{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 108,
  "input_formula": "Al12F76Pb20",
  "input_spacegroup": "I4cm",
  "input_pointgroup": "4mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -557.4843152403857,
  "input_cartesian_polarization_e_A2": [
    -1.8909088688594657e-18,
    1.1042806589829703e-18,
    -0.008715152256115058
  ],
  "input_reduced_polarization": [
    -2.068750813112233e-16,
    1.2081394025895371e-16,
    -1.8055935422802452
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -2.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -2.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -1.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -2.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -1.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "I4/mcm",
      "spacegroup_number": 140,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.6335010202625804e-15,
      "parent_symmetrization_rmsd_A": 0.5114800362136972,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -548.7929786257332,
      "reduced_polarization": [
        8.249016929321599e-16,
        1.0474311381815038e-15,
        3.3800524954524994e-15
      ],
      "cartesian_polarization_e_A2": [
        7.539883088944973e-18,
        9.573878188486877e-18,
        1.631467517009876e-17
      ],
      "ranking_score": 0.5114800362137044
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P4/mcc",
      "spacegroup_number": 124,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.850812654494097e-15,
      "parent_symmetrization_rmsd_A": 0.8581718344490966,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -511.61874936897675,
      "reduced_polarization": [
        9.227145602090313e-16,
        -5.819848227296949e-16,
        -4.7265500013742165e-15
      ],
      "cartesian_polarization_e_A2": [
        8.43392608846971e-18,
        -5.3195399652103056e-18,
        -2.281388471078374e-17
      ],
      "ranking_score": 0.8581718344491063
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P4_2/nbc",
      "spacegroup_number": 133,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.793306367709484e-15,
      "parent_symmetrization_rmsd_A": 0.8581718344490968,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -511.36572321814424,
      "reduced_polarization": [
        -3.9680327676496866e-16,
        -1.1524174695095432e-15,
        -7.697408997610754e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.626917415435816e-18,
        -1.0533489098408672e-17,
        -3.7153484336817387e-17
      ],
      "ranking_score": 0.8581718344491124
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "I4cm",
      "spacegroup_number": 108,
      "pointgroup": "4mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -2.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00021132230501819116,
      "parent_symmetrization_rmsd_A": 0.009037603160923844,
      "parent_cell_rmsd_A": 0.040438397037314264,
      "energy_eV": -557.6393392994319,
      "reduced_polarization": [
        1.620224600583302e-15,
        -4.7043131397353036e-15,
        -1.9997886776949818
      ],
      "cartesian_polarization_e_A2": [
        2.4039964969114042e-17,
        -5.957616042895792e-17,
        -0.009695935569554424
      ],
      "ranking_score": 0.5195698470302887
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "I4/mcm",
      "spacegroup_number": 140,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -2.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8765274984085266e-15,
      "parent_symmetrization_rmsd_A": 0.5114806741744751,
      "parent_cell_rmsd_A": 0.040438397037314264,
      "energy_eV": -548.6763925048795,
      "reduced_polarization": [
        1.0947428936093599e-15,
        -7.402407800357208e-16,
        1.3596658816776739e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0096282819662648e-17,
        -6.826881739255567e-18,
        6.592312943817391e-18
      ],
      "ranking_score": 0.5215902734338074
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "I4/mcm",
      "spacegroup_number": 140,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -2.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0142685956786748e-14,
      "parent_symmetrization_rmsd_A": 0.9285245996430099,
      "parent_cell_rmsd_A": 0.040438397037314264,
      "energy_eV": -490.441557312097,
      "reduced_polarization": [
        -2.4266961731876336e-15,
        -4.254307649775039e-15,
        -8.999390699277154e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.23802419955587e-17,
        -3.923541635469386e-17,
        -4.3633366544516305e-17
      ],
      "ranking_score": 0.9386341989023588
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "I4cm",
      "spacegroup_number": 108,
      "pointgroup": "4mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006065516440194596,
      "parent_symmetrization_rmsd_A": 0.01396448093693115,
      "parent_cell_rmsd_A": 0.06412413964226996,
      "energy_eV": -556.9781406320834,
      "reduced_polarization": [
        -5.2095222426561245e-15,
        6.8235508691914626e-15,
        -1.5006065516440195
      ],
      "cartesian_polarization_e_A2": [
        -5.772302760201931e-17,
        8.039966621306867e-17,
        -0.007192097540203019
      ],
      "ranking_score": 0.5312086191355375
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -2.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0001599973615282499,
      "parent_symmetrization_rmsd_A": 0.06279093952661391,
      "parent_cell_rmsd_A": 0.24281301236707198,
      "energy_eV": -556.4166935722682,
      "reduced_polarization": [
        -0.49999822065442967,
        8.103228818952904e-16,
        -1.9998400125329117
