{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "H4K8N4O24S8",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -268.97425765312346,
  "input_cartesian_polarization_e_A2": [
    0.0007190457353743471,
    1.8884847776266216e-18,
    -0.0018351183647829577
  ],
  "input_reduced_polarization": [
    0.039972722889933386,
    1.7580211476360452e-16,
    -0.175262796406887
  ],
  "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": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.52693027739766e-15,
      "parent_symmetrization_rmsd_A": 0.18660030443306605,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -262.58636731801244,
      "reduced_polarization": [
        -1.0650245758296445e-15,
        5.607354952147469e-15,
        -3.1660877971901604e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.9199595239203986e-17,
        6.023479571971579e-17,
        -3.247800383189117e-17
      ],
      "ranking_score": 0.1866003044330791
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0006630420755181082,
      "parent_symmetrization_rmsd_A": 0.019396046189597824,
      "parent_cell_rmsd_A": 0.002693552532188462,
      "energy_eV": -268.521745324998,
      "reduced_polarization": [
        -0.0001133297426898455,
        -1.4785621077317412e-15,
        0.000653284902113323
      ],
      "cartesian_polarization_e_A2": [
        -2.035646723656402e-06,
        -1.5947766448205552e-17,
        6.8232253158276535e-06
      ],
      "ranking_score": 0.5213955184736812
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.733160507786516e-15,
      "parent_symmetrization_rmsd_A": 0.18660121804395477,
      "parent_cell_rmsd_A": 0.002693552532188462,
      "energy_eV": -262.4735835702321,
      "reduced_polarization": [
        4.581555964317879e-16,
        -2.6944512528407347e-15,
        -1.3865671533482885e-17
      ],
      "cartesian_polarization_e_A2": [
        8.249183754651331e-18,
        -2.894588435481945e-17,
        -3.1462917776977663e-19
      ],
      "ranking_score": 0.18727460617700736
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.2082392849138157e-06,
      "parent_symmetrization_rmsd_A": 0.03317813032243478,
      "parent_cell_rmsd_A": 0.006014753345089223,
      "energy_eV": -267.83461054614776,
      "reduced_polarization": [
        -3.555638802370904e-07,
        2.944753541746492e-15,
        -0.5000011547365486
      ],
      "cartesian_polarization_e_A2": [
        2.434756465619716e-07,
        -5.642693138596085e-17,
        -0.005196672271978573
      ],
      "ranking_score": 0.5346842351372769
    },
    {
      "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": 0.00025023754910581935,
      "parent_symmetrization_rmsd_A": 0.08321938623216667,
      "parent_cell_rmsd_A": 0.010563331057440041,
      "energy_eV": -263.5702564875359,
      "reduced_polarization": [
        0.5000191419045543,
        1.5298151145532507e-15,
        0.0002495043455984697
      ],
      "cartesian_polarization_e_A2": [
        0.009001864908455696,
        1.6036068771898106e-16,
        -0.00017751408422894658
      ],
      "ranking_score": 0.5863606940947383
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.0699277540930192e-05,
      "parent_symmetrization_rmsd_A": 0.05868696997603675,
      "parent_cell_rmsd_A": 0.020417032654772627,
      "energy_eV": -264.4810789650916,
      "reduced_polarization": [
        -7.705142642753778e-06,
        0.5000012387213034,
        7.319213501813089e-06
      ],
      "cartesian_polarization_e_A2": [
        -8.980599217521326e-06,
        0.005371435844874013,
        1.203723060614089e-05
      ],
      "ranking_score": 0.5638126266948118
    },
    {
      "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": 0.0007773771125025117,
      "parent_symmetrization_rmsd_A": 0.09291889235271353,
      "parent_cell_rmsd_A": 0.007856187590068103,
      "energy_eV": -259.84859851245653,
      "reduced_polarization": [
        0.49956736445767114,
        -1.5581862864405707e-15,
        -0.49935413495019737
      ],
      "cartesian_polarization_e_A2": [
        0.008999982090107661,
        -5.690533582101934e-17,
        -0.005379048035846142
      ],
      "ranking_score": 0.5964376934752356
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.8213891804004728e-05,
      "parent_symmetrization_rmsd_A": 0.06487089263390014,
      "parent_cell_rmsd_A": 0.021127504101332302,
      "energy_eV": -263.60425398993243,
      "reduced_polarization": [
        -9.515919399023224e-06,
        0.4999864389691645,
        -0.49999243088014905
      ],
      "cartesian_polarization_e_A2": [
        -8.758907566891145e-06,
        0.00536046028772041,
        -0.005184637625971675
      ],
      "ranking_score": 0.5701891964428412
    },
    {
      "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": 2.1127395819038333e-06,
      "parent_symmetrization_rmsd_A": 0.09950350443226531,
      "parent_cell_rmsd_A": 0.022713596932788176,
      "energy_eV": -259.2049573936382,
      "reduced_polarization": [
        0.5000010448055883,
        0.4999985677625873,
        1.1492370587742037e-06
      ],
      "cartesian_polarization_e_A2": [
        0.008992848995974625,
        0.005348598682343811,
        -0.00016828163063822876
      ],
      "ranking_score": 0.6051861291446261
    },
    {
      "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": 2.2717922659550094e-05,
      "parent_symmetrization_rmsd_A": 0.10964332549525341,
      "parent_cell_rmsd_A": 0.02228612923524106,
      "energy_eV": -254.80933497593955,
      "reduced_polarization": [
        0.4999961643539569,
        0.4999797753132926,
        -0.4999903899075455
      ],
      "cartesian_polarization_e_A2": [
        0.008998967473008728,
        0.005336559862609894,
        -0.005373905331203302
      ],
      "ranking_score": 0.6152602936493827
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "target_residual": 0.17976336217259992,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.028040640551587667,
