{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 84,
  "input_formula": "Cl16Hf4O64",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -411.43839979693485,
  "input_cartesian_polarization_e_A2": [
    -7.118268361182342e-05,
    -1.2227703481131934e-12,
    4.886170960549393e-05
  ],
  "input_reduced_polarization": [
    -0.005672571852555539,
    -2.034407751158992e-10,
    0.005169394245734266
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.9348236734198307e-15,
      "parent_symmetrization_rmsd_A": 0.13244100139345116,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -411.60703012825843,
      "reduced_polarization": [
        -2.910593165830273e-15,
        3.5011252707019557e-16,
        1.3805301690329062e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.873343464027111e-17,
        2.1043333931485576e-18,
        1.3048930109475124e-18
      ],
      "ranking_score": 0.13244100139345702
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.973633849547015e-07,
      "parent_symmetrization_rmsd_A": 0.0020640569086711595,
      "parent_cell_rmsd_A": 0.0004889551287381894,
      "energy_eV": -411.4372355114861,
      "reduced_polarization": [
        -5.220048121275522e-07,
        2.0223996100813873e-13,
        -4.624139560946633e-07
      ],
      "cartesian_polarization_e_A2": [
        -3.6436955200606043e-09,
        1.2155312120668866e-15,
        -4.370668365830851e-09
      ],
      "ranking_score": 0.5021876904176256
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8709765871759313e-15,
      "parent_symmetrization_rmsd_A": 0.13244100334482486,
      "parent_cell_rmsd_A": 0.0004889551287381894,
      "energy_eV": -411.6075907137204,
      "reduced_polarization": [
        9.493815513445552e-16,
        -1.1052661297028777e-15,
        1.1737183828579675e-15
      ],
      "cartesian_polarization_e_A2": [
        5.5959409584715374e-18,
        -6.6429234603791155e-18,
        1.1093888480803941e-17
      ],
      "ranking_score": 0.13256324212701315
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 8.726736531356044e-06,
      "parent_symmetrization_rmsd_A": 0.10760773708800221,
      "parent_cell_rmsd_A": 0.028356310584264653,
      "energy_eV": -406.4765198272498,
      "reduced_polarization": [
        -0.5000087235225517,
        6.633272305189279e-13,
        2.3682225072337139e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.004857106130550152,
        -9.820314949416347e-13,
        -7.359955929762391e-06
      ],
      "ranking_score": 0.614714268207131
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.504983284358437e-05,
      "parent_symmetrization_rmsd_A": 0.10835644962244628,
      "parent_cell_rmsd_A": 0.017717207849739097,
      "energy_eV": -406.398478507514,
      "reduced_polarization": [
        -1.1270705461148212e-05,
        -7.065706416371461e-13,
        0.499990026602032
      ],
      "cartesian_polarization_e_A2": [
        -0.00155071793152126,
        -4.1385327656898383e-13,
        0.004734700716823376
      ],
      "ranking_score": 0.6128158512505683
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.499999999999999,
      "parent_symmetrization_rmsd_A": 1.661291410823916,
      "parent_cell_rmsd_A": 0.017717207849735135,
      "energy_eV": -390.0748816532107,
      "reduced_polarization": [
        -2.663460964323669e-16,
        1.9171319599176497e-15,
        9.754861037827203e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.617525126289467e-18,
        1.1545410756793822e-17,
        9.238397675463156e-18
      ],
      "ranking_score": 2.6657207127863476
    },
    {
      "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": 2.4535294125953094e-06,
      "parent_symmetrization_rmsd_A": 0.05549425244469479,
      "parent_cell_rmsd_A": 0.01609075794209135,
      "energy_eV": -409.636745719702,
      "reduced_polarization": [
        1.6274542694475257e-06,
        -0.5000005281561509,
        1.7584795306079683e-06
      ],
      "cartesian_polarization_e_A2": [
        -6.627903608449725e-07,
        -0.0030051286337249494,
        -6.0309662013329086e-06
      ],
      "ranking_score": 0.5595218489890428
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.3379647627725961e-05,
      "parent_symmetrization_rmsd_A": 0.19321232018587237,
      "parent_cell_rmsd_A": 0.04431270462391304,
      "energy_eV": -395.89797934885326,
      "reduced_polarization": [
        -0.5000109970397303,
        -3.7538373906219894e-13,
        0.5000076210293145
      ],
      "cartesian_polarization_e_A2": [
        -0.00640817747172221,
        -2.008491152118804e-12,
        0.004719614944575761
      ],
      "ranking_score": 0.704317255637106
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.4310141854215649e-05,
      "parent_symmetrization_rmsd_A": 0.12160299265702292,
      "parent_cell_rmsd_A": 0.03274811834302166,
      "energy_eV": -404.6381478017505,
      "reduced_polarization": [
        -0.5000084469041459,
        -0.5000105809992981,
        4.633834706982298e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.004857773260543117,
        -0.0030097871587694822,
        -1.3432053600784707e-05
      ],
      "ranking_score": 0.6298186425264868
    },
    {
      "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": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.1598455480731882e-05,
      "parent_symmetrization_rmsd_A": 0.12212849179283268,
      "parent_cell_rmsd_A": 0.023948501779446893,
      "energy_eV": -404.44975736403546,
      "reduced_polarization": [
