{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "As2Se6Tl6",
  "input_spacegroup": "R3m",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -47.23750284930867,
  "input_cartesian_polarization_e_A2": [
    0.0006568732741937479,
    1.0709729333732572e-17,
    0.0008075750281856078
  ],
  "input_reduced_polarization": [
    0.06340100247197376,
    4.59470439013063e-16,
    0.06340101026785706
  ],
  "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": "R-3m",
      "spacegroup_number": 166,
      "pointgroup": "-3m",
      "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": 1.5297449587868463e-15,
      "parent_symmetrization_rmsd_A": 0.7188415074717186,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -41.80076390886508,
      "reduced_polarization": [
        1.433063238667554e-15,
        3.690685133809017e-18,
        -5.351969466996928e-16
      ],
      "cartesian_polarization_e_A2": [
        2.859840904009847e-17,
        8.602564057010294e-20,
        -6.81711044492579e-18
      ],
      "ranking_score": 0.7188415074717217
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.2809493468861628e-15,
      "parent_symmetrization_rmsd_A": 0.7379941805651455,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -35.2271590189244,
      "reduced_polarization": [
        1.0848245170758006e-15,
        1.7121637373496854e-15,
        2.5799766899118976e-15
      ],
      "cartesian_polarization_e_A2": [
        7.93762244624403e-19,
        3.9908574404556623e-17,
        3.2862642712968154e-17
      ],
      "ranking_score": 0.7379941805651521
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.5029832389287274e-15,
      "parent_symmetrization_rmsd_A": 0.7379941805651458,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -35.2271590189244,
      "reduced_polarization": [
        -2.354131949351826e-15,
        2.3694312590046016e-16,
        -8.166062787461483e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.5131975999443933e-17,
        5.522872703917963e-18,
        -1.0401582495118416e-17
      ],
      "ranking_score": 0.7379941805651508
    },
    {
      "candidate_id": "bec_projection_00",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.2071993859563684e-05,
      "parent_symmetrization_rmsd_A": 0.019484451245900328,
      "parent_cell_rmsd_A": 0.035296166572153995,
      "energy_eV": -47.24587544518149,
      "reduced_polarization": [
        1.655105398240584e-05,
        5.154768389637332e-15,
        1.4602586243816702e-05
      ],
      "cartesian_polarization_e_A2": [
        1.8620449705843767e-07,
        1.1977512365657854e-16,
        1.8738312154291235e-07
      ],
      "ranking_score": 0.528352636876658
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.178511843144807e-15,
      "parent_symmetrization_rmsd_A": 0.7188415074717178,
      "parent_cell_rmsd_A": 0.035296166572153995,
      "energy_eV": -41.81252872034064,
      "reduced_polarization": [
        -5.794493824261928e-16,
        8.176588047762613e-16,
        6.201311608122347e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.4326161574139856e-17,
        1.8998861399320032e-17,
        7.813870243568046e-18
      ],
      "ranking_score": 0.7276655491147587
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1205385097111554e-14,
      "parent_symmetrization_rmsd_A": 0.7379994741518328,
      "parent_cell_rmsd_A": 0.035296166572153995,
      "energy_eV": -35.0398889390059,
      "reduced_polarization": [
        -3.878469560624049e-15,
        4.466469224124517e-15,
        -9.51676319511161e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.575198974130389e-18,
        1.0378146634975547e-16,
        -1.213463761393563e-16
      ],
      "ranking_score": 0.7468235157948937
    },
    {
      "candidate_id": "bec_projection_01",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006279223547102114,
      "parent_symmetrization_rmsd_A": 0.1161753930059693,
      "parent_cell_rmsd_A": 0.10483903878447555,
      "energy_eV": -46.83993049316428,
      "reduced_polarization": [
        0.0006137053716990544,
        7.099996674046279e-15,
        0.499867138416792
      ],
      "cartesian_polarization_e_A2": [
        -0.0035700760275296354,
        1.3112895733858643e-16,
        0.00650278566107695
      ],
      "ranking_score": 0.6436409974115086
    },
    {
      "candidate_id": "bec_projection_02",
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.5149521178046255e-05,
      "parent_symmetrization_rmsd_A": 0.13921420657943684,
      "parent_cell_rmsd_A": 0.14568790649350735,
      "energy_eV": -46.620786033136866,
      "reduced_polarization": [
        0.4999785335405455,
        1.5745554552277654e-15,
        -2.7833073088220605e-05
      ],
      "cartesian_polarization_e_A2": [
        0.008754452714209887,
        4.230101356596153e-16,
        -0.0001514927696921387
      ],
      "ranking_score": 0.6757064822451697
    },
    {
      "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": 0.0005843949040757948,
      "parent_symmetrization_rmsd_A": 0.19335147508456416,
      "parent_cell_rmsd_A": 0.3365484875952812,
      "energy_eV": -45.866105513917155,
      "reduced_polarization": [
        -0.0002969671837780749,
        0.4996938579722016,
        0.0003995058879217803
      ],
      "cartesian_polarization_e_A2": [
        0.00042238011431142565,
        0.011643040121994316,
        0.00020135562497762183
      ],
      "ranking_score": 0.7786573867915361
    },
    {
      "candidate_id": "bec_projection_04",
      "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": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0009067685069051173,
      "parent_symmetrization_rmsd_A": 0.13842755161707254,
      "parent_cell_rmsd_A": 0.24136002897918063,
      "energy_eV": -46.65114117105811,
      "reduced_polarization": [
        0.49937318183993346,
        -1.0616774308397412e-14,
        0.4993447686520581
      ],
      "cartesian_polarization_e_A2": [
        0.004918691850701564,
        -4.207277335821975e-16,
        0.006098217883585657
      ],
      "ranking_score": 0.700581095875678
    },
    {
      "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": 0.0003820891616347046,
      "parent_symmetrization_rmsd_A": 0.20514807096218454,
      "parent_cell_rmsd_A": 0.30409672397083554,
      "energy_eV": -44.90225421985938,
      "reduced_polarization": [
        9.516732490751992e-05,
        0.49999256068675857,
        0.5003699729237757
      ],
      "cartesian_polarization_e_A2": [
        -0.003199359610400991,
        0.011630741271597285,
        0.006667877527715704
      ],
      "ranking_score": 0.7819364302781628
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0011723849035046219,
      "parent_symmetrization_rmsd_A": 0.3183608526799104,
      "parent_cell_rmsd_A": 0.5928150218695705,
      "energy_eV": -45.125466287144526,
      "reduced_polarization": [
        0.4991461683388663,
        0.499205394255133,
        -0.00011857304346099362
      ],
      "cartesian_polarization_e_A2": [
        0.009612339895103366,