            "max_log_strain_component": 0.0004382765180434425,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0004383725752293,
              1.0001922892313184,
              0.9997453655532504
            ],
            "cell_volume_ratio": 1.0003759510444392,
            "cell_rmsd_from_input_A": 0.002693552532188462
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0001133297426898455,
              -1.4785621077317412e-15,
              0.000653284902113323
            ],
            "branch_aligned_reduced_polarization": [
              -0.0001133297426898455,
              -1.4785621077317412e-15,
              0.000653284902113323
            ],
            "target_residual": 0.0006630420755181082,
            "energy_eV": -268.521745324998
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.52693027739766e-15,
        "parent_symmetrization_rmsd_A": 0.18660030443306605,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -262.58636731801244,
        "reduced_polarization": [
          -1.0650245758296445e-15,
          5.607354952147469e-15,
          -3.1660877971901604e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.9199595239203986e-17,
          6.023479571971579e-17,
          -3.247800383189117e-17
        ],
        "ranking_score": 0.1866003044330791
      },
      "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": [
          -268.97425765312346,
          -268.78336923348013,
          -268.2270532967751,
          -267.32643086845457,
          -266.15914893459205,
          -264.8799822774446,
          -263.70968440522677,
          -262.8843718411165,
          -262.5863673180123
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0007190457353743705,
            2.4569973825579694e-17,
            -0.001835118364782937
          ],
          [
            0.0006347924554306224,
            1.0819444038485853e-17,
            -0.001617693227660912
          ],
          [
            0.0005445692930415066,
            9.973560231840596e-18,
            -0.0013865142643076107
          ],
          [
            0.0004476860291071353,
            2.0576615389556734e-17,
            -0.0011442389348924168
          ],
          [
            0.00034840660959246646,
            -3.2655049279793666e-18,
            -0.000899534857709184
          ],
          [
            0.0002517528432683321,
            -1.721275187940931e-17,
            -0.0006611039508429174
          ],
          [
            0.00016146212446097583,
            3.6550049133648574e-17,
            -0.0004330899652681932
          ],
          [
            7.835392122524615e-05,
            1.1704671277998333e-17,
            -0.000214104820660652
          ],
          [
            -5.999873512251246e-18,
            6.037249773475107e-17,
            -8.399822917151745e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.039911567787328e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872626e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3286971372110247e-16,
            5.620173856348982e-15,
            -8.209312817420364e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.0399115677873286e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872622e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3306690738754696e-16,
            5.620173856348982e-15,
            -8.222589276130066e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0399727228899347,
            2.3314683517128287e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818975,
            9.992007221626409e-16,
            -0.1544957389936482
          ],
          [
            0.030273248190078705,
            8.881784197001252e-16,
            -0.13241629314829184
          ],
          [
            0.02488751795631583,
            1.887379141862766e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345606,
            -2.7755575615628914e-16,
            -0.08591814905136996
          ],
          [
            0.013995806685814571,
            -1.609823385706477e-15,
            -0.06315333347627455
          ],
          [
            0.008976492344295428,
            3.4416913763379853e-15,
            -0.0413787914264806
          ],
          [
            0.0043562003747270595,
            1.1102230246251565e-15,
            -0.020459209416291035
          ],
          [
            -3.3306690738754696e-16,
            5.662137425588298e-15,
            -8.326672684688674e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -262.5863673180124,
          -262.88437184111655,
          -263.70968440522677,
          -264.8799822774446,
          -266.1591489345921,
          -267.3264308684546,
          -268.227053296775,
          -268.78336923348013,
          -268.9742576531235
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6317688781680028e-17,
            5.905449273369915e-17,
            7.4752522447720445e-19
          ],
          [
            -7.83539212251685e-05,
            1.8471741731160392e-17,
            0.00021410482066063237
          ],
          [
            -0.00016146212446089249,
            4.327777615394342e-18,
            0.00043308996526816043
          ],
          [
            -0.00025175284326831775,
            3.0687877636432604e-18,
            0.0006611039508428743
          ],
          [
            -0.0003484066095924835,
            2.7678105022090173e-17,
            0.0008995348577091512
          ],
          [
            -0.0004476860291070909,
            6.7670704531620614e-18,
            0.0011442389348924158
          ],
          [
            -0.0005445692930415156,
            2.6851892931878527e-17,
            0.001386514264307621
          ],
          [
            -0.0006347924554306341,
            -1.8117650835355403e-17,
            0.001617693227660899
          ],
          [
            -0.0007190457353743227,
            2.4412600094110806e-17,
            0.0018351183647829393