      ],
      "cartesian_polarization_e_A2": [
        -0.0043237089887533916,
        -3.421106801350559e-16,
        -0.009561644896617084
      ],
      "ranking_score": 0.6238141873414385
    },
    {
      "candidate_id": "bec_projection_03",
      "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,
        -1.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0001959265426839676,
      "parent_symmetrization_rmsd_A": 0.06446387268934489,
      "parent_cell_rmsd_A": 0.26574975331212686,
      "energy_eV": -555.8048598011861,
      "reduced_polarization": [
        -0.49984375020538885,
        5.915461723029687e-16,
        -1.4998817916592957
      ],
      "cartesian_polarization_e_A2": [
        -0.004283774590809981,
        -1.9859195871540794e-16,
        -0.007050088538224232
      ],
      "ranking_score": 0.6312931641027446
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -2.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0005813853602621663,
      "parent_symmetrization_rmsd_A": 0.08944286492825408,
      "parent_cell_rmsd_A": 0.34700587161967755,
      "energy_eV": -555.0556074151033,
      "reduced_polarization": [
        -0.4998846739037558,
        0.49988467390418284,
        -1.999441959929507
      ],
      "cartesian_polarization_e_A2": [
        -0.0043169291801851755,
        0.004316929180103832,
        -0.00942051270655456
      ],
      "ranking_score": 0.6773571035536978
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -1.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0007595677485544289,
      "parent_symmetrization_rmsd_A": 0.09136308976375912,
      "parent_cell_rmsd_A": 0.37855377954934766,
      "energy_eV": -554.4847410463738,
      "reduced_polarization": [
        -0.4994747651644537,
        0.49947476516223516,
        -1.499841255244588
      ],
      "cartesian_polarization_e_A2": [
        -0.004272325835801449,
        0.004272325836157051,
        -0.0069061018816652915
      ],
      "ranking_score": 0.6875206701482048
    }
  ],
  "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,
        -2.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.19440645771975484,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.008720047211397172,
            "max_log_strain_component": 0.006704301277020521,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              0.9977567742992628,
              0.9977567742556411,
              0.9933181224110812
            ],
            "cell_volume_ratio": 0.988866647323372,
            "cell_rmsd_from_input_A": 0.040438397037314264
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.620224600583302e-15,
              -4.7043131397353036e-15,
              -1.9997886776949818
            ],
            "branch_aligned_reduced_polarization": [
              1.620224600583302e-15,
              -4.7043131397353036e-15,
              -1.9997886776949818
            ],
            "target_residual": 0.00021132230501819116,
            "energy_eV": -557.6393392994319
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "I4/mcm",
        "spacegroup_number": 140,
        "pointgroup": "4/mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.6335010202625804e-15,
        "parent_symmetrization_rmsd_A": 0.5114800362136972,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -548.7929786257332,
        "reduced_polarization": [
          8.249016929321599e-16,
          1.0474311381815038e-15,
          3.3800524954524994e-15
        ],
        "cartesian_polarization_e_A2": [
          7.539883088944973e-18,
          9.573878188486877e-18,
          1.631467517009876e-17
        ],
        "ranking_score": 0.5114800362137044
      },
      "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": [
          -557.4843152403857,
          -556.742787503086,
          -555.5049847982443,
          -554.0004023722279,
          -552.4404616305192,
          -550.9959074608188,
          -549.8296673036109,
          -549.0644044404953,
          -548.7929786257332
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.480525027040661e-19,
            1.3981350928064194e-18,
            -0.008715152256115051
          ],
          [
            8.488786293651415e-18,
            2.8105095020663963e-18,
            -0.007444893658026772
          ],
          [
            1.5249851184954807e-17,
            2.057527048750135e-17,
            -0.006239645941958496
          ],
          [
            -2.8261742788129673e-17,
            -2.3344399455337875e-17,
            -0.005099800558035713
          ],
          [
            1.4571363310381065e-17,
            8.492782853329177e-18,
            -0.004018679395497203
          ],
          [
            1.921037139185266e-17,
            3.7346047009431546e-17,
            -0.00298554686410065
          ],
          [
            -1.0681953917354182e-20,
            -7.93527952747329e-18,
            -0.0019902054721716617
          ],
          [
            -9.440196917048122e-18,
            -2.1092556345360526e-17,
            -0.0009978058644372625
          ],
          [
            5.248976816667812e-18,
            -1.2159242240935996e-18,
            4.632035325663789e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.091978906851134e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084874e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784555575e-18,
            -8.681600813811238e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300927e-16,
            -1.3302831610249565e-16,
            9.59658859174163e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.0919789068511335e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084878e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784554966e-18,