        0.012592223594916038,
        0.00021989912888474952
      ],
      "ranking_score": 0.9689093779543123
    },
    {
      "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": 3.874287097074375e-05,
      "parent_symmetrization_rmsd_A": 0.24336734644623348,
      "parent_cell_rmsd_A": 0.47099268490118523,
      "energy_eV": -45.167837091346506,
      "reduced_polarization": [
        0.49997666099789945,
        0.4999859695925929,
        0.49997244190318624
      ],
      "cartesian_polarization_e_A2": [
        0.00550897933859522,
        0.012329350142757092,
        0.006342353985342368
      ],
      "ranking_score": 0.8611930034134713
    }
  ],
  "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "target_residual": 0.08966256307643754,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.015181343695768991,
            "max_log_strain_component": 0.006356516695152038,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0079749467178978,
              0.9982250691915281,
              0.9951594965143095
            ],
            "cell_volume_ratio": 1.0013154147637122,
            "cell_rmsd_from_input_A": 0.034717464921244404
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.001067408515545569,
              2.062046703949535e-14,
              0.0009537941242909845
            ],
            "branch_aligned_reduced_polarization": [
              0.001067408515545569,
              2.062046703949535e-14,
              0.0009537941242909845
            ],
            "target_residual": 0.001431462249097475,
            "energy_eV": -47.24584838732058,
            "max_atomic_step_A": 0.00026144519422537527,
            "max_log_strain_component": 0.00010502697854252997,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0081084858621248,
              0.9981941978929947,
              0.9950804466721314
            ],
            "cell_volume_ratio": 1.0013375537512323,
            "cell_rmsd_from_input_A": 0.035296166572153995
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.655105398240584e-05,
              5.154768389637332e-15,
              1.4602586243816702e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.655105398240584e-05,
              5.154768389637332e-15,
              1.4602586243816702e-05
            ],
            "target_residual": 2.2071993859563684e-05,
            "energy_eV": -47.24587544518149
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.2071993859563684e-05,
        "parent_symmetrization_rmsd_A": 0.019484451245900328,
        "parent_cell_rmsd_A": 0.035296166572153995,
        "energy_eV": -47.24587544518149,
        "reduced_polarization": [
          1.655105398240584e-05,
          5.154768389637332e-15,
          1.4602586243816702e-05
        ],
        "cartesian_polarization_e_A2": [
          1.8620449705843767e-07,
          1.1977512365657854e-16,
          1.8738312154291235e-07
        ],
        "ranking_score": 0.528352636876658
      },
      "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": [
          -47.237502849308676,
          -47.23922605848477,
          -47.24075066082565,
          -47.2420794317071,
          -47.24321503553357,
          -47.2441600306391,
          -47.24491687369762,
          -47.24548792365855,
          -47.24587544518148
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0006568732741937272,
            -1.1439180030088568e-17,
            0.0008075750281856024
          ],
          [
            0.0005743285357913956,
            1.9509710887731827e-17,
            0.0007061900324005136
          ],
          [
            0.0004918570891487159,
            4.2203908669917595e-17,
            0.000604871630325126
          ],
          [
            0.00040948729900107877,
            1.3791241425559893e-17,
            0.0005036520317411831
          ],
          [
            0.00032724803858093725,
            4.4894251757418295e-18,
            0.0004025638775690434
          ],
          [
            0.00024516859636342146,
            -2.1391773953808818e-17,
            0.0003016401302459743
          ],
          [
            0.00016327857788417057,
            7.722816184361316e-17,
            0.00020091396076789446
          ],
          [
            8.160780311422361e-05,
            3.8107792822276126e-17,
            0.00010041863299904738
          ],
          [
            1.8620449707840216e-07,
            4.090560665627929e-17,
            1.8738312158977662e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498325e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698616e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.655105398501617e-05,
            1.7604410324171577e-15,
            1.4602586247482285e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498324e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698615997e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.6551053985016176e-05,
            1.7604410324171577e-15,
            1.4602586247481827e-05
          ]
        ],
        "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": [
          [
            0.06340100247197245,
            -4.996003610813204e-16,
            0.0634010102678566
          ],
          [
            0.05538875187582082,
            7.771561172376096e-16,
            0.055398332256042515
          ],
          [
            0.04739668882193859,
            1.7763568394002505e-15,
            0.04741330829461465
          ],
          [
            0.03942742829086776,
            5.551115123125783e-16,
            0.039448428102290434
          ],
          [
            0.03148361916918785,
            1.1102230246251565e-16,
            0.031506206738271314
          ],
          [
            0.023567935300413456,
            -9.43689570931383e-16,
            0.02358917586732623
          ],
          [
            0.015683066193603823,
            3.3306690738754696e-15,
            0.01569987480690005
          ],
          [
            0.007831707438251123,
            1.6653345369377348e-15,
            0.007840841405724497
          ],
          [
            1.655105398501444e-05,
            1.7763568394002505e-15,
            1.4602586247525196e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -47.2458754451815,
          -47.241558295090336,
          -47.237182340894634,
          -47.232749560602706,
          -47.22826194750666,
          -47.22372150539249,
          -47.2191302431555,
          -47.21449016902682,
          -47.20980328454507
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8620449709920015e-07,
            5.568123536783996e-17,
            1.8738312156027415e-07
          ],
          [
            -3.710229739658065e-05,
            1.7736078462011082e-17,
            -2.901160750690084e-05
          ],
          [
            -7.467582708548326e-05,
            1.2508715720138336e-16,
            -5.84532681543325e-05
          ],
          [
            -0.00011253771319034219,
            1.6790638244733815e-16,
            -8.813934753963154e-05
          ],
          [