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.05922106071152e-16,
            5.4974786304202165e-15,
            1.0483654103207604e-16
          ],
          [
            -0.00435620037472271,
            1.7195644350315066e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332604e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029163e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.686601538513331e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.272608587725346e-15,
            0.17526279640688527
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.05922106071152e-16,
            5.4974786304202165e-15,
            1.0483654103207604e-16
          ],
          [
            -0.00435620037472271,
            1.719564435031507e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332605e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029164e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.6866015385133308e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.2726085877253455e-15,
            0.17526279640688527
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.03997272288993536,
          8.953088948742319e-15,
          0.17526279640688333
        ],
        "actual_opposite_endpoint_branch_residual": 7.71043597043554e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.039911567787328e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872626e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3286971372110247e-16,
            5.620173856348982e-15,
            -8.209312817420364e-16
          ],
          [
            -0.00435620037472271,
            1.7195644350315066e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332604e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029163e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.686601538513331e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.272608587725346e-15,
            0.17526279640688527
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.0399115677873286e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872622e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3306690738754696e-16,
            5.620173856348982e-15,
            -8.222589276130066e-16
          ],
          [
            -0.00435620037472271,
            1.719564435031507e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332605e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029164e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.6866015385133308e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.2726085877253455e-15,
            0.17526279640688527
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0399727228899347,
            2.3314683517128287e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818975,
            9.992007221626409e-16,
            -0.1544957389936482
          ],
          [
            0.030273248190078705,
            8.881784197001252e-16,
            -0.13241629314829184
          ],
          [
            0.02488751795631583,
            1.887379141862766e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345606,
            -2.7755575615628914e-16,
            -0.08591814905136996
          ],
          [
            0.013995806685814571,
            -1.609823385706477e-15,
            -0.06315333347627455
          ],
          [
            0.008976492344295428,
            3.4416913763379853e-15,
            -0.0413787914264806
          ],
          [
            0.0043562003747270595,
            1.1102230246251565e-15,
            -0.020459209416291035
          ],
          [
            -3.3306690738754696e-16,
            5.662137425588298e-15,
            -8.326672684688674e-16
          ],
          [
            -0.00435620037472273,
            1.6653345369377348e-15,
            0.020459209416289315
          ],
          [
            -0.008976492344290765,
            4.440892098500626e-16,
            0.0413787914264776
          ],
          [
            -0.013995806685813794,
            3.3306690738754696e-16,
            0.06315333347627039
          ],
          [
            -0.01936868657634655,
            2.55351295663786e-15,
            0.08591814905136674
          ],
          [
            -0.024887517956313332,
            6.661338147750939e-16,
            0.10928174554739356
          ],
          [
            -0.03027324819007926,
            2.55351295663786e-15,
            0.13241629314829284
          ],
          [
            -0.035288901468190415,
            -1.6653345369377348e-15,
            0.154495738993647
          ],
          [
            -0.03997272288993203,
            2.220446049250313e-15,
            0.17526279640688525
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.17526279640688702
            ],
            "target_residual": 0.3271881262709732,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.05168896748298352,
            "max_log_strain_component": 0.0006332604432177672,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0004559280031378,
              0.9993669400238583,
              0.9993370297980164
            ],
            "cell_volume_ratio": 0.9991597268198146,
            "cell_rmsd_from_input_A": 0.005969003986971632
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.000418080427749247,
              2.846614205255843e-16,
              -0.49715715772072866
            ],
            "branch_aligned_reduced_polarization": [
              -0.000418080427749247,
              2.846614205255843e-16,
              -0.49715715772072866
            ],
            "target_residual": 0.00287342016921989,
            "energy_eV": -267.85522068054377,
            "max_atomic_step_A": 0.00045044042702517187,
            "max_log_strain_component": 7.0582848530922265e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0004601846408403,
              0.9993598862322168,
              0.9993331305139804
            ],
            "cell_volume_ratio": 0.9991530270021978,
            "cell_rmsd_from_input_A": 0.006014753345089223