            -8.681600813811237e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300926e-16,
            -1.3302831610249585e-16,
            9.603429163007604e-15
          ]
        ],
        "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": [
          [
            0.0,
            1.1102230246251565e-16,
            0.19440645771975618
          ],
          [
            8.881784197001252e-16,
            3.3306690738754696e-16,
            0.4575769284507585
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-15,
            -0.29272146806274435
          ],
          [
            -3.1086244689504383e-15,
            -2.55351295663786e-15,
            -0.05656983193213705
          ],
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            0.16741539886315515
          ],
          [
            2.1094237467877974e-15,
            4.107825191113079e-15,
            0.38145840949448107
          ],
          [
            0.0,
            -8.881784197001252e-16,
            -0.41232809740559007
          ],
          [
            -1.0547118733938987e-15,
            -2.3314683517128287e-15,
            -0.20672407920505909
          ],
          [
            5.551115123125783e-16,
            -1.1102230246251565e-16,
            9.547918011776346e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -548.7929786257332,
          -549.0644044404954,
          -549.8296673036111,
          -550.9959074608194,
          -552.4404616305192,
          -554.0004023722279,
          -555.5049847982443,
          -556.7427875030858,
          -557.4843152403857
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.797608404647888e-18,
            -6.130474067623359e-19,
            2.075194114261357e-17
          ],
          [
            -1.957555313449737e-17,
            1.9171720006970157e-17,
            0.0009978058644373152
          ],
          [
            4.009001545095797e-18,
            -6.453442738522547e-18,
            0.0019902054721717454
          ],
          [
            -1.2248129949445466e-17,
            -6.53837267649174e-18,
            0.002985546864100588
          ],
          [
            2.553503781115338e-18,
            6.784797589875974e-18,
            0.004018679395497241
          ],
          [
            2.7331531848096374e-17,
            -1.537412584991105e-18,
            0.00509980055803572
          ],
          [
            1.3090686170871082e-17,
            1.6850042256927658e-17,
            0.006239645941958455
          ],
          [
            4.005652846958839e-17,
            3.9556968895438346e-17,
            0.007444893658026755
          ],
          [
            4.199262298964223e-17,
            2.806617312769088e-17,
            0.008715152256115057
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.1547774217886213e-16,
            -6.707051524809288e-17,
            4.299359301564922e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787038e-16,
            -7.060395734853355e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732654e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.1547774217886213e-16,
            -6.707051524809288e-17,
            4.299359301564922e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787039e-16,
            -7.060395734853354e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732651e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.1756679180975046e-15,
          -4.19019747335369e-16,
          1.8055935422802625
        ],
        "actual_opposite_endpoint_branch_residual": 1.842303172473188e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.091978906851134e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084874e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784555575e-18,
            -8.681600813811238e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300927e-16,
            -1.3302831610249565e-16,
            9.59658859174163e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787038e-16,
            -7.060395734853355e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732654e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.0919789068511335e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084878e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784554966e-18,
            -8.681600813811237e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300926e-16,
            -1.3302831610249585e-16,
            9.603429163007604e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787039e-16,
            -7.060395734853354e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732651e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "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": [
          [
            0.0,
            1.1102230246251565e-16,
            0.19440645771975618
          ],
          [
            8.881784197001252e-16,
            3.3306690738754696e-16,
            0.4575769284507585
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-15,
            -0.29272146806274435
          ],
          [
            -3.1086244689504383e-15,
            -2.55351295663786e-15,
            -0.05656983193213705
          ],
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            0.16741539886315515
          ],
          [
            2.1094237467877974e-15,
            4.107825191113079e-15,
            0.38145840949448107
          ],
          [
            0.0,
            -8.881784197001252e-16,
            -0.41232809740559007
          ],
          [
            -1.0547118733938987e-15,
            -2.3314683517128287e-15,