            -0.0001506915138307273,
            1.681444629503155e-17,
            -0.00011807156936948085
          ],
          [
            -0.00018914101871597951,
            1.0844290102032454e-16,
            -0.00014825164461429146
          ],
          [
            -0.00022789024537798027,
            1.223420458450778e-16,
            -0.00017868129008555744
          ],
          [
            -0.000266943434271526,
            1.6869595288063673e-16,
            -0.0002093622503594004
          ],
          [
            -0.0003063050429393139,
            1.7666602466767427e-16,
            -0.00024029632283218682
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6551053985290543e-05,
            2.396343503527624e-15,
            1.4602586245157766e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056347e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384024e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6551053985290543e-05,
            2.396343503527624e-15,
            1.4602586245157766e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056348e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384021e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.06336768470857353,
          4.000642577617243e-15,
          -0.06337158816142369
        ],
        "actual_opposite_endpoint_branch_residual": 0.05859499236072586
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498325e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698616e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.655105398501617e-05,
            1.7604410324171577e-15,
            1.4602586247482285e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056347e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384024e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498324e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698615997e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.6551053985016176e-05,
            1.7604410324171577e-15,
            1.4602586247481827e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056346e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384021e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "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": [
          [
            0.06340100247197245,
            -4.996003610813204e-16,
            0.0634010102678566
          ],
          [
            0.05538875187582082,
            7.771561172376096e-16,
            0.055398332256042515
          ],
          [
            0.04739668882193859,
            1.7763568394002505e-15,
            0.04741330829461465
          ],
          [
            0.03942742829086776,
            5.551115123125783e-16,
            0.039448428102290434
          ],
          [
            0.03148361916918785,
            1.1102230246251565e-16,
            0.031506206738271314
          ],
          [
            0.023567935300413456,
            -9.43689570931383e-16,
            0.02358917586732623
          ],
          [
            0.015683066193603823,
            3.3306690738754696e-15,
            0.01569987480690005
          ],
          [
            0.007831707438251123,
            1.6653345369377348e-15,
            0.007840841405724497
          ],
          [
            1.655105398501444e-05,
            1.7763568394002505e-15,
            1.4602586247525196e-05
          ],
          [
            -0.003040260896546243,
            7.771561172376096e-16,
            -0.0022592686821076846
          ],
          [
            -0.006125615725219358,
            5.329070518200751e-15,
            -0.004557335448724276
          ],
          [
            -0.009239821417200422,
            7.216449660063518e-15,
            -0.006879799797268216
          ],
          [
            -0.012383199130934497,
            7.771561172376096e-16,
            -0.00922686278960183
          ],
          [
            -0.015556083725445646,
            4.6629367034256575e-15,
            -0.011598725501353213
          ],
          [
            -0.01875882415283875,
            5.218048215738236e-15,
            -0.013995590554504445
          ],
          [
            -0.021991783896436135,
            7.216449660063518e-15,
            -0.01641766391235211
          ],
          [
            -0.025255341460148628,
            7.549516567451064e-15,
            -0.018865156919773196
          ]
        ]
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785705
            ],
            "target_residual": 0.4411783822328323,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.10964025157949626,
            "max_log_strain_component": 0.017957034074929615,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0200999879535793,
              0.9976858257191301,
              0.9807074308781587
            ],
            "cell_volume_ratio": 0.9981044930274751,
            "cell_rmsd_from_input_A": 0.10319369202803927
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.025771579293556387,
              -2.5483510168507573e-14,
              0.4879966487737917
            ],
            "branch_aligned_reduced_polarization": [
              0.025771579293556387,
              -2.5483510168507573e-14,
              0.4879966487737917
            ],
            "target_residual": 0.028429821313961528,
            "energy_eV": -46.8827215473667,
            "max_atomic_step_A": 0.009565194849382685,
            "max_log_strain_component": 0.0016036897563003855,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.020679623290523,
              0.9968374138188406,
              0.9812590307490601
            ],
            "cell_volume_ratio": 0.9983836061935712,
            "cell_rmsd_from_input_A": 0.10483903878447555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0006137053716990544,
              7.099996674046279e-15,
              0.499867138416792
            ],
            "branch_aligned_reduced_polarization": [
              0.0006137053716990544,
              7.099996674046279e-15,
              0.499867138416792
            ],
            "target_residual": 0.0006279223547102114,
            "energy_eV": -46.83993049316428
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006279223547102114,
        "parent_symmetrization_rmsd_A": 0.1161753930059693,
        "parent_cell_rmsd_A": 0.10483903878447555,
        "energy_eV": -46.83993049316428,
        "reduced_polarization": [
          0.0006137053716990544,
          7.099996674046279e-15,
          0.499867138416792
        ],
        "cartesian_polarization_e_A2": [
          -0.0035700760275296354,
          1.3112895733858643e-16,
          0.00650278566107695
        ],
        "ranking_score": 0.6436409974115086
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197378,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "target_residual": 0.44117839106812834,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01939987905985691,
            "step_scale": 0.8957739070556645,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.012384228524005,
              1.0115082726210336,