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.555638802370904e-07,
              2.944753541746492e-15,
              -0.5000011547365486
            ],
            "branch_aligned_reduced_polarization": [
              -3.555638802370904e-07,
              2.944753541746492e-15,
              -0.5000011547365486
            ],
            "target_residual": 1.2082392849138157e-06,
            "energy_eV": -267.83461054614776
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.2082392849138157e-06,
        "parent_symmetrization_rmsd_A": 0.03317813032243478,
        "parent_cell_rmsd_A": 0.006014753345089223,
        "energy_eV": -267.83461054614776,
        "reduced_polarization": [
          -3.555638802370904e-07,
          2.944753541746492e-15,
          -0.5000011547365486
        ],
        "cartesian_polarization_e_A2": [
          2.434756465619716e-07,
          -5.642693138596085e-17,
          -0.005196672271978573
        ],
        "ranking_score": 0.5346842351372769
      },
      "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": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933365,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "target_residual": 0.49228258499530936,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0008220376660759927,
            "step_scale": 0.9025465923605507,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.001443101562656,
              0.9997797552817694,
              0.9996880378926787
            ],
            "cell_volume_ratio": 1.0009101955157613,
            "cell_rmsd_from_input_A": 0.009534327246358169
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4523824059149237,
              -7.314560065003998e-17,
              -0.01574939982914973
            ],
            "branch_aligned_reduced_polarization": [
              0.4523824059149237,
              -7.314560065003998e-17,
              -0.01574939982914973
            ],
            "target_residual": 0.050154549758018134,
            "energy_eV": -264.6142450142283,
            "max_atomic_step_A": 0.015314901502671008,
            "max_log_strain_component": 8.573209365820225e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0015998407525337,
              0.9997620088342378,
              0.9996400046391513
            ],
            "cell_volume_ratio": 1.001000983355491,
            "cell_rmsd_from_input_A": 0.010563331057440041
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000191419045543,
              1.5298151145532507e-15,
              0.0002495043455984697
            ],
            "branch_aligned_reduced_polarization": [
              0.5000191419045543,
              1.5298151145532507e-15,
              0.0002495043455984697
            ],
            "target_residual": 0.00025023754910581935,
            "energy_eV": -263.5702564875359
          }
        ],
        "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": 0.00025023754910581935,
        "parent_symmetrization_rmsd_A": 0.08321938623216667,
        "parent_cell_rmsd_A": 0.010563331057440041,
        "energy_eV": -263.5702564875359,
        "reduced_polarization": [
          0.5000191419045543,
          1.5298151145532507e-15,
          0.0002495043455984697
        ],
        "cartesian_polarization_e_A2": [
          0.009001864908455696,
          1.6036068771898106e-16,
          -0.00017751408422894658
        ],
        "ranking_score": 0.5863606940947383
      },
      "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": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933386,
              1.6653345369377348e-16,
              -0.175262796406887
            ],
            "target_residual": 0.5313331030338663,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.08967340334631396,
            "max_log_strain_component": 0.002194586183439507,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0028470802315252,
              1.0001922825241605,
              0.9973441144984102
            ],
            "cell_volume_ratio": 1.0003759510444443,
            "cell_rmsd_from_input_A": 0.02012420709166232
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0008917067969884408,
              0.4930921716960151,
              -0.00037901786993225735
            ],
            "branch_aligned_reduced_polarization": [
              0.0008917067969884408,
              0.4930921716960151,
              -0.00037901786993225735
            ],
            "target_residual": 0.0069754489056159125,
            "energy_eV": -264.5973172751562,
            "max_atomic_step_A": 0.0012123803226200664,
            "max_log_strain_component": 3.2481736851470054e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.002888273408741,
              1.00019045864938,
              0.9973047469484633
            ],
            "cell_volume_ratio": 1.0003757296586127,
            "cell_rmsd_from_input_A": 0.020417032654772627
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -7.705142642753778e-06,
              0.5000012387213034,
              7.319213501813089e-06
            ],
            "branch_aligned_reduced_polarization": [
              -7.705142642753778e-06,
              0.5000012387213034,
              7.319213501813089e-06
            ],
            "target_residual": 1.0699277540930192e-05,
            "energy_eV": -264.4810789650916
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.0699277540930192e-05,
        "parent_symmetrization_rmsd_A": 0.05868696997603675,
        "parent_cell_rmsd_A": 0.020417032654772627,
        "energy_eV": -264.4810789650916,
        "reduced_polarization": [
          -7.705142642753778e-06,
          0.5000012387213034,
          7.319213501813089e-06
        ],
        "cartesian_polarization_e_A2": [
          -8.980599217521326e-06,
          0.005371435844874013,
          1.203723060614089e-05
        ],
        "ranking_score": 0.5638126266948118
      },
      "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": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933365,