        -1.0958589553405207e-05,
        -0.4999822474087272,
        0.4999944100002456
      ],
      "cartesian_polarization_e_A2": [
        -0.0015513809766729463,
        -0.0030018339390405786,
        0.004728671434165274
      ],
      "ranking_score": 0.6281588141486558
    },
    {
      "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": 1.747237043103951e-05,
      "parent_symmetrization_rmsd_A": 0.20300312097053982,
      "parent_cell_rmsd_A": 0.04744694856508634,
      "energy_eV": -394.03694402835373,
      "reduced_polarization": [
        -0.5000129698190091,
        -0.5000014363927234,
        0.5000116191350493
      ],
      "cartesian_polarization_e_A2": [
        -0.006408807997643351,
        -0.0030064705568595305,
        0.004713399909222284
      ],
      "ranking_score": 0.7148998028526735
    }
  ],
  "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "target_residual": 0.007674679686490894,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.001870611463917948,
            "max_log_strain_component": 2.075425994503275e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0000375464595053,
              0.9999958642181281,
              0.9999919146997152
            ],
            "cell_volume_ratio": 1.0000253249519302,
            "cell_rmsd_from_input_A": 0.0004889551287381894
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.220048121275522e-07,
              2.0223996100813873e-13,
              -4.624139560946633e-07
            ],
            "branch_aligned_reduced_polarization": [
              -5.220048121275522e-07,
              2.0223996100813873e-13,
              -4.624139560946633e-07
            ],
            "target_residual": 6.973633849547015e-07,
            "energy_eV": -411.4372355114861
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9348236734198307e-15,
        "parent_symmetrization_rmsd_A": 0.13244100139345116,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -411.60703012825843,
        "reduced_polarization": [
          -2.910593165830273e-15,
          3.5011252707019557e-16,
          1.3805301690329062e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.873343464027111e-17,
          2.1043333931485576e-18,
          1.3048930109475124e-18
        ],
        "ranking_score": 0.13244100139345702
      },
      "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": [
          -411.4383997969348,
          -411.48044708849204,
          -411.51596964218186,
          -411.5451491211004,
          -411.56825424146416,
          -411.58563732253566,
          -411.5976733955394,
          -411.6047162157403,
          -411.6070301282586
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.118268361182815e-05,
            -1.222777506972874e-12,
            4.886170960547802e-05
          ],
          [
            -6.1781859766167e-05,
            -1.107021262885142e-12,
            4.282599363024673e-05
          ],
          [
            -5.254955806314715e-05,
            -9.79228603141552e-13,
            3.670857137267208e-05
          ],
          [
            -4.3486009372025634e-05,
            -8.367358955422078e-13,
            3.054742997221479e-05
          ],
          [
            -3.458507006477946e-05,
            -6.831103978028871e-13,
            2.4372725209179048e-05
          ],
          [
            -2.5819755578055222e-05,
            -5.215395148311845e-13,
            1.8219845564130425e-05
          ],
          [
            -1.7156623185750382e-05,
            -3.523977354482024e-13,
            1.2110382013600853e-05
          ],
          [
            -8.560967165725613e-06,
            -1.7747502214272856e-13,
            6.044046656797519e-06
          ],
          [
            -3.621207047376476e-17,
            1.2791046115216722e-17,
            -6.003539386335591e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.9258960665700116e-15,
            2.1281349684632603e-15,
            -6.351256326420085e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0056725718525565405,
            -2.0344198548016834e-10,
            0.005169394245732595
          ],
          [
            -0.004909352765826602,
            -1.8418278013854206e-10,
            0.00453083706705093
          ],
          [
            -0.004166216324083982,
            -1.6292106552739938e-10,
            0.00388363565571348
          ],
          [
            -0.003441905868579842,
            -1.3921352959300748e-10,
            0.0032318089153102747
          ],
          [
            -0.00273477323402177,
            -1.1365380858663343e-10,
            0.0025785472196213632
          ],
          [
            -0.002040850868059274,
            -8.677214502483821e-11,
            0.0019275945434130692
          ],
          [
            -0.0013559722042031375,
            -5.863087793045452e-11,
            0.0012812351348368
          ],
          [
            -0.0006765782573859291,
            -2.952776911868682e-11,
            0.000639438535017689
          ],
          [
            -3.941291737419306e-15,
            2.1094237467877974e-15,
            -6.106226635438361e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -411.6070301282586,
          -411.60471621574044,
          -411.59767339553935,
          -411.5856373225356,
          -411.56825424146416,
          -411.5451491211003,
          -411.5159696421815,
          -411.48044708849216,
          -411.43839979693473
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.621207047376476e-17,