              0.9714334295905638
            ],
            "cell_volume_ratio": 0.9947818536590292,
            "cell_rmsd_from_input_A": 0.13560785364917272
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.45928014099068054,
              -9.95968684208629e-14,
              0.03324968850220087
            ],
            "branch_aligned_reduced_polarization": [
              0.45928014099068054,
              -9.95968684208629e-14,
              0.03324968850220087
            ],
            "target_residual": 0.05257041661649871,
            "energy_eV": -46.77784030094914,
            "max_atomic_step_A": 0.017856209737540357,
            "max_log_strain_component": 0.0025097415898704444,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0128055312977784,
              1.0127593795308674,
              0.9694829351669297
            ],
            "cell_volume_ratio": 0.9944260843857204,
            "cell_rmsd_from_input_A": 0.14675399545900403
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.502527136625774,
              -1.82729845998513e-14,
              0.0018619782561775794
            ],
            "branch_aligned_reduced_polarization": [
              0.502527136625774,
              -1.82729845998513e-14,
              0.0018619782561775794
            ],
            "target_residual": 0.0031390098043501493,
            "energy_eV": -46.61555488830815,
            "max_atomic_step_A": 0.0006450683576877251,
            "max_log_strain_component": 0.00020915829225351987,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.012735645017647,
              1.0126230719116431,
              0.9697248234881696
            ],
            "cell_volume_ratio": 0.9944716966221325,
            "cell_rmsd_from_input_A": 0.14568790649350735
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999785335405455,
              1.5745554552277654e-15,
              -2.7833073088220605e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999785335405455,
              1.5745554552277654e-15,
              -2.7833073088220605e-05
            ],
            "target_residual": 3.5149521178046255e-05,
            "energy_eV": -46.620786033136866
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.5149521178046255e-05,
        "parent_symmetrization_rmsd_A": 0.13921420657943684,
        "parent_cell_rmsd_A": 0.14568790649350735,
        "energy_eV": -46.620786033136866,
        "reduced_polarization": [
          0.4999785335405455,
          1.5745554552277654e-15,
          -2.7833073088220605e-05
        ],
        "cartesian_polarization_e_A2": [
          0.008754452714209887,
          4.230101356596153e-16,
          -0.0001514927696921387
        ],
        "ranking_score": 0.6757064822451697
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197376,
              4.440892098500626e-16,
              0.06340101026785706
            ],
            "target_residual": 0.5079757624310787,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.10425730770113614,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6046103254958696,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0237872163591277,
              0.9983363112868566,
              0.9791711371610432
            ],
            "cell_volume_ratio": 1.0007951066531209,
            "cell_rmsd_from_input_A": 0.1808661787091208
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.03353091800133876,
              0.3014700626373245,
              0.06555453100890624
            ],
            "branch_aligned_reduced_polarization": [
              0.03353091800133876,
              0.3014700626373245,
              0.06555453100890624
            ],
            "target_residual": 0.21174478748492961,
            "energy_eV": -46.72349332319824,
            "max_atomic_step_A": 0.07857481207633871,
            "max_log_strain_component": 0.014241825927767175,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.042808939424098,
              0.9942799256946563,
              0.9659173138445457
            ],
            "cell_volume_ratio": 1.0015055663372325,
            "cell_rmsd_from_input_A": 0.312481638191403
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.021439930197670626,
              0.4866158201699265,
              0.016451780676550398
            ],
            "branch_aligned_reduced_polarization": [
              -0.021439930197670626,
              0.4866158201699265,
              0.016451780676550398
            ],
            "target_residual": 0.03015738655842134,
            "energy_eV": -45.9371948226655,
            "max_atomic_step_A": 0.013677436199770274,
            "max_log_strain_component": 0.002259974248469781,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0454220446309284,
              0.9933496414697993,
              0.9640710658733941
            ],
            "cell_volume_ratio": 1.0011585068929383,
            "cell_rmsd_from_input_A": 0.3331516567982786
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.001973411083495119,
              0.4977280557347207,
              0.0025888314378763955
            ],
            "branch_aligned_reduced_polarization": [
              -0.001973411083495119,
              0.4977280557347207,
              0.0025888314378763955
            ],
            "target_residual": 0.003969651151264322,
            "energy_eV": -45.87613874903241,
            "max_atomic_step_A": 0.0017754813904192956,
            "max_log_strain_component": 0.0003649785820265566,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0458717456695263,
              0.9932045958472953,
              0.9637611041346061
            ],
            "cell_volume_ratio": 1.0011209414111362,
            "cell_rmsd_from_input_A": 0.3365484875952812
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.0002969671837780749,
              0.4996938579722016,
              0.0003995058879217803
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002969671837780749,
              0.4996938579722016,
              0.0003995058879217803
            ],
            "target_residual": 0.0005843949040757948,
            "energy_eV": -45.866105513917155
          }
        ],
        "iterations": 4
      },
      "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": 0.0005843949040757948,
        "parent_symmetrization_rmsd_A": 0.19335147508456416,
        "parent_cell_rmsd_A": 0.3365484875952812,
        "energy_eV": -45.866105513917155,
        "reduced_polarization": [
          -0.0002969671837780749,
          0.4996938579722016,
          0.0003995058879217803
        ],
        "cartesian_polarization_e_A2": [
          0.00042238011431142565,
          0.011643040121994316,
          0.00020135562497762183
        ],
        "ranking_score": 0.7786573867915361
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197378,
              4.59470439013063e-16,
              0.06340101026785705
            ],
            "target_residual": 0.6174442181101102,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.04776623906393646,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4569032255176176,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0153841666127692,