            -0.20672407920505909
          ],
          [
            5.551115123125783e-16,
            -1.1102230246251565e-16,
            9.547918011776346e-15
          ],
          [
            -2.1649348980190553e-15,
            2.1094237467877974e-15,
            0.20672407920506997
          ],
          [
            4.440892098500626e-16,
            -7.216449660063518e-16,
            0.4123280974056075
          ],
          [
            -1.3322676295501878e-15,
            -7.216449660063518e-16,
            -0.38145840949449394
          ],
          [
            3.3306690738754696e-16,
            7.771561172376096e-16,
            -0.1674153988631475
          ],
          [
            2.9976021664879227e-15,
            -1.6653345369377348e-16,
            0.0565698319321386
          ],
          [
            1.4432899320127035e-15,
            1.887379141862766e-15,
            0.2927214680627359
          ],
          [
            4.3298697960381105e-15,
            4.3298697960381105e-15,
            -0.45757692845076203
          ],
          [
            4.551914400963142e-15,
            3.1086244689504383e-15,
            -0.1944064577197553
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.30559354228024516,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.013707312747929617,
            "max_log_strain_component": 0.01053869917588896,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0105944268597673,
              1.0035363954376357,
              1.0035363953686678
            ],
            "cell_volume_ratio": 1.0177547884182923,
            "cell_rmsd_from_input_A": 0.06412413964226996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.2095222426561245e-15,
              6.8235508691914626e-15,
              -1.5006065516440195
            ],
            "branch_aligned_reduced_polarization": [
              -5.2095222426561245e-15,
              6.8235508691914626e-15,
              -1.5006065516440195
            ],
            "target_residual": 0.0006065516440194596,
            "energy_eV": -556.9781406320834
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "I4cm",
        "spacegroup_number": 108,
        "pointgroup": "4mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -1.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006065516440194596,
        "parent_symmetrization_rmsd_A": 0.01396448093693115,
        "parent_cell_rmsd_A": 0.06412413964226996,
        "energy_eV": -556.9781406320834,
        "reduced_polarization": [
          -5.2095222426561245e-15,
          6.8235508691914626e-15,
          -1.5006065516440195
        ],
        "cartesian_polarization_e_A2": [
          -5.772302760201931e-17,
          8.039966621306867e-17,
          -0.007192097540203019
        ],
        "ranking_score": 0.5312086191355375
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -2.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.5364642306837825,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.03797875718094082,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6795468118178817,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0171619049984688,
              0.9984750746572916,
              0.9771664443369354
            ],
            "cell_volume_ratio": 0.9924208030918589,
            "cell_rmsd_from_input_A": 0.16530581812316458
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3401804477480994,
              4.659240533607301e-15,
              -1.9432484296082408
            ],
            "branch_aligned_reduced_polarization": [
              -0.3401804477480994,
              4.659240533607301e-15,
              -1.9432484296082408
            ],
            "target_residual": 0.16959666866990275,
            "energy_eV": -557.0541645794859,
            "max_atomic_step_A": 0.01764746421057898,
            "max_log_strain_component": 0.009412312954739486,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0257405234475143,
              0.9979609964062234,
              0.9670073134839845
            ],
            "cell_volume_ratio": 0.9898761031252252,
            "cell_rmsd_from_input_A": 0.2419360460695148
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49821070510420556,
              -6.727570687372116e-16,
              -1.9955381469073674
            ],
            "branch_aligned_reduced_polarization": [
              -0.49821070510420556,
              -6.727570687372116e-16,
              -1.9955381469073674
            ],
            "target_residual": 0.004807255895451268,
            "energy_eV": -556.4244193864342,
            "max_atomic_step_A": 0.0002566681852245696,
            "max_log_strain_component": 0.000147878148822728,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0257461118187188,
              0.9979115637620914,
              0.9668111651773229
            ],
            "cell_volume_ratio": 0.9896316854922922,
            "cell_rmsd_from_input_A": 0.24281301236707198
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999822065442967,
              8.103228818952904e-16,
              -1.9998400125329117
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999822065442967,
              8.103228818952904e-16,
              -1.9998400125329117
            ],
            "target_residual": 0.0001599973615282499,
            "energy_eV": -556.4166935722682
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -2.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0001599973615282499,
        "parent_symmetrization_rmsd_A": 0.06279093952661391,
        "parent_cell_rmsd_A": 0.24281301236707198,
        "energy_eV": -556.4166935722682,
        "reduced_polarization": [