            1.2791046115216722e-17,
            -6.003539386335591e-18
          ],
          [
            8.560967165689766e-06,
            1.7743994991950943e-13,
            -6.044046656799675e-06
          ],
          [
            1.7156623185731083e-05,
            3.524077207164601e-13,
            -1.2110382013628673e-05
          ],
          [
            2.5819755577998786e-05,
            5.215186159122899e-13,
            -1.821984556411033e-05
          ],
          [
            3.4585070064762906e-05,
            6.831384349507429e-13,
            -2.437272520921753e-05
          ],
          [
            4.348600937197938e-05,
            8.367436526927551e-13,
            -3.054742997223031e-05
          ],
          [
            5.254955806308491e-05,
            9.792230741087152e-13,
            -3.670857137267872e-05
          ],
          [
            6.178185976611142e-05,
            1.1070026333453969e-12,
            -4.2825993630257355e-05
          ],
          [
            7.118268361176348e-05,
            1.22273366669385e-12,
            -4.886170960548381e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.005672571852548711,
          2.0344622245492334e-10,
          -0.005169394245733853
        ],
        "actual_opposite_endpoint_branch_residual": 1.1612695698118726e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.9258960665700116e-15,
            2.1281349684632603e-15,
            -6.351256326420085e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "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": [
          [
            -0.0056725718525565405,
            -2.0344198548016834e-10,
            0.005169394245732595
          ],
          [
            -0.004909352765826602,
            -1.8418278013854206e-10,
            0.00453083706705093
          ],
          [
            -0.004166216324083982,
            -1.6292106552739938e-10,
            0.00388363565571348
          ],
          [
            -0.003441905868579842,
            -1.3921352959300748e-10,
            0.0032318089153102747
          ],
          [
            -0.00273477323402177,
            -1.1365380858663343e-10,
            0.0025785472196213632
          ],
          [
            -0.002040850868059274,
            -8.677214502483821e-11,
            0.0019275945434130692
          ],
          [
            -0.0013559722042031375,
            -5.863087793045452e-11,
            0.0012812351348368
          ],
          [
            -0.0006765782573859291,
            -2.952776911868682e-11,
            0.000639438535017689
          ],
          [
            -3.941291737419306e-15,
            2.1094237467877974e-15,
            -6.106226635438361e-16
          ],
          [
            0.0006765782573822099,
            2.952194044780754e-11,
            -0.0006394385350179665
          ],
          [
            0.0013559722042002509,
            5.863254326499145e-11,
            -0.0012812351348397422
          ],
          [
            0.002040850868054167,
            8.676870333346187e-11,
            -0.0019275945434109043
          ],
          [
            0.002734773234018717,
            1.1365852703448809e-10,
            -0.0025785472196254156
          ],
          [
            0.003441905868574624,
            1.3921486186063703e-10,
            -0.00323180891531194
          ],
          [
            0.004166216324077321,
            1.6292012183782845e-10,
            -0.003883635655714257
          ],
          [
            0.004909352765820496,
            1.841796715140731e-10,
            -0.00453083706705204
          ],
          [
            0.005672571852549768,
            2.0343471351935705e-10,
            -0.005169394245733205
          ]
        ]
      },
      "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": [
        0.5,
        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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555541,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "target_residual": 0.49435445669654354,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.09668520426046645,
            "max_log_strain_component": 0.0015382987414799465,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0015394825299178,
              1.000950399303426,
              0.9979279783403382
            ],
            "cell_volume_ratio": 1.0004141611760948,
            "cell_rmsd_from_input_A": 0.028211710681429056
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4962521432792045,
              5.893279874165123e-10,
              0.0025342080769104255
            ],
            "branch_aligned_reduced_polarization": [
              -0.4962521432792045,
              5.893279874165123e-10,
              0.0025342080769104255
            ],
            "target_residual": 0.004524228174693466,
            "energy_eV": -406.53153711529814,
            "max_atomic_step_A": 0.0006680869744811619,
            "max_log_strain_component": 1.675518096059678e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0015562636457722,
              1.000961182464549,
              0.9979186474293736
            ],
            "cell_volume_ratio": 1.00043234658669,
            "cell_rmsd_from_input_A": 0.028356310584264653
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000087235225517,
              6.633272305189279e-13,
              2.3682225072337139e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000087235225517,