              1.0056052152382773,
              0.9753170647880627
            ],
            "cell_volume_ratio": 0.9958724702037323,
            "cell_rmsd_from_input_A": 0.10968924461891917
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.26617629866757764,
              -6.857855236008607e-14,
              0.2653742245786579
            ],
            "branch_aligned_reduced_polarization": [
              0.26617629866757764,
              -6.857855236008607e-14,
              0.2653742245786579
            ],
            "target_residual": 0.33124428719128113,
            "energy_eV": -47.11724722086472,
            "max_atomic_step_A": 0.04661337935037562,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8540235624876978,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.030990339846308,
              1.011272684936525,
              0.9512207206085593
            ],
            "cell_volume_ratio": 0.9917544890697192,
            "cell_rmsd_from_input_A": 0.2203656786470011
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.46389767804776694,
              -8.098061149176644e-14,
              0.46273806954581714
            ],
            "branch_aligned_reduced_polarization": [
              0.46389767804776694,
              -8.098061149176644e-14,
              0.46273806954581714
            ],
            "target_residual": 0.05188284024140399,
            "energy_eV": -46.75842863668059,
            "max_atomic_step_A": 0.008824311347418195,
            "max_log_strain_component": 0.003776404042177668,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0339669757982688,
              1.0123399598503247,
              0.9467428175838651
            ],
            "cell_volume_ratio": 0.990980404623547,
            "cell_rmsd_from_input_A": 0.24136002897918063
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49937318183993346,
              -1.0616774308397412e-14,
              0.4993447686520581
            ],
            "branch_aligned_reduced_polarization": [
              0.49937318183993346,
              -1.0616774308397412e-14,
              0.4993447686520581
            ],
            "target_residual": 0.0009067685069051173,
            "energy_eV": -46.65114117105811
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0009067685069051173,
        "parent_symmetrization_rmsd_A": 0.13842755161707254,
        "parent_cell_rmsd_A": 0.24136002897918063,
        "energy_eV": -46.65114117105811,
        "reduced_polarization": [
          0.49937318183993346,
          -1.0616774308397412e-14,
          0.4993447686520581
        ],
        "cartesian_polarization_e_A2": [
          0.004918691850701564,
          -4.207277335821975e-16,
          0.006098217883585657
        ],
        "ranking_score": 0.700581095875678
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197376,
              4.440892098500626e-16,
              0.06340101026785705
            ],
            "target_residual": 0.6668120911842996,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.019610202486011925,
            "step_scale": 0.5928265454055802,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0168589762658542,
              1.0106816161649226,
              0.9719332157447739
            ],
            "cell_volume_ratio": 0.9988758591251813,
            "cell_rmsd_from_input_A": 0.18422836213166152
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.050951091914967286,
              0.30128403674459353,
              0.35455031577448104
            ],
            "branch_aligned_reduced_polarization": [
              0.050951091914967286,
              0.30128403674459353,
              0.35455031577448104
            ],
            "target_residual": 0.2514749658736525,
            "energy_eV": -46.44409503308383,
            "max_atomic_step_A": 0.0855861651767768,
            "max_log_strain_component": 0.0129349467840492,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0279228889911078,
              1.0175032419139094,
              0.95460782115651
            ],
            "cell_volume_ratio": 0.9984385170617106,
            "cell_rmsd_from_input_A": 0.3019029755978595
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.002913385779818427,
              0.4978227366507927,
              0.498578426339203
            ],
            "branch_aligned_reduced_polarization": [
              -0.002913385779818427,
              0.4978227366507927,
              0.498578426339203
            ],
            "target_residual": 0.0039050178062233483,
            "energy_eV": -44.92549498111101,
            "max_atomic_step_A": 0.001778687936405519,
            "max_log_strain_component": 0.00023550108333198372,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0282263359368964,
              1.017491029265845,
              0.9542852165983038
            ],
            "cell_volume_ratio": 0.9983837602819418,
            "cell_rmsd_from_input_A": 0.30409672397083554
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              9.516732490751992e-05,
              0.49999256068675857,
              0.5003699729237757
            ],
            "branch_aligned_reduced_polarization": [
              9.516732490751992e-05,
              0.49999256068675857,
              0.5003699729237757
            ],
            "target_residual": 0.0003820891616347046,
            "energy_eV": -44.90225421985938
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0003820891616347046,
        "parent_symmetrization_rmsd_A": 0.20514807096218454,
        "parent_cell_rmsd_A": 0.30409672397083554,
        "energy_eV": -44.90225421985938,
        "reduced_polarization": [
          9.516732490751992e-05,
          0.49999256068675857,
          0.5003699729237757
        ],
        "cartesian_polarization_e_A2": [
          -0.003199359610400991,
          0.011630741271597285,
          0.006667877527715704
        ],
        "ranking_score": 0.7819364302781628
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197378,
              4.440892098500626e-16,
              0.06340101026785706
            ],
            "target_residual": 0.6668120970299368,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.017258402687606863,
            "step_scale": 0.5217304233240417,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0218217971994863,
              1.0005358025644562,
              0.9751441631397056
            ],
            "cell_volume_ratio": 0.996957447607437,
            "cell_rmsd_from_input_A": 0.17563604876745986
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2952150479052593,
              0.24008166859885643,
              0.06088839366367728
            ],
            "branch_aligned_reduced_polarization": [
              0.2952150479052593,
              0.24008166859885643,
              0.06088839366367728
            ],
            "target_residual": 0.33645476974735083,
            "energy_eV": -46.84565043205409,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.016881197585932768,