          -0.49999822065442967,
          8.103228818952904e-16,
          -1.9998400125329117
        ],
        "cartesian_polarization_e_A2": [
          -0.0043237089887533916,
          -3.421106801350559e-16,
          -0.009561644896617084
        ],
        "ranking_score": 0.6238141873414385
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.5859926732335378,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.0385881812329282,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6795468118179381,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.025234627167981,
              1.0024017866784083,
              0.984756334482848
            ],
            "cell_volume_ratio": 1.0120311523808392,
            "cell_rmsd_from_input_A": 0.172576856283373
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.33421187132642344,
              1.1841234393395021e-14,
              -1.606509728550015
            ],
            "branch_aligned_reduced_polarization": [
              -0.33421187132642344,
              1.1841234393395021e-14,
              -1.606509728550015
            ],
            "target_residual": 0.19705335796398965,
            "energy_eV": -556.6760967521011,
            "max_atomic_step_A": 0.019670566663460027,
            "max_log_strain_component": 0.010071946302133476,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0386640917772705,
              1.0038336066384872,
              0.9775690337018867
            ],
            "cell_volume_ratio": 1.0192583658123429,
            "cell_rmsd_from_input_A": 0.2628806275471969
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4944416798295478,
              4.988077999880866e-15,
              -1.5003371595589865
            ],
            "branch_aligned_reduced_polarization": [
              -0.4944416798295478,
              4.988077999880866e-15,
              -1.5003371595589865
            ],
            "target_residual": 0.0055685365838316885,
            "energy_eV": -555.8321050151795,
            "max_atomic_step_A": 0.0006465029435241405,
            "max_log_strain_component": 0.0003413136842303009,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0390455403396732,
              1.0038471414494388,
              0.9772626652480847
            ],
            "cell_volume_ratio": 1.0193268800300468,
            "cell_rmsd_from_input_A": 0.26574975331212686
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49984375020538885,
              5.915461723029687e-16,
              -1.4998817916592957
            ],
            "branch_aligned_reduced_polarization": [
              -0.49984375020538885,
              5.915461723029687e-16,
              -1.4998817916592957
            ],
            "target_residual": 0.0001959265426839676,
            "energy_eV": -555.8048598011861
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "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,
          -1.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0001959265426839676,
        "parent_symmetrization_rmsd_A": 0.06446387268934489,
        "parent_cell_rmsd_A": 0.26574975331212686,
        "energy_eV": -555.8048598011861,
        "reduced_polarization": [
          -0.49984375020538885,
          5.915461723029687e-16,
          -1.4998817916592957
        ],
        "cartesian_polarization_e_A2": [
          -0.004283774590809981,
          -1.9859195871540794e-16,
          -0.007050088538224232
        ],
        "ranking_score": 0.6312931641027446
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        -2.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              1.1102230246251565e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.7333443057685404,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.05624219592516058,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6795468118179909,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0256061699513204,
              0.9984750746721108,
              0.9691210048538903
            ],
            "cell_volume_ratio": 0.9924208030918461,
            "cell_rmsd_from_input_A": 0.23230394145004055
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3382175542500855,
              0.3382175542671476,
              -1.9495090790794862
            ],
            "branch_aligned_reduced_polarization": [
              -0.3382175542500855,
              0.3382175542671476,
              -1.9495090790794862
            ],
            "target_residual": 0.2342999201782385,
            "energy_eV": -556.4852679340552,
            "max_atomic_step_A": 0.02699326485263638,
            "max_log_strain_component": 0.009684492258669566,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0391437839849482,
              0.9981840468220472,
              0.955385027882005
            ],
            "cell_volume_ratio": 0.9909795666579041,
            "cell_rmsd_from_input_A": 0.3438480564041601
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49537535773891544,
              0.49537535773194125,
              -1.9930560392263745
            ],
            "branch_aligned_reduced_polarization": [
              -0.49537535773891544,
              0.49537535773194125,
              -1.9930560392263745
            ],
            "target_residual": 0.00953903681595653,
            "energy_eV": -555.104762572835,
            "max_atomic_step_A": 0.0008231806064207073,
            "max_log_strain_component": 0.00027594741822237786,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0394095404422876,
              0.9981153518902762,
              0.9548788149656507
            ],
            "cell_volume_ratio": 0.990639617862989,
            "cell_rmsd_from_input_A": 0.34700587161967755