              6.633272305189279e-13,
              2.3682225072337139e-07
            ],
            "target_residual": 8.726736531356044e-06,
            "energy_eV": -406.4765198272498
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 8.726736531356044e-06,
        "parent_symmetrization_rmsd_A": 0.10760773708800221,
        "parent_cell_rmsd_A": 0.028356310584264653,
        "energy_eV": -406.4765198272498,
        "reduced_polarization": [
          -0.5000087235225517,
          6.633272305189279e-13,
          2.3682225072337139e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.004857106130550152,
          -9.820314949416347e-13,
          -7.359955929762391e-06
        ],
        "ranking_score": 0.614714268207131
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.00516939424573426
            ],
            "target_residual": 0.4948631189152774,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.09612727611829418,
            "max_log_strain_component": 0.0009893355233751202,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              0.9993491681519299,
              0.9990774734404825,
              0.9987240668022588
            ],
            "cell_volume_ratio": 0.9971533155384786,
            "cell_rmsd_from_input_A": 0.017484161705854116
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00159808780148903,
              5.162772714709189e-10,
              0.49160812098644907
            ],
            "branch_aligned_reduced_polarization": [
              -0.00159808780148903,
              5.162772714709189e-10,
              0.49160812098644907
            ],
            "target_residual": 0.008542687984431179,
            "energy_eV": -406.55462809385523,
            "max_atomic_step_A": 0.0016354255819027556,
            "max_log_strain_component": 2.186718517434781e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              0.9993342255929023,
              0.999055626667232,
              0.9987085176543774
            ],
            "cell_volume_ratio": 0.9971010773194807,
            "cell_rmsd_from_input_A": 0.017717207849739097
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.1270705461148212e-05,
              -7.065706416371461e-13,
              0.499990026602032
            ],
            "branch_aligned_reduced_polarization": [
              -1.1270705461148212e-05,
              -7.065706416371461e-13,
              0.499990026602032
            ],
            "target_residual": 1.504983284358437e-05,
            "energy_eV": -406.398478507514
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.504983284358437e-05,
        "parent_symmetrization_rmsd_A": 0.10835644962244628,
        "parent_cell_rmsd_A": 0.017717207849739097,
        "energy_eV": -406.398478507514,
        "reduced_polarization": [
          -1.1270705461148212e-05,
          -7.065706416371461e-13,
          0.499990026602032
        ],
        "cartesian_polarization_e_A2": [
          -0.00155071793152126,
          -4.1385327656898383e-13,
          0.004734700716823376
        ],
        "ranking_score": 0.6128158512505683
      },
      "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555539,
              -2.0344076423484125e-10,
              0.005169394245734266
            ],
            "target_residual": 0.5000588970359886,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.0493684368430226,
            "max_log_strain_component": 0.001998938577888577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0020145356343162,
              1.0000231170441578,
              0.9979917180415295
            ],
            "cell_volume_ratio": 1.0000253250154751,
            "cell_rmsd_from_input_A": 0.01598276582560496
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.880154236212474e-05,
              -0.496704855316325,
              0.0003996831073013555
            ],
            "branch_aligned_reduced_polarization": [
              1.880154236212474e-05,
              -0.496704855316325,
              0.0003996831073013555
            ],
            "target_residual": 0.0033193491185183775,
            "energy_eV": -409.6598732306643,
            "max_atomic_step_A": 0.0003498130663617318,
            "max_log_strain_component": 1.346577946779282e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.002028867778598,
              1.0000239490962173,
              0.9979789471790325
            ],
            "cell_volume_ratio": 1.0000276636938592,
            "cell_rmsd_from_input_A": 0.01609075794209135
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.6274542694475257e-06,
              -0.5000005281561509,
              1.7584795306079683e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.6274542694475257e-06,
              -0.5000005281561509,
              1.7584795306079683e-06
            ],
            "target_residual": 2.4535294125953094e-06,
            "energy_eV": -409.636745719702
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.4535294125953094e-06,
        "parent_symmetrization_rmsd_A": 0.05549425244469479,
        "parent_cell_rmsd_A": 0.01609075794209135,
        "energy_eV": -409.636745719702,
        "reduced_polarization": [
          1.6274542694475257e-06,
          -0.5000005281561509,
          1.7584795306079683e-06
        ],
        "cartesian_polarization_e_A2": [
          -6.627903608449725e-07,
          -0.0030051286337249494,
          -6.0309662013329086e-06
        ],
        "ranking_score": 0.5595218489890428
      },
      "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555541,