              1.7580211476360452e-16,
              -0.17526279640688702
            ],
            "target_residual": 0.5630979906577336,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012230523032728514,
            "step_scale": 0.8629833503498711,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0007944808577227,
              1.0002489939103534,
              0.9987776953203701
            ],
            "cell_volume_ratio": 0.9998200922234521,
            "cell_rmsd_from_input_A": 0.006548359884548323
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.43029682484762954,
              -3.771641525755843e-16,
              -0.44088288035870765
            ],
            "branch_aligned_reduced_polarization": [
              0.43029682484762954,
              -3.771641525755843e-16,
              -0.44088288035870765
            ],
            "target_residual": 0.09139675301127993,
            "energy_eV": -262.52294521344845,
            "max_atomic_step_A": 0.02325557696891162,
            "max_log_strain_component": 0.00027381080273127304,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0009374680191698,
              1.0003009617520788,
              0.9985042566348056
            ],
            "cell_volume_ratio": 0.9997411157529463,
            "cell_rmsd_from_input_A": 0.007856187590068103
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49956736445767114,
              -1.5581862864405707e-15,
              -0.49935413495019737
            ],
            "branch_aligned_reduced_polarization": [
              0.49956736445767114,
              -1.5581862864405707e-15,
              -0.49935413495019737
            ],
            "target_residual": 0.0007773771125025117,
            "energy_eV": -259.84859851245653
          }
        ],
        "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": 0.0007773771125025117,
        "parent_symmetrization_rmsd_A": 0.09291889235271353,
        "parent_cell_rmsd_A": 0.007856187590068103,
        "energy_eV": -259.84859851245653,
        "reduced_polarization": [
          0.49956736445767114,
          -1.5581862864405707e-15,
          -0.49935413495019737
        ],
        "cartesian_polarization_e_A2": [
          0.008999982090107661,
          -5.690533582101934e-17,
          -0.005379048035846142
        ],
        "ranking_score": 0.5964376934752356
      },
      "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": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933386,
              1.6653345369377348e-16,
              -0.17526279640688702
            ],
            "target_residual": 0.597538341843191,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.09656200952932545,
            "max_log_strain_component": 0.0021945861834646464,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.002695261125308,
              0.9993439691752268,
              0.9971281160484459
            ],
            "cell_volume_ratio": 0.9991597268198198,
            "cell_rmsd_from_input_A": 0.020813470299655874
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.000847671989182885,
              0.4928271626304458,
              -0.49565524968336583
            ],
            "branch_aligned_reduced_polarization": [
              -0.000847671989182885,
              0.4928271626304458,
              -0.49565524968336583
            ],
            "target_residual": 0.00842881955229861,
            "energy_eV": -263.7579582362298,
            "max_atomic_step_A": 0.0014507868369085743,
            "max_log_strain_component": 3.3820363122844515e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0027360367957574,
              0.9993384806564721,
              0.9970829023154416
            ],
            "cell_volume_ratio": 0.999149563536125,
            "cell_rmsd_from_input_A": 0.021127504101332302
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.515919399023224e-06,
              0.4999864389691645,
              -0.49999243088014905
            ],
            "branch_aligned_reduced_polarization": [
              -9.515919399023224e-06,
              0.4999864389691645,
              -0.49999243088014905
            ],
            "target_residual": 1.8213891804004728e-05,
            "energy_eV": -263.60425398993243
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.8213891804004728e-05,
        "parent_symmetrization_rmsd_A": 0.06487089263390014,
        "parent_cell_rmsd_A": 0.021127504101332302,
        "energy_eV": -263.60425398993243,
        "reduced_polarization": [
          -9.515919399023224e-06,
          0.4999864389691645,
          -0.49999243088014905
        ],
        "cartesian_polarization_e_A2": [
          -8.758907566891145e-06,
          0.00536046028772041,
          -0.005184637625971675
        ],
        "ranking_score": 0.5701891964428412
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933365,
              1.6653345369377348e-16,
              -0.175262796406887
            ],
            "target_residual": 0.7016709652605442,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0016044524676407815,
            "step_scale": 0.7310956752359584,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.001873151396292,
              1.0010578100353693,
              0.9978107060690289
            ],
            "cell_volume_ratio": 1.0007372278650097,
            "cell_rmsd_from_input_A": 0.016487649978917624
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3741451462375511,
              0.36377763352354303,
              -0.04652117715254604
            ],
            "branch_aligned_reduced_polarization": [
              0.3741451462375511,
              0.36377763352354303,
              -0.04652117715254604
            ],
            "target_residual": 0.19120721029206017,
            "energy_eV": -263.80454283609765,
            "max_atomic_step_A": 0.05047570636983902,