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4998846739037558,
              0.49988467390418284,
              -1.999441959929507
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998846739037558,
              0.49988467390418284,
              -1.999441959929507
            ],
            "target_residual": 0.0005813853602621663,
            "energy_eV": -555.0556074151033
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -2.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0005813853602621663,
        "parent_symmetrization_rmsd_A": 0.08944286492825408,
        "parent_cell_rmsd_A": 0.34700587161967755,
        "energy_eV": -555.0556074151033,
        "reduced_polarization": [
          -0.4998846739037558,
          0.49988467390418284,
          -1.999441959929507
        ],
        "cartesian_polarization_e_A2": [
          -0.0043169291801851755,
          0.004316929180103832,
          -0.00942051270655456
        ],
        "ranking_score": 0.6773571035536978
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.068750813112233e-16,
              1.2081394025895371e-16,
              -1.8055935422802452
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              1.1102230246251565e-16,
              -1.8055935422802452
            ],
            "target_residual": 0.7703164369811848,
            "energy_eV": -557.4843152403857,
            "max_atomic_step_A": 0.05673361549843874,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6795468118180473,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0337206359745021,
              1.0024017866549808,
              0.9766722829390432
            ],
            "cell_volume_ratio": 1.0120311523808296,
            "cell_rmsd_from_input_A": 0.24030246182624299
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3321983532742915,
              0.3321983532461504,
              -1.615668684040606
            ],
            "branch_aligned_reduced_polarization": [
              -0.3321983532742915,
              0.3321983532461504,
              -1.615668684040606
            ],
            "target_residual": 0.26399626846765994,
            "energy_eV": -556.1607503147715,
            "max_atomic_step_A": 0.02901066755049511,
            "max_log_strain_component": 0.010382000839908787,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.052735973881268,
              1.0041390031195272,
              0.9656718556066836
            ],
            "cell_volume_ratio": 1.0208052015912736,
            "cell_rmsd_from_input_A": 0.3711226740531722
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4908394292731787,
              0.49083942923940493,
              -1.5036603280322447
            ],
            "branch_aligned_reduced_polarization": [
              -0.4908394292731787,
              0.49083942923940493,
              -1.5036603280322447
            ],
            "target_residual": 0.013462173450249443,
            "energy_eV": -554.5871839470556,
            "max_atomic_step_A": 0.0016328675586922748,
            "max_log_strain_component": 0.0005910886704532652,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.522014271988548,
            "cell_principal_stretches": [
              1.0537850499088632,
              1.0042178576090102,
              0.9650124561366904
            ],
            "cell_volume_ratio": 1.0212049048724912,
            "cell_rmsd_from_input_A": 0.37855377954934766
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4994747651644537,
              0.49947476516223516,
              -1.499841255244588
            ],
            "branch_aligned_reduced_polarization": [
              -0.4994747651644537,
              0.49947476516223516,
              -1.499841255244588
            ],
            "target_residual": 0.0007595677485544289,
            "energy_eV": -554.4847410463738
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -1.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0007595677485544289,
        "parent_symmetrization_rmsd_A": 0.09136308976375912,
        "parent_cell_rmsd_A": 0.37855377954934766,
        "energy_eV": -554.4847410463738,
        "reduced_polarization": [
          -0.4994747651644537,
          0.49947476516223516,
          -1.499841255244588
        ],
        "cartesian_polarization_e_A2": [
          -0.004272325835801449,
          0.004272325836157051,
          -0.0069061018816652915
        ],
        "ranking_score": 0.6875206701482048
      },
      "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,
          84,
          85,
          86,
          87,
          88,
          89,
          90,
          91,
          92,
          93,
          94,
          95,
          96,
          97,
          98,
          99,
          100,
          101,
          102,
          103,
          104,
          105,
          106,
          107
        ],
        "endpoint_rmsd_A": 0.5114800362136972,
        "minimum_distance_A_by_image": [
          1.8020332583881797,
          1.7811111855627109,
          1.7610592728413363,
          1.7421142528269655,
          1.7264591598232328,
          1.7141841337395818,
          1.7053621642876322,
          1.700047008642808,
          1.6982715934146737
        ],
        "minimum_distance_A": 1.6982715934146737,
        "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": [
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706,
          1574.744463182706
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.742648541300927e-16,
        -1.3302831610249565e-16,
        9.59658859174163e-15
      ],
      "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": [