              -2.034407751158992e-10,
              0.00516939424573426
            ],
            "target_residual": 0.6994404439335778,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.001293084944372193,
            "step_scale": 0.7034908266248663,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0004386746894707,
              1.0002131963702507,
              0.9976190970990073
            ],
            "cell_volume_ratio": 0.998269509418212,
            "cell_rmsd_from_input_A": 0.030935877074269348
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3522015248930931,
              3.4448532580255837e-10,
              0.34911337512058443
            ],
            "branch_aligned_reduced_polarization": [
              -0.3522015248930931,
              3.4448532580255837e-10,
              0.34911337512058443
            ],
            "target_residual": 0.21121354788798102,
            "energy_eV": -404.5014778526879,
            "max_atomic_step_A": 0.054240626495341726,
            "max_log_strain_component": 0.0005414769938356449,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.000600538221169,
              1.0002875439132566,
              0.9966089079562939
            ],
            "cell_volume_ratio": 0.997494150617992,
            "cell_rmsd_from_input_A": 0.04402995544863083
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4968875361747661,
              1.0898520664032956e-10,
              0.4975360753863754
            ],
            "branch_aligned_reduced_polarization": [
              -0.4968875361747661,
              1.0898520664032956e-10,
              0.4975360753863754
            ],
            "target_residual": 0.0039696795292585955,
            "energy_eV": -396.10325108084197,
            "max_atomic_step_A": 0.0011476227975630057,
            "max_log_strain_component": 1.2239976335877265e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.000605741078216,
              1.0002902783567504,
              0.9965871337135894
            ],
            "cell_volume_ratio": 0.9974802703874627,
            "cell_rmsd_from_input_A": 0.04431270462391304
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000109970397303,
              -3.7538373906219894e-13,
              0.5000076210293145
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000109970397303,
              -3.7538373906219894e-13,
              0.5000076210293145
            ],
            "target_residual": 1.3379647627725961e-05,
            "energy_eV": -395.89797934885326
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.3379647627725961e-05,
        "parent_symmetrization_rmsd_A": 0.19321232018587237,
        "parent_cell_rmsd_A": 0.04431270462391304,
        "energy_eV": -395.89797934885326,
        "reduced_polarization": [
          -0.5000109970397303,
          -3.7538373906219894e-13,
          0.5000076210293145
        ],
        "cartesian_polarization_e_A2": [
          -0.00640817747172221,
          -2.008491152118804e-12,
          0.004719614944575761
        ],
        "ranking_score": 0.704317255637106
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555541,
              -2.0344076423484125e-10,
              0.005169394245734266
            ],
            "target_residual": 0.7031261114851972,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.11033616911795524,
            "max_log_strain_component": 0.00199893865248672,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0030680984986318,
              0.9998516993400212,
              0.9975021105975798
            ],
            "cell_volume_ratio": 1.0004141612396644,
            "cell_rmsd_from_input_A": 0.03242071685600742
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4941500003369551,
              -0.4942806647098005,
              0.002566958016575401
            ],
            "branch_aligned_reduced_polarization": [
              -0.4941500003369551,
              -0.4942806647098005,
              0.002566958016575401
            ],
            "target_residual": 0.008574530055822751,
            "energy_eV": -404.7720375949565,
            "max_atomic_step_A": 0.0013123198337739526,
            "max_log_strain_component": 2.374141713564257e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0031094943724599,
              0.9998544410344655,
              0.9974785083740751
            ],
            "cell_volume_ratio": 1.0004345187691728,
            "cell_rmsd_from_input_A": 0.03274811834302166
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000084469041459,
              -0.5000105809992981,
              4.633834706982298e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000084469041459,
              -0.5000105809992981,
              4.633834706982298e-06
            ],
            "target_residual": 1.4310141854215649e-05,
            "energy_eV": -404.6381478017505
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.4310141854215649e-05,
        "parent_symmetrization_rmsd_A": 0.12160299265702292,
        "parent_cell_rmsd_A": 0.03274811834302166,
        "energy_eV": -404.6381478017505,
        "reduced_polarization": [
          -0.5000084469041459,
          -0.5000105809992981,
          4.633834706982298e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.004857773260543117,
          -0.0030097871587694822,
          -1.3432053600784707e-05
        ],
        "ranking_score": 0.6298186425264868
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555539,
              -2.0344076423484125e-10,