            "max_log_strain_component": 0.0006134593715863372,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0025861764516009,
              1.0014396317975087,
              0.9969726614256034
            ],
            "cell_volume_ratio": 1.0009899940607503,
            "cell_rmsd_from_input_A": 0.022706523917130857
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996594200719313,
              0.49964037705418285,
              0.0013605173005424326
            ],
            "branch_aligned_reduced_polarization": [
              0.49996594200719313,
              0.49964037705418285,
              0.0013605173005424326
            ],
            "target_residual": 0.0014076561849782447,
            "energy_eV": -259.2149551084936,
            "max_atomic_step_A": 0.00023249270154951284,
            "max_log_strain_component": 3.1992778229828617e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0025876354921508,
              1.0014376564090257,
              0.9969698137411402
            ],
            "cell_volume_ratio": 1.0009866171161708,
            "cell_rmsd_from_input_A": 0.022713596932788176
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000010448055883,
              0.4999985677625873,
              1.1492370587742037e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000010448055883,
              0.4999985677625873,
              1.1492370587742037e-06
            ],
            "target_residual": 2.1127395819038333e-06,
            "energy_eV": -259.2049573936382
          }
        ],
        "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": 2.1127395819038333e-06,
        "parent_symmetrization_rmsd_A": 0.09950350443226531,
        "parent_cell_rmsd_A": 0.022713596932788176,
        "energy_eV": -259.2049573936382,
        "reduced_polarization": [
          0.5000010448055883,
          0.4999985677625873,
          1.1492370587742037e-06
        ],
        "cartesian_polarization_e_A2": [
          0.008992848995974625,
          0.005348598682343811,
          -0.00016828163063822876
        ],
        "ranking_score": 0.6051861291446261
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.039972722889933386,
              1.7580211476360452e-16,
              -0.175262796406887
            ],
            "branch_aligned_reduced_polarization": [
              0.039972722889933365,
              1.6653345369377348e-16,
              -0.17526279640688702
            ],
            "target_residual": 0.7530467097616035,
            "energy_eV": -268.97425765312346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001537050542600641,
            "step_scale": 0.7003828576822195,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0017542187488702,
              1.000442739188908,
              0.9976613924214442
            ],
            "cell_volume_ratio": 0.999853987381819,
            "cell_rmsd_from_input_A": 0.014932439618105626
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.35718769416917034,
              0.3456409118578555,
              -0.39190331007324447
            ],
            "branch_aligned_reduced_polarization": [
              0.35718769416917034,
              0.3456409118578555,
              -0.39190331007324447
            ],
            "target_residual": 0.2364465630156503,
            "energy_eV": -262.48375269550803,
            "max_atomic_step_A": 0.057526400072662874,
            "max_log_strain_component": 0.0007348344501287535,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0025989814960115,
              1.0006093209609304,
              0.9965204506931525
            ],
            "cell_volume_ratio": 0.9997191678071442,
            "cell_rmsd_from_input_A": 0.022088692167380054
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49722535670313806,
              0.49605445101040024,
              -0.49645717334753636
            ],
            "branch_aligned_reduced_polarization": [
              0.49722535670313806,
              0.49605445101040024,
              -0.49645717334753636
            ],
            "target_residual": 0.005984782614561642,
            "energy_eV": -255.02122715276056,
            "max_atomic_step_A": 0.0013487664849211997,
            "max_log_strain_component": 2.0669514472811146e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41748730136220047,
            "cell_principal_stretches": [
              1.0026230981716961,
              1.0006099223037341,
              0.9964884765474219
            ],
            "cell_volume_ratio": 0.9997117384636722,
            "cell_rmsd_from_input_A": 0.02228612923524106
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999961643539569,
              0.4999797753132926,
              -0.4999903899075455
            ],
            "branch_aligned_reduced_polarization": [
              0.4999961643539569,
              0.4999797753132926,
              -0.4999903899075455
            ],
            "target_residual": 2.2717922659550094e-05,
            "energy_eV": -254.80933497593955
          }
        ],
        "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": 2.2717922659550094e-05,
        "parent_symmetrization_rmsd_A": 0.10964332549525341,
        "parent_cell_rmsd_A": 0.02228612923524106,
        "energy_eV": -254.80933497593955,
        "reduced_polarization": [
          0.4999961643539569,
          0.4999797753132926,
          -0.4999903899075455
        ],
        "cartesian_polarization_e_A2": [
          0.008998967473008728,
          0.005336559862609894,
          -0.005373905331203302
        ],
        "ranking_score": 0.6152602936493827
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          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,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.18660030443306605,
        "minimum_distance_A_by_image": [
          1.0294512275958343,
          0.9796707871995624,
          0.9343849330335077,
          0.894276738690007,
          0.8600708680906584,
          0.8324951900212896,
          0.8122252859725125,