          -557.4843152403857,
          -556.742787503086,
          -555.5049847982443,
          -554.0004023722279,
          -552.4404616305192,
          -550.9959074608188,
          -549.8296673036109,
          -549.0644044404953,
          -548.7929786257332
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.480525027040661e-19,
            1.3981350928064194e-18,
            -0.008715152256115051
          ],
          [
            8.488786293651415e-18,
            2.8105095020663963e-18,
            -0.007444893658026772
          ],
          [
            1.5249851184954807e-17,
            2.057527048750135e-17,
            -0.006239645941958496
          ],
          [
            -2.8261742788129673e-17,
            -2.3344399455337875e-17,
            -0.005099800558035713
          ],
          [
            1.4571363310381065e-17,
            8.492782853329177e-18,
            -0.004018679395497203
          ],
          [
            1.921037139185266e-17,
            3.7346047009431546e-17,
            -0.00298554686410065
          ],
          [
            -1.0681953917354182e-20,
            -7.93527952747329e-18,
            -0.0019902054721716617
          ],
          [
            -9.440196917048122e-18,
            -2.1092556345360526e-17,
            -0.0009978058644372625
          ],
          [
            5.248976816667812e-18,
            -1.2159242240935996e-18,
            4.632035325663789e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.091978906851134e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084874e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784555575e-18,
            -8.681600813811238e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300927e-16,
            -1.3302831610249565e-16,
            9.59658859174163e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.0919789068511335e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084878e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784554966e-18,
            -8.681600813811237e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300926e-16,
            -1.3302831610249585e-16,
            9.603429163007604e-15
          ]
        ],
        "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": [
          [
            0.0,
            1.1102230246251565e-16,
            0.19440645771975618
          ],
          [
            8.881784197001252e-16,
            3.3306690738754696e-16,
            0.4575769284507585
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-15,
            -0.29272146806274435
          ],
          [
            -3.1086244689504383e-15,
            -2.55351295663786e-15,
            -0.05656983193213705
          ],
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            0.16741539886315515
          ],
          [
            2.1094237467877974e-15,
            4.107825191113079e-15,
            0.38145840949448107
          ],
          [
            0.0,
            -8.881784197001252e-16,
            -0.41232809740559007
          ],
          [
            -1.0547118733938987e-15,
            -2.3314683517128287e-15,
            -0.20672407920505909
          ],
          [
            5.551115123125783e-16,
            -1.1102230246251565e-16,
            9.547918011776346e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -548.7929786257332,
          -549.0644044404954,
          -549.8296673036111,
          -550.9959074608194,
          -552.4404616305192,
          -554.0004023722279,
          -555.5049847982443,
          -556.7427875030858,
          -557.4843152403857
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.797608404647888e-18,
            -6.130474067623359e-19,
            2.075194114261357e-17
          ],
          [
            -1.957555313449737e-17,
            1.9171720006970157e-17,
            0.0009978058644373152
          ],
          [
            4.009001545095797e-18,
            -6.453442738522547e-18,
            0.0019902054721717454
          ],
          [
            -1.2248129949445466e-17,
            -6.53837267649174e-18,
            0.002985546864100588
          ],
          [
            2.553503781115338e-18,
            6.784797589875974e-18,
            0.004018679395497241
          ],
          [
            2.7331531848096374e-17,
            -1.537412584991105e-18,
            0.00509980055803572
          ],
          [
            1.3090686170871082e-17,
            1.6850042256927658e-17,
            0.006239645941958455
          ],
          [
            4.005652846958839e-17,
            3.9556968895438346e-17,
            0.007444893658026755
          ],
          [
            4.199262298964223e-17,
            2.806617312769088e-17,
            0.008715152256115057
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.1547774217886213e-16,
            -6.707051524809288e-17,
            4.299359301564922e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787038e-16,
            -7.060395734853355e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732654e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.1547774217886213e-16,
            -6.707051524809288e-17,
            4.299359301564922e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787039e-16,
            -7.060395734853354e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732651e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.1756679180975046e-15,
          -4.19019747335369e-16,
          1.8055935422802625
        ],
        "actual_opposite_endpoint_branch_residual": 1.842303172473188e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.091978906851134e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084874e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784555575e-18,