            "step_scale": 0.7566700729863081,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0433728680316114,
              0.9984632752240792,
              0.9549215186379741
            ],
            "cell_volume_ratio": 0.9948081045069407,
            "cell_rmsd_from_input_A": 0.34389365287953527
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.41442690093027634,
              0.38217068708705043,
              0.0415528782368841
            ],
            "branch_aligned_reduced_polarization": [
              0.41442690093027634,
              0.38217068708705043,
              0.0415528782368841
            ],
            "target_residual": 0.15143693062032074,
            "energy_eV": -46.0895166852028,
            "max_atomic_step_A": 0.06790919304731602,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9130565171795487,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0694876775046143,
              0.9941687594647554,
              0.9338302663784888
            ],
            "cell_volume_ratio": 0.9928961864423675,
            "cell_rmsd_from_input_A": 0.5448267216356892
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.47248373697575596,
              0.4442098957705592,
              0.04017234601926631
            ],
            "branch_aligned_reduced_polarization": [
              0.47248373697575596,
              0.4442098957705592,
              0.04017234601926631
            ],
            "target_residual": 0.07405064378817316,
            "energy_eV": -45.427697455497984,
            "max_atomic_step_A": 0.04179028721774842,
            "max_log_strain_component": 0.011906594335286926,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0855632952235776,
              0.9899667621543076,
              0.9233089265704226
            ],
            "cell_volume_ratio": 0.9922538633943107,
            "cell_rmsd_from_input_A": 0.6652642225936138
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4825658536760207,
              0.47183621435868967,
              0.015462005426276721
            ],
            "branch_aligned_reduced_polarization": [
              0.4825658536760207,
              0.47183621435868967,
              0.015462005426276721
            ],
            "target_residual": 0.03655436897961461,
            "energy_eV": -45.167654853264956,
            "max_atomic_step_A": 0.016804747530313874,
            "max_log_strain_component": 0.005625070477030512,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.781665987282739,
            "cell_principal_stretches": [
              1.0758195939578765,
              0.991112562563944,
              0.9217209394027454
            ],
            "cell_volume_ratio": 0.9827926154013062,
            "cell_rmsd_from_input_A": 0.5928150218695705
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4991461683388663,
              0.499205394255133,
              -0.00011857304346099362
            ],
            "branch_aligned_reduced_polarization": [
              0.4991461683388663,
              0.499205394255133,
              -0.00011857304346099362
            ],
            "target_residual": 0.0011723849035046219,
            "energy_eV": -45.125466287144526
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0011723849035046219,
        "parent_symmetrization_rmsd_A": 0.3183608526799104,
        "parent_cell_rmsd_A": 0.5928150218695705,
        "energy_eV": -45.125466287144526,
        "reduced_polarization": [
          0.4991461683388663,
          0.499205394255133,
          -0.00011857304346099362
        ],
        "cartesian_polarization_e_A2": [
          0.009612339895103366,
          0.012592223594916038,
          0.00021989912888474952
        ],
        "ranking_score": 0.9689093779543123
      },
      "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": [
              0.06340100247197376,
              4.59470439013063e-16,
              0.06340101026785706
            ],
            "branch_aligned_reduced_polarization": [
              0.06340100247197378,
              4.440892098500626e-16,
              0.06340101026785705
            ],
            "target_residual": 0.794504476058886,
            "energy_eV": -47.23750284930867,
            "max_atomic_step_A": 0.10232502184668557,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4569032255172024,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0202670207418179,
              1.0072262562281296,
              0.9690871611202728
            ],
            "cell_volume_ratio": 0.9958724702037572,
            "cell_rmsd_from_input_A": 0.17464827721451548
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.27264842675584594,
              0.21798824949149262,
              0.2867144085657553
            ],
            "branch_aligned_reduced_polarization": [
              0.27264842675584594,
              0.21798824949149265,
              0.2867144085657553
            ],
            "target_residual": 0.4203690150271784,
            "energy_eV": -46.87340798463197,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.016277098869469958,
            "step_scale": 0.784166753626818,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0399616666796243,
              1.013135495359159,
              0.9418263198684202
            ],
            "cell_volume_ratio": 0.9923290045618907,
            "cell_rmsd_from_input_A": 0.34568727041599207
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4417442849786236,
              0.41527969743302345,
              0.4893772761093542
            ],
            "branch_aligned_reduced_polarization": [
              0.4417442849786236,
              0.41527969743302345,
              0.4893772761093542
            ],
            "target_residual": 0.10336392147431699,
            "energy_eV": -45.84843768908088,
            "max_atomic_step_A": 0.05580729707339332,
            "max_log_strain_component": 0.010843586211289087,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0518186994106686,
              1.0136637046833585,
              0.9294886140424595
            ],
            "cell_volume_ratio": 0.9910118739160366,
            "cell_rmsd_from_input_A": 0.44703345047502724
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49031070480025113,
              0.4808805690467814,
              0.5198773820991923
            ],
            "branch_aligned_reduced_polarization": [
              0.49031070480025113,
              0.4808805690467814,
              0.5198773820991923
            ],
            "target_residual": 0.02923260851446654,
            "energy_eV": -45.27509596369911,
            "max_atomic_step_A": 0.015653193105553492,
            "max_log_strain_component": 0.0037949035671680435,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.724873249049242,
            "cell_principal_stretches": [
              1.0559605009853146,
              1.0128642321053973,
              0.9263621991266711
            ],
            "cell_volume_ratio": 0.9907857080667878,
            "cell_rmsd_from_input_A": 0.48033646680881587