              0.00516939424573426
            ],
            "target_residual": 0.703483835108608,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.11009180762293114,
            "max_log_strain_component": 0.0019989385331854698,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0011360712122102,
              0.9989461825354199,
              0.9970724963591995
            ],
            "cell_volume_ratio": 0.9971533156018411,
            "cell_rmsd_from_input_A": 0.023646026803395392
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0003576425486217361,
              -0.49622351550022586,
              0.4915063090971068
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003576425486217361,
              -0.49622351550022586,
              0.4915063090971068
            ],
            "target_residual": 0.009302286198752955,
            "energy_eV": -404.64317578734926,
            "max_atomic_step_A": 0.0019000475886404753,
            "max_log_strain_component": 1.8106394746629863e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0011353105456218,
              0.9989279873841688,
              0.9970395099100777
            ],
            "cell_volume_ratio": 0.9971014069828625,
            "cell_rmsd_from_input_A": 0.023948501779446893
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0958589553405207e-05,
              -0.4999822474087272,
              0.4999944100002456
            ],
            "branch_aligned_reduced_polarization": [
              -1.0958589553405207e-05,
              -0.4999822474087272,
              0.4999944100002456
            ],
            "target_residual": 2.1598455480731882e-05,
            "energy_eV": -404.44975736403546
          }
        ],
        "iterations": 2
      },
      "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": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.1598455480731882e-05,
        "parent_symmetrization_rmsd_A": 0.12212849179283268,
        "parent_cell_rmsd_A": 0.023948501779446893,
        "energy_eV": -404.44975736403546,
        "reduced_polarization": [
          -1.0958589553405207e-05,
          -0.4999822474087272,
          0.4999944100002456
        ],
        "cartesian_polarization_e_A2": [
          -0.0015513809766729463,
          -0.0030018339390405786,
          0.004728671434165274
        ],
        "ranking_score": 0.6281588141486558
      },
      "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": [
              -0.005672571852555539,
              -2.034407751158992e-10,
              0.005169394245734266
            ],
            "branch_aligned_reduced_polarization": [
              -0.005672571852555541,
              -2.0344076423484125e-10,
              0.00516939424573426
            ],
            "target_residual": 0.8597772586004817,
            "energy_eV": -411.43839979693485,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013328762479314687,
            "step_scale": 0.6667919878786762,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0014938598813918,
              0.999375118381336,
              0.9974938401537071
            ],
            "cell_volume_ratio": 0.9983597094718888,
            "cell_rmsd_from_input_A": 0.031191875905552866
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3333502714261623,
              -0.3309007648699986,
              0.3313338697952712
            ],
            "branch_aligned_reduced_polarization": [
              -0.3333502714261623,
              -0.3309007648699986,
              0.3313338697952712
            ],
            "target_residual": 0.2912300582589713,
            "energy_eV": -404.4238695510758,
            "max_atomic_step_A": 0.06440416053725283,
            "max_log_strain_component": 0.0007022285870502772,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0022601834124014,
              0.9990304922138753,
              0.9962133589428828
            ],
            "cell_volume_ratio": 0.997496964275961,
            "cell_rmsd_from_input_A": 0.0470142839821566
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49525674627813815,
              -0.49741225729189503,
              0.4966562200193574
            ],
            "branch_aligned_reduced_polarization": [
              -0.49525674627813815,
              -0.49741225729189503,
              0.4966562200193574
            ],
            "target_residual": 0.006354190172811407,
            "energy_eV": -394.347953626257,
            "max_atomic_step_A": 0.0017451828103820042,
            "max_log_strain_component": 1.8730692914846156e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5668138621989213,
            "cell_principal_stretches": [
              1.0022781874889846,
              0.9990270538619888,
              0.9961801126883616
            ],
            "cell_volume_ratio": 0.9974781600777258,
            "cell_rmsd_from_input_A": 0.04744694856508634
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000129698190091,
              -0.5000014363927234,
              0.5000116191350493
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000129698190091,
              -0.5000014363927234,
              0.5000116191350493
            ],
            "target_residual": 1.747237043103951e-05,
            "energy_eV": -394.03694402835373
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.747237043103951e-05,
        "parent_symmetrization_rmsd_A": 0.20300312097053982,
        "parent_cell_rmsd_A": 0.04744694856508634,
        "energy_eV": -394.03694402835373,
        "reduced_polarization": [