            -8.681600813811238e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300927e-16,
            -1.3302831610249565e-16,
            9.59658859174163e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787038e-16,
            -7.060395734853355e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732654e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7138209837319222e-17,
            1.529631151303777e-16,
            -1.8055935422802438
          ],
          [
            9.287165466583101e-16,
            3.07484084157185e-16,
            -1.5424230715492415
          ],
          [
            1.6684115537384206e-15,
            2.2510396059804e-15,
            -1.2927214680627443
          ],
          [
            -3.0919789068511335e-15,
            -2.553996448489673e-15,
            -1.056569831932137
          ],
          [
            1.5941815173084878e-15,
            9.291537906852e-16,
            -0.8325846011368448
          ],
          [
            2.101712678573131e-15,
            4.085848154273542e-15,
            -0.6185415905055189
          ],
          [
            -1.1686602784554966e-18,
            -8.681600813811237e-16,
            -0.41232809740559007
          ],
          [
            -1.0328057247868536e-15,
            -2.307633319018675e-15,
            -0.20672407920505909
          ],
          [
            5.742648541300926e-16,
            -1.3302831610249585e-16,
            9.603429163007604e-15
          ],
          [
            -2.1416654250788715e-15,
            2.097484019793196e-15,
            0.20672407920507
          ],
          [
            4.386052306787039e-16,
            -7.060395734853354e-16,
            0.4123280974056075
          ],
          [
            -1.3400079300121349e-15,
            -7.153313421752416e-16,
            0.6185415905055061
          ],
          [
            2.793663465470859e-16,
            7.422914854338765e-16,
            0.8325846011368525
          ],
          [
            2.9902090822841518e-15,
            -1.6820078363732651e-16,
            1.0565698319321386
          ],
          [
            1.4321878809802828e-15,
            1.8434806242682708e-15,
            1.292721468062736
          ],
          [
            4.382388660110148e-15,
            4.327734292983283e-15,
            1.5424230715492382
          ],
          [
            4.594207282286233e-15,
            3.0705825878261528e-15,
            1.8055935422802447
          ]
        ],
        "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": [
          [
            0.0,
            1.1102230246251565e-16,
            0.19440645771975618
          ],
          [
            8.881784197001252e-16,
            3.3306690738754696e-16,
            0.4575769284507585
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-15,
            -0.29272146806274435
          ],
          [
            -3.1086244689504383e-15,
            -2.55351295663786e-15,
            -0.05656983193213705
          ],
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            0.16741539886315515
          ],
          [
            2.1094237467877974e-15,
            4.107825191113079e-15,
            0.38145840949448107
          ],
          [
            0.0,
            -8.881784197001252e-16,
            -0.41232809740559007
          ],
          [
            -1.0547118733938987e-15,
            -2.3314683517128287e-15,
            -0.20672407920505909
          ],
          [
            5.551115123125783e-16,
            -1.1102230246251565e-16,
            9.547918011776346e-15
          ],
          [
            -2.1649348980190553e-15,
            2.1094237467877974e-15,
            0.20672407920506997
          ],
          [
            4.440892098500626e-16,
            -7.216449660063518e-16,
            0.4123280974056075
          ],
          [
            -1.3322676295501878e-15,
            -7.216449660063518e-16,
            -0.38145840949449394
          ],
          [
            3.3306690738754696e-16,
            7.771561172376096e-16,
            -0.1674153988631475
          ],
          [
            2.9976021664879227e-15,
            -1.6653345369377348e-16,
            0.0565698319321386
          ],
          [
            1.4432899320127035e-15,
            1.887379141862766e-15,
            0.2927214680627359
          ],
          [
            4.3298697960381105e-15,
            4.3298697960381105e-15,
            -0.45757692845076203
          ],
          [
            4.551914400963142e-15,
            3.1086244689504383e-15,
            -0.1944064577197553
          ]
        ]
      },
      "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": "I4/mcm",
        "spacegroup_number": 140,
        "pointgroup": "4/mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.6335010202625804e-15,
        "parent_symmetrization_rmsd_A": 0.5114800362136972,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -548.7929786257332,
        "reduced_polarization": [
          8.249016929321599e-16,
          1.0474311381815038e-15,
          3.3800524954524994e-15
        ],
        "cartesian_polarization_e_A2": [
          7.539883088944973e-18,
          9.573878188486877e-18,
          1.631467517009876e-17
        ],
        "ranking_score": 0.5114800362137044
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 50,
      "full_response": 15,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 40,
      "energy_polarization": 35
    },
    "elapsed_seconds": 2451.583285906003
  }
}