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49695200705398557,
              0.4941727105726085,
              0.5064364399190459
            ],
            "branch_aligned_reduced_polarization": [
              0.49695200705398557,
              0.4941727105726085,
              0.5064364399190459
            ],
            "target_residual": 0.00920191946829735,
            "energy_eV": -45.18611030279603,
            "max_atomic_step_A": 0.005007483263245875,
            "max_log_strain_component": 0.0009346114202658175,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.333818196106299,
            "cell_principal_stretches": [
              1.0544412365081142,
              1.0130915210467215,
              0.9257937097476651
            ],
            "cell_volume_ratio": 0.9889749422845797,
            "cell_rmsd_from_input_A": 0.47099268490118523
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49997666099789945,
              0.4999859695925929,
              0.49997244190318624
            ],
            "branch_aligned_reduced_polarization": [
              0.49997666099789945,
              0.4999859695925929,
              0.49997244190318624
            ],
            "target_residual": 3.874287097074375e-05,
            "energy_eV": -45.167837091346506
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.874287097074375e-05,
        "parent_symmetrization_rmsd_A": 0.24336734644623348,
        "parent_cell_rmsd_A": 0.47099268490118523,
        "energy_eV": -45.167837091346506,
        "reduced_polarization": [
          0.49997666099789945,
          0.4999859695925929,
          0.49997244190318624
        ],
        "cartesian_polarization_e_A2": [
          0.00550897933859522,
          0.012329350142757092,
          0.006342353985342368
        ],
        "ranking_score": 0.8611930034134713
      },
      "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
        ],
        "endpoint_rmsd_A": 0.019484451245900328,
        "minimum_distance_A_by_image": [
          2.432224879554823,
          2.4307856644533445,
          2.4293458761598052,
          2.4279055684339554,
          2.4264647408548043,
          2.4250233930166707,
          2.423581524529302,
          2.4221391350179724,
          2.420696223813033
        ],
        "minimum_distance_A": 2.420696223813033,
        "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": [
          440.6402839295123,
          440.71391336194597,
          440.78755509759725,
          440.86120913852244,
          440.9348754867765,
          441.0085541444171,
          441.0822451135011,
          441.1559483960849,
          441.2296639942261
        ],
        "cell_deformation_log_strain_norm": 0.00963362810157609
      },
      "parent_reduced_polarization": [
        1.655105398501617e-05,
        1.7604410324171577e-15,
        1.4602586247482285e-05
      ],
      "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": [
          -47.237502849308676,
          -47.23922605848477,
          -47.24075066082565,
          -47.2420794317071,
          -47.24321503553357,
          -47.2441600306391,
          -47.24491687369762,
          -47.24548792365855,
          -47.24587544518148
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0006568732741937272,
            -1.1439180030088568e-17,
            0.0008075750281856024
          ],
          [
            0.0005743285357913956,
            1.9509710887731827e-17,
            0.0007061900324005136
          ],
          [
            0.0004918570891487159,
            4.2203908669917595e-17,
            0.000604871630325126
          ],
          [
            0.00040948729900107877,
            1.3791241425559893e-17,
            0.0005036520317411831
          ],
          [
            0.00032724803858093725,
            4.4894251757418295e-18,
            0.0004025638775690434
          ],
          [
            0.00024516859636342146,
            -2.1391773953808818e-17,
            0.0003016401302459743
          ],
          [
            0.00016327857788417057,
            7.722816184361316e-17,
            0.00020091396076789446
          ],
          [
            8.160780311422361e-05,
            3.8107792822276126e-17,
            0.00010041863299904738
          ],
          [
            1.8620449707840216e-07,
            4.090560665627929e-17,
            1.8738312158977662e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498325e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698616e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.655105398501617e-05,
            1.7604410324171577e-15,
            1.4602586247482285e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498324e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698615997e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.6551053985016176e-05,
            1.7604410324171577e-15,
            1.4602586247481827e-05
          ]
        ],
        "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": [
          [
            0.06340100247197245,
            -4.996003610813204e-16,
            0.0634010102678566
          ],
          [
            0.05538875187582082,
            7.771561172376096e-16,
            0.055398332256042515
          ],
          [
            0.04739668882193859,
            1.7763568394002505e-15,
            0.04741330829461465
          ],
          [
            0.03942742829086776,
            5.551115123125783e-16,
            0.039448428102290434
          ],
          [
            0.03148361916918785,
            1.1102230246251565e-16,
            0.031506206738271314
          ],
          [
            0.023567935300413456,
            -9.43689570931383e-16,
            0.02358917586732623
          ],
          [
            0.015683066193603823,
            3.3306690738754696e-15,
            0.01569987480690005
          ],
          [
            0.007831707438251123,
            1.6653345369377348e-15,
            0.007840841405724497
          ],
          [
            1.655105398501444e-05,
            1.7763568394002505e-15,
            1.4602586247525196e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -47.2458754451815,
          -47.241558295090336,
          -47.237182340894634,
          -47.232749560602706,
          -47.22826194750666,
          -47.22372150539249,
          -47.2191302431555,
          -47.21449016902682,
          -47.20980328454507
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8620449709920015e-07,
            5.568123536783996e-17,
            1.8738312156027415e-07
          ],
          [
            -3.710229739658065e-05,
            1.7736078462011082e-17,
            -2.901160750690084e-05
          ],
          [
            -7.467582708548326e-05,
            1.2508715720138336e-16,
            -5.84532681543325e-05
          ],
          [
            -0.00011253771319034219,
            1.6790638244733815e-16,
            -8.813934753963154e-05
          ],
          [
            -0.0001506915138307273,