          0.7998168036693518,
          0.7956376399999989
        ],
        "minimum_distance_A": 0.7956376399999989,
        "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": [
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136,
          705.4690857633136
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.3286971372110247e-16,
        5.620173856348982e-15,
        -8.209312817420364e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -268.97425765312346,
          -268.78336923348013,
          -268.2270532967751,
          -267.32643086845457,
          -266.15914893459205,
          -264.8799822774446,
          -263.70968440522677,
          -262.8843718411165,
          -262.5863673180123
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0007190457353743705,
            2.4569973825579694e-17,
            -0.001835118364782937
          ],
          [
            0.0006347924554306224,
            1.0819444038485853e-17,
            -0.001617693227660912
          ],
          [
            0.0005445692930415066,
            9.973560231840596e-18,
            -0.0013865142643076107
          ],
          [
            0.0004476860291071353,
            2.0576615389556734e-17,
            -0.0011442389348924168
          ],
          [
            0.00034840660959246646,
            -3.2655049279793666e-18,
            -0.000899534857709184
          ],
          [
            0.0002517528432683321,
            -1.721275187940931e-17,
            -0.0006611039508429174
          ],
          [
            0.00016146212446097583,
            3.6550049133648574e-17,
            -0.0004330899652681932
          ],
          [
            7.835392122524615e-05,
            1.1704671277998333e-17,
            -0.000214104820660652
          ],
          [
            -5.999873512251246e-18,
            6.037249773475107e-17,
            -8.399822917151745e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.039911567787328e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872626e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3286971372110247e-16,
            5.620173856348982e-15,
            -8.209312817420364e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.0399115677873286e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872622e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3306690738754696e-16,
            5.620173856348982e-15,
            -8.222589276130066e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0399727228899347,
            2.3314683517128287e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818975,
            9.992007221626409e-16,
            -0.1544957389936482
          ],
          [
            0.030273248190078705,
            8.881784197001252e-16,
            -0.13241629314829184
          ],
          [
            0.02488751795631583,
            1.887379141862766e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345606,
            -2.7755575615628914e-16,
            -0.08591814905136996
          ],
          [
            0.013995806685814571,
            -1.609823385706477e-15,
            -0.06315333347627455
          ],
          [
            0.008976492344295428,
            3.4416913763379853e-15,
            -0.0413787914264806
          ],
          [
            0.0043562003747270595,
            1.1102230246251565e-15,
            -0.020459209416291035
          ],
          [
            -3.3306690738754696e-16,
            5.662137425588298e-15,
            -8.326672684688674e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -262.5863673180124,
          -262.88437184111655,
          -263.70968440522677,
          -264.8799822774446,
          -266.1591489345921,
          -267.3264308684546,
          -268.227053296775,
          -268.78336923348013,
          -268.9742576531235
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6317688781680028e-17,
            5.905449273369915e-17,
            7.4752522447720445e-19
          ],
          [
            -7.83539212251685e-05,
            1.8471741731160392e-17,
            0.00021410482066063237
          ],
          [
            -0.00016146212446089249,
            4.327777615394342e-18,
            0.00043308996526816043
          ],
          [
            -0.00025175284326831775,
            3.0687877636432604e-18,
            0.0006611039508428743
          ],
          [
            -0.0003484066095924835,
            2.7678105022090173e-17,
            0.0008995348577091512
          ],
          [
            -0.0004476860291070909,
            6.7670704531620614e-18,
            0.0011442389348924158
          ],
          [
            -0.0005445692930415156,
            2.6851892931878527e-17,
            0.001386514264307621
          ],
          [
            -0.0006347924554306341,
            -1.8117650835355403e-17,
            0.001617693227660899
          ],
          [
            -0.0007190457353743227,
            2.4412600094110806e-17,
            0.0018351183647829393
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.05922106071152e-16,
            5.4974786304202165e-15,
            1.0483654103207604e-16
          ],
          [
            -0.00435620037472271,
            1.7195644350315066e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332604e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029163e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.686601538513331e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.272608587725346e-15,
            0.17526279640688527
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.05922106071152e-16,
            5.4974786304202165e-15,
            1.0483654103207604e-16
          ],
          [
            -0.00435620037472271,
            1.719564435031507e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332605e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029164e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.6866015385133308e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.2726085877253455e-15,
