676295501878e-15,
            1.2212453270876722e-15,
            -0.24643539004979265
          ],
          [
            -1.7763568394002505e-15,
            1.1102230246251565e-15,
            -0.21567756823008355
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            -0.18489908559276869
          ],
          [
            -5.551115123125783e-17,
            -7.216449660063518e-16,
            -0.15410094400243946
          ],
          [
            -2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.12328412990463788
          ],
          [
            -2.886579864025407e-15,
            -2.3314683517128287e-15,
            -0.09244961636981958
          ],
          [
            -1.27675647831893e-15,
            3.3306690738754696e-16,
            -0.06159836561098753
          ],
          [
            -7.216449660063518e-16,
            -3.219646771412954e-15,
            -0.030731329442324096
          ],
          [
            -3.2751579226442118e-15,
            -3.885780586188048e-15,
            0.00015054883455345447
          ],
          [
            -1.3322676295501878e-15,
            -3.774758283725532e-15,
            0.029527625246608125
          ],
          [
            -1.1102230246251565e-15,
            -5.162537064506978e-15,
            0.0589013541782043
          ],
          [
            -1.5543122344752192e-15,
            -8.881784197001252e-16,
            0.08827085737001328
          ],
          [
            -7.382983113757291e-15,
            -1.149080830487037e-14,
            0.11763525887265247
          ],
          [
            -1.27675647831893e-15,
            -9.43689570931383e-15,
            0.14699368423225223
          ],
          [
            -4.9404924595819466e-15,
            -3.608224830031759e-15,
            0.1763452596682753
          ],
          [
            1.1102230246251565e-15,
            -5.88418203051333e-15,
            0.20568911124476918
          ],
          [
            -5.551115123125783e-17,
            -6.217248937900877e-15,
            0.2350243640361528
          ]
        ]
      },
      "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": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00015054883455380017,
        "parent_symmetrization_rmsd_A": 0.015349629114250042,
        "parent_cell_rmsd_A": 0.010836045873482837,
        "energy_eV": -246.09087130181524,
        "reduced_polarization": [
          -2.3882697785089153e-15,
          -3.597956429176629e-15,
          0.00015054883455380017
        ],
        "cartesian_polarization_e_A2": [
          -3.505229795390998e-17,
          -7.096814010096443e-17,
          1.3774865418081231e-06
        ],
        "ranking_score": 0.5183597382517283
      }
    }
  ],
  "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": 52,
      "full_response": 17,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 42,
      "energy_polarization": 35
    },
    "elapsed_seconds": 486.08316356298747
  }
}