            1.681444629503155e-17,
            -0.00011807156936948085
          ],
          [
            -0.00018914101871597951,
            1.0844290102032454e-16,
            -0.00014825164461429146
          ],
          [
            -0.00022789024537798027,
            1.223420458450778e-16,
            -0.00017868129008555744
          ],
          [
            -0.000266943434271526,
            1.6869595288063673e-16,
            -0.0002093622503594004
          ],
          [
            -0.0003063050429393139,
            1.7666602466767427e-16,
            -0.00024029632283218682
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6551053985290543e-05,
            2.396343503527624e-15,
            1.4602586245157766e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056347e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384024e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6551053985290543e-05,
            2.396343503527624e-15,
            1.4602586245157766e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056348e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384021e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.06336768470857353,
          4.000642577617243e-15,
          -0.06337158816142369
        ],
        "actual_opposite_endpoint_branch_residual": 0.05859499236072586
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498325e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698616e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.655105398501617e-05,
            1.7604410324171577e-15,
            1.4602586247482285e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056347e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384024e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0634010024719724,
            -4.907654438865673e-16,
            0.06340101026785665
          ],
          [
            0.0553887518758208,
            8.247519704498324e-16,
            0.05539833225604249
          ],
          [
            0.047396688821938614,
            1.790500931845124e-15,
            0.047413308294614646
          ],
          [
            0.0394274282908678,
            5.65440043655258e-16,
            0.039448428102290475
          ],
          [
            0.0314836191691879,
            1.6420485698615997e-16,
            0.03150620673827134
          ],
          [
            0.023567935300413432,
            -9.464454036588184e-16,
            0.023589175867326184
          ],
          [
            0.01568306619360383,
            3.2995849222506168e-15,
            0.015699874806900056
          ],
          [
            0.00783170743825107,
            1.6268795561375514e-15,
            0.007840841405724497
          ],
          [
            1.6551053985016176e-05,
            1.7604410324171577e-15,
            1.4602586247481827e-05
          ],
          [
            -0.0030402608965462647,
            7.641821471056346e-16,
            -0.002259268682107684
          ],
          [
            -0.006125615725219339,
            5.381214744333393e-15,
            -0.004557335448724293
          ],
          [
            -0.00923982141720042,
            7.220287372172075e-15,
            -0.006879799797268231
          ],
          [
            -0.012383199130934499,
            7.252803720384021e-16,
            -0.009226862789601826
          ],
          [
            -0.015556083725445653,
            4.660541095362365e-15,
            -0.011598725501353237
          ],
          [
            -0.01875882415283877,
            5.2549764053133536e-15,
            -0.01399559055450442
          ],
          [
            -0.021991783896436128,
            7.241506238756373e-15,
            -0.016417663912352134
          ],
          [
            -0.025255341460148604,
            7.579352697278524e-15,
            -0.01886515691977322
          ]
        ],
        "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": [
          [
            0.06340100247197245,
            -4.996003610813204e-16,
            0.0634010102678566
          ],
          [
            0.05538875187582082,
            7.771561172376096e-16,
            0.055398332256042515
          ],
          [
            0.04739668882193859,
            1.7763568394002505e-15,
            0.04741330829461465
          ],
          [
            0.03942742829086776,
            5.551115123125783e-16,
            0.039448428102290434
          ],
          [
            0.03148361916918785,
            1.1102230246251565e-16,
            0.031506206738271314
          ],
          [
            0.023567935300413456,
            -9.43689570931383e-16,
            0.02358917586732623
          ],
          [
            0.015683066193603823,
            3.3306690738754696e-15,
            0.01569987480690005
          ],
          [
            0.007831707438251123,
            1.6653345369377348e-15,
            0.007840841405724497
          ],
          [
            1.655105398501444e-05,
            1.7763568394002505e-15,
            1.4602586247525196e-05
          ],
          [
            -0.003040260896546243,
            7.771561172376096e-16,
            -0.0022592686821076846
          ],
          [
            -0.006125615725219358,
            5.329070518200751e-15,
            -0.004557335448724276
          ],
          [
            -0.009239821417200422,
            7.216449660063518e-15,
            -0.006879799797268216
          ],
          [
            -0.012383199130934497,
            7.771561172376096e-16,
            -0.00922686278960183
          ],
          [
            -0.015556083725445646,
            4.6629367034256575e-15,
            -0.011598725501353213
          ],
          [
            -0.01875882415283875,
            5.218048215738236e-15,
            -0.013995590554504445
          ],
          [
            -0.021991783896436135,
            7.216449660063518e-15,
            -0.01641766391235211
          ],
          [
            -0.025255341460148628,
            7.549516567451064e-15,
            -0.018865156919773196
          ]
        ]
      },
      "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": "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.2071993859563684e-05,
        "parent_symmetrization_rmsd_A": 0.019484451245900328,
        "parent_cell_rmsd_A": 0.035296166572153995,
        "energy_eV": -47.24587544518149,
        "reduced_polarization": [
          1.655105398240584e-05,
          5.154768389637332e-15,
          1.4602586243816702e-05
        ],
        "cartesian_polarization_e_A2": [
          1.8620449705843767e-07,
          1.1977512365657854e-16,
          1.8738312154291235e-07
        ],
        "ranking_score": 0.528352636876658
      }
    }
  ],
  "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": 87,
      "full_response": 28,
      "energy_polarization": 59
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 112,
      "full_response": 53,
      "energy_polarization": 59
    },
    "elapsed_seconds": 156.40324804798001
  }
}