          -0.5000129698190091,
          -0.5000014363927234,
          0.5000116191350493
        ],
        "cartesian_polarization_e_A2": [
          -0.006408807997643351,
          -0.0030064705568595305,
          0.004713399909222284
        ],
        "ranking_score": 0.7148998028526735
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79,
          80,
          81,
          82,
          83
        ],
        "endpoint_rmsd_A": 0.13244100139345116,
        "minimum_distance_A_by_image": [
          1.4140045249159892,
          1.414117864507655,
          1.4142534646302851,
          1.4144113188815093,
          1.4145914198113085,
          1.4147937589237884,
          1.4150183266791687,
          1.4152651124960332,
          1.415534104753816
        ],
        "minimum_distance_A": 1.4140045249159892,
        "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": [
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243,
          1345.3517973966243
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.92593843145336e-15,
        2.1281349684658943e-15,
        -6.351530105748233e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -411.4383997969348,
          -411.48044708849204,
          -411.51596964218186,
          -411.5451491211004,
          -411.56825424146416,
          -411.58563732253566,
          -411.5976733955394,
          -411.6047162157403,
          -411.6070301282586
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.118268361182815e-05,
            -1.222777506972874e-12,
            4.886170960547802e-05
          ],
          [
            -6.1781859766167e-05,
            -1.107021262885142e-12,
            4.282599363024673e-05
          ],
          [
            -5.254955806314715e-05,
            -9.79228603141552e-13,
            3.670857137267208e-05
          ],
          [
            -4.3486009372025634e-05,
            -8.367358955422078e-13,
            3.054742997221479e-05
          ],
          [
            -3.458507006477946e-05,
            -6.831103978028871e-13,
            2.4372725209179048e-05
          ],
          [
            -2.5819755578055222e-05,
            -5.215395148311845e-13,
            1.8219845564130425e-05
          ],
          [
            -1.7156623185750382e-05,
            -3.523977354482024e-13,
            1.2110382013600853e-05
          ],
          [
            -8.560967165725613e-06,
            -1.7747502214272856e-13,
            6.044046656797519e-06
          ],
          [
            -3.621207047376476e-17,
            1.2791046115216722e-17,
            -6.003539386335591e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.9258960665700116e-15,
            2.1281349684632603e-15,
            -6.351256326420085e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0056725718525565405,
            -2.0344198548016834e-10,
            0.005169394245732595
          ],
          [
            -0.004909352765826602,
            -1.8418278013854206e-10,
            0.00453083706705093
          ],
          [
            -0.004166216324083982,
            -1.6292106552739938e-10,
            0.00388363565571348
          ],
          [
            -0.003441905868579842,
            -1.3921352959300748e-10,
            0.0032318089153102747
          ],
          [
            -0.00273477323402177,
            -1.1365380858663343e-10,
            0.0025785472196213632
          ],
          [
            -0.002040850868059274,
            -8.677214502483821e-11,
            0.0019275945434130692
          ],
          [
            -0.0013559722042031375,
            -5.863087793045452e-11,
            0.0012812351348368
          ],
          [
            -0.0006765782573859291,
            -2.952776911868682e-11,
            0.000639438535017689
          ],
          [
            -3.941291737419306e-15,
            2.1094237467877974e-15,
            -6.106226635438361e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -411.6070301282586,
          -411.60471621574044,
          -411.59767339553935,
          -411.5856373225356,
          -411.56825424146416,
          -411.5451491211003,
          -411.5159696421815,
          -411.48044708849216,
          -411.43839979693473
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.621207047376476e-17,
            1.2791046115216722e-17,
            -6.003539386335591e-18
          ],
          [
            8.560967165689766e-06,
            1.7743994991950943e-13,
            -6.044046656799675e-06
          ],
          [
            1.7156623185731083e-05,
            3.524077207164601e-13,
            -1.2110382013628673e-05
          ],
          [
            2.5819755577998786e-05,
            5.215186159122899e-13,
            -1.821984556411033e-05
          ],
          [
            3.4585070064762906e-05,
            6.831384349507429e-13,
            -2.437272520921753e-05
          ],
          [
            4.348600937197938e-05,
            8.367436526927551e-13,
            -3.054742997223031e-05
          ],
          [
            5.254955806308491e-05,
            9.792230741087152e-13,
            -3.670857137267872e-05
          ],
          [
            6.178185976611142e-05,
            1.1070026333453969e-12,
            -4.2825993630257355e-05
          ],
          [
            7.118268361176348e-05,
            1.22273366669385e-12,
            -4.886170960548381e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.005672571852548711,
          2.0344622245492334e-10,