            0.17526279640688527
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.03997272288993536,
          8.953088948742319e-15,
          0.17526279640688333
        ],
        "actual_opposite_endpoint_branch_residual": 7.71043597043554e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.039911567787328e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872626e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3286971372110247e-16,
            5.620173856348982e-15,
            -8.209312817420364e-16
          ],
          [
            -0.00435620037472271,
            1.7195644350315066e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332604e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029163e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.686601538513331e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.272608587725346e-15,
            0.17526279640688527
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.039972722889934684,
            2.2872587639556466e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818976,
            1.0071996158331509e-15,
            -0.15449573899364824
          ],
          [
            0.03027324819007875,
            9.284549185952865e-16,
            -0.13241629314829184
          ],
          [
            0.024887517956315785,
            1.9155105421117745e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345624,
            -3.0399115677873286e-16,
            -0.08591814905136998
          ],
          [
            0.013995806685814575,
            -1.6023630251891037e-15,
            -0.06315333347627457
          ],
          [
            0.008976492344295388,
            3.4025034294872622e-15,
            -0.04137879142648062
          ],
          [
            0.004356200374727022,
            1.0896068571285906e-15,
            -0.02045920941629102
          ],
          [
            -3.3306690738754696e-16,
            5.620173856348982e-15,
            -8.222589276130066e-16
          ],
          [
            -0.00435620037472271,
            1.719564435031507e-15,
            0.02045920941628929
          ],
          [
            -0.008976492344290762,
            4.028798463332605e-16,
            0.041378791426477636
          ],
          [
            -0.013995806685813775,
            2.8567843649085735e-16,
            0.06315333347627045
          ],
          [
            -0.019368686576346567,
            2.5765997445040788e-15,
            0.08591814905136679
          ],
          [
            -0.024887517956313318,
            6.299575779029164e-16,
            0.1092817455473935
          ],
          [
            -0.030273248190079247,
            2.4996863192950014e-15,
            0.1324162931482928
          ],
          [
            -0.03528890146819041,
            -1.6866015385133308e-15,
            0.15449573899364696
          ],
          [
            -0.03997272288993203,
            2.2726085877253455e-15,
            0.17526279640688527
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0399727228899347,
            2.3314683517128287e-15,
            -0.17526279640688497
          ],
          [
            0.03528890146818975,
            9.992007221626409e-16,
            -0.1544957389936482
          ],
          [
            0.030273248190078705,
            8.881784197001252e-16,
            -0.13241629314829184
          ],
          [
            0.02488751795631583,
            1.887379141862766e-15,
            -0.1092817455473935
          ],
          [
            0.019368686576345606,
            -2.7755575615628914e-16,
            -0.08591814905136996
          ],
          [
            0.013995806685814571,
            -1.609823385706477e-15,
            -0.06315333347627455
          ],
          [
            0.008976492344295428,
            3.4416913763379853e-15,
            -0.0413787914264806
          ],
          [
            0.0043562003747270595,
            1.1102230246251565e-15,
            -0.020459209416291035
          ],
          [
            -3.3306690738754696e-16,
            5.662137425588298e-15,
            -8.326672684688674e-16
          ],
          [
            -0.00435620037472273,
            1.6653345369377348e-15,
            0.020459209416289315
          ],
          [
            -0.008976492344290765,
            4.440892098500626e-16,
            0.0413787914264776
          ],
          [
            -0.013995806685813794,
            3.3306690738754696e-16,
            0.06315333347627039
          ],
          [
            -0.01936868657634655,
            2.55351295663786e-15,
            0.08591814905136674
          ],
          [
            -0.024887517956313332,
            6.661338147750939e-16,
            0.10928174554739356
          ],
          [
            -0.03027324819007926,
            2.55351295663786e-15,
            0.13241629314829284
          ],
          [
            -0.035288901468190415,
            -1.6653345369377348e-15,
            0.154495738993647
          ],
          [
            -0.03997272288993203,
            2.220446049250313e-15,
            0.17526279640688525
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.52693027739766e-15,
        "parent_symmetrization_rmsd_A": 0.18660030443306605,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -262.58636731801244,
        "reduced_polarization": [
          -1.0650245758296445e-15,
          5.607354952147469e-15,
          -3.1660877971901604e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.9199595239203986e-17,
          6.023479571971579e-17,
          -3.247800383189117e-17
        ],
        "ranking_score": 0.1866003044330791
      }
    }
  ],
  "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": 50,
      "full_response": 18,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 43,
      "energy_polarization": 32
    },
    "elapsed_seconds": 830.0974658159539
  }
}