          -0.005169394245733853
        ],
        "actual_opposite_endpoint_branch_residual": 1.1612695698118726e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.92593843145336e-15,
            2.1281349684658943e-15,
            -6.351530105748233e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.005672571852556562,
            -2.0344196618498641e-10,
            0.005169394245732583
          ],
          [
            -0.004909352765826582,
            -1.841827978071698e-10,
            0.004530837067050917
          ],
          [
            -0.004166216324083966,
            -1.6292104755907528e-10,
            0.003883635655713533
          ],
          [
            -0.00344190586857986,
            -1.3921354849589859e-10,
            0.0032318089153102873
          ],
          [
            -0.002734773234021746,
            -1.1365381000053884e-10,
            0.0025785472196213598
          ],
          [
            -0.002040850868059271,
            -8.677214271228318e-11,
            0.0019275945434130439
          ],
          [
            -0.0013559722042031206,
            -5.863085293104709e-11,
            0.0012812351348368087
          ],
          [
            -0.0006765782573859386,
            -2.9527749118337085e-11,
            0.0006394385350177246
          ],
          [
            -3.9258960665700116e-15,
            2.1281349684632603e-15,
            -6.351256326420085e-16
          ],
          [
            0.00067657825738218,
            2.952191390955259e-11,
            -0.0006394385350179528
          ],
          [
            0.0013559722042001982,
            5.863251424931279e-11,
            -0.001281235134839752
          ],
          [
            0.002040850868054145,
            8.676866561434278e-11,
            -0.001927594543410918
          ],
          [
            0.0027347732340187473,
            1.1365847473509068e-10,
            -0.0025785472196254307
          ],
          [
            0.003441905868574581,
            1.392148391067827e-10,
            -0.0032318089153119288
          ],
          [
            0.004166216324077342,
            1.6292012765557279e-10,
            -0.0038836356557142354
          ],
          [
            0.004909352765820509,
            1.841796982815625e-10,
            -0.004530837067052042
          ],
          [
            0.005672571852549717,
            2.0343467217400576e-10,
            -0.005169394245733195
          ]
        ],
        "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": [
          [
            -0.0056725718525565405,
            -2.0344198548016834e-10,
            0.005169394245732595
          ],
          [
            -0.004909352765826602,
            -1.8418278013854206e-10,
            0.00453083706705093
          ],
          [
            -0.004166216324083982,
            -1.6292106552739938e-10,
            0.00388363565571348
          ],
          [
            -0.003441905868579842,
            -1.3921352959300748e-10,
            0.0032318089153102747
          ],
          [
            -0.00273477323402177,
            -1.1365380858663343e-10,
            0.0025785472196213632
          ],
          [
            -0.002040850868059274,
            -8.677214502483821e-11,
            0.0019275945434130692
          ],
          [
            -0.0013559722042031375,
            -5.863087793045452e-11,
            0.0012812351348368
          ],
          [
            -0.0006765782573859291,
            -2.952776911868682e-11,
            0.000639438535017689
          ],
          [
            -3.941291737419306e-15,
            2.1094237467877974e-15,
            -6.106226635438361e-16
          ],
          [
            0.0006765782573822099,
            2.952194044780754e-11,
            -0.0006394385350179665
          ],
          [
            0.0013559722042002509,
            5.863254326499145e-11,
            -0.0012812351348397422
          ],
          [
            0.002040850868054167,
            8.676870333346187e-11,
            -0.0019275945434109043
          ],
          [
            0.002734773234018717,
            1.1365852703448809e-10,
            -0.0025785472196254156
          ],
          [
            0.003441905868574624,
            1.3921486186063703e-10,
            -0.00323180891531194
          ],
          [
            0.004166216324077321,
            1.6292012183782845e-10,
            -0.003883635655714257
          ],
          [
            0.004909352765820496,
            1.841796715140731e-10,
            -0.00453083706705204
          ],
          [
            0.005672571852549768,
            2.0343471351935705e-10,
            -0.005169394245733205
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9348236734198307e-15,
        "parent_symmetrization_rmsd_A": 0.13244100139345116,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -411.60703012825843,
        "reduced_polarization": [
          -2.910593165830273e-15,
          3.5011252707019557e-16,
          1.3805301690329062e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.873343464027111e-17,
          2.1043333931485576e-18,
          1.3048930109475124e-18
        ],
        "ranking_score": 0.13244100139345702
      }
    }
  ],
  "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": 51,
      "full_response": 18,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 43,
      "energy_polarization": 33
    },
    "elapsed_seconds": 1912.7412483500084
  }
}
