{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 10,
  "input_formula": "N2O4Sr2Ta2",
  "input_spacegroup": "Pmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -84.7173865215012,
  "input_cartesian_polarization_e_A2": [
    4.672611726414261e-19,
    -1.630653050684264e-17,
    0.027506234613920297
  ],
  "input_reduced_polarization": [
    1.586416829572304e-17,
    -3.810889556261825e-16,
    0.6427854685425668
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        1.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        1.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        1.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmma",
      "spacegroup_number": 51,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1871313801108217e-15,
      "parent_symmetrization_rmsd_A": 0.16837188129760133,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -84.57442636149172,
      "reduced_polarization": [
        1.139837763538066e-17,
        -9.289043293388198e-16,
        7.391128043585113e-16
      ],
      "cartesian_polarization_e_A2": [
        3.3572634889114617e-19,
        -3.9747168110428935e-17,
        3.162829777240285e-17
      ],
      "ranking_score": 0.16837188129760372
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmc2_1",
      "spacegroup_number": 26,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 7.838651227165538e-06,
      "parent_symmetrization_rmsd_A": 0.016937257023003346,
      "parent_cell_rmsd_A": 0.0019109140437251469,
      "energy_eV": -84.67088212650613,
      "reduced_polarization": [
        2.9687486897283406e-15,
        -6.480388021382984e-16,
        0.49999216134877283
      ],
      "cartesian_polarization_e_A2": [
        9.366080152594542e-17,
        -4.8079342197430987e-17,
        0.02138902806248366
      ],
      "ranking_score": 0.5174306628363889
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmma",
      "spacegroup_number": 51,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999795,
      "parent_symmetrization_rmsd_A": 0.16837250245152172,
      "parent_cell_rmsd_A": 0.0019109140437251469,
      "energy_eV": -84.57258099374923,
      "reduced_polarization": [
        4.476272874681806e-16,
        2.9046518563238506e-16,
        2.065931903945216e-15
      ],
      "cartesian_polarization_e_A2": [
        1.3176467268639967e-17,
        1.2427287601878348e-17,
        8.83779364649693e-17
      ],
      "ranking_score": 1.1688502309624489
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmc2_1",
      "spacegroup_number": 26,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0005972732790463509,
      "parent_symmetrization_rmsd_A": 0.050381558156598595,
      "parent_cell_rmsd_A": 0.005809268915788399,
      "energy_eV": -84.58373152812192,
      "reduced_polarization": [
        -1.93813993658165e-15,
        2.238336109290934e-15,
        0.9994027267209536
      ],
      "cartesian_polarization_e_A2": [
        -9.599701558586099e-17,
        2.185462912908711e-16,
        0.042807851353324974
      ],
      "ranking_score": 0.5530284219436384
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.811632590178266e-05,
      "parent_symmetrization_rmsd_A": 0.06861962976026625,
      "parent_cell_rmsd_A": 0.022105419176172814,
      "energy_eV": -84.4527347747352,
      "reduced_polarization": [
        -2.901914112187932e-15,
        -0.49997350682273,
        0.4999725962437175
      ],
      "cartesian_polarization_e_A2": [
        -3.4795074845095175e-18,
        -0.021313461322891587,
        0.02131117862832413
      ],
      "ranking_score": 0.574222217206113
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 5.4017813669091354e-05,
      "parent_symmetrization_rmsd_A": 0.052338955603260136,
      "parent_cell_rmsd_A": 0.0038614953470997374,
      "energy_eV": -84.55669481035797,
      "reduced_polarization": [
        0.4999672595339237,
        -5.926456613019139e-16,
        0.4999570350599361
      ],
      "cartesian_polarization_e_A2": [
        0.0147351600328167,
        -2.770751669738588e-17,
        0.02139995639788308
      ],
      "ranking_score": 0.5534123650673732
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        1.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.3364039725701565e-05,
      "parent_symmetrization_rmsd_A": 0.09608035057775602,
      "parent_cell_rmsd_A": 0.026768844980782722,
      "energy_eV": -83.66122889029364,
      "reduced_polarization": [
        -1.312739508581288e-15,
        -0.5000169772792288,
        1.000016051490345
      ],
      "cartesian_polarization_e_A2": [
        -1.2369580942580451e-18,
        -0.021221497230884172,
        0.04275084934779322
      ],
      "ranking_score": 0.6028192899024031
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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,
        1.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.318898832480227e-06,
      "parent_symmetrization_rmsd_A": 0.0761224515167413,
      "parent_cell_rmsd_A": 0.007343089231130739,
      "energy_eV": -84.39477253777814,
      "reduced_polarization": [
        0.49999501906939103,
        8.740901499705626e-16,
        1.0000038882917488
      ],
      "cartesian_polarization_e_A2": [
        0.014794772494255442,
        1.927466913212713e-16,
        0.042850480466270276
      ],
      "ranking_score": 0.5779708616221889
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00022697900611328532,
      "parent_symmetrization_rmsd_A": 0.08642435549799056,
      "parent_cell_rmsd_A": 0.02285420714827744,
      "energy_eV": -84.30948557086322,
      "reduced_polarization": [
        0.49983703287533393,
        -0.4998712458565875,
        0.4999084382391587
      ],
      "cartesian_polarization_e_A2": [
        0.014732887819063024,
        -0.021307534618510857,
        0.02131963116752387
      ],
      "ranking_score": 0.5925918652972865
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00010921058971452001,
      "parent_symmetrization_rmsd_A": 0.11510649995318221,
      "parent_cell_rmsd_A": 0.028497860401312972,
      "energy_eV": -83.42330100244462,
      "reduced_polarization": [
        0.4999602078326303,
        -0.5000785598433481,
        1.0000645901489
      ],
      "cartesian_polarization_e_A2": [
        0.014803509168842767,
        -0.02121600640546323,
        0.042768317743862215
      ],
      "ranking_score": 0.6224493862329394
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "target_residual": 0.1427854685425668,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.02489355497756362,
            "max_log_strain_component": 0.0004096116214064578,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0004096955237016,
              1.0002090295302655,
              0.9999169840486505
            ],
            "cell_volume_ratio": 1.000535743369923,
            "cell_rmsd_from_input_A": 0.001974972482276608
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.363330224439004e-15,
              8.561445408441663e-16,
              0.49467750616370315
            ],
            "branch_aligned_reduced_polarization": [
              2.363330224439004e-15,
              8.561445408441663e-16,
              0.49467750616370315
            ],
            "target_residual": 0.005322493836296849,
            "energy_eV": -84.6688350447546,
            "max_atomic_step_A": 0.000872234892379204,
            "max_log_strain_component": 1.3281105965235019e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0003964090647566,
              1.0002022513435243,
              0.9999196756211238
            ],
            "cell_volume_ratio": 1.0005183681102052,
            "cell_rmsd_from_input_A": 0.0019109140437251469
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.9687486897283406e-15,
              -6.480388021382984e-16,
              0.49999216134877283
            ],
            "branch_aligned_reduced_polarization": [
              2.9687486897283406e-15,
              -6.480388021382984e-16,
              0.49999216134877283
            ],
            "target_residual": 7.838651227165538e-06,
            "energy_eV": -84.67088212650613
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmc2_1",
        "spacegroup_number": 26,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 7.838651227165538e-06,
        "parent_symmetrization_rmsd_A": 0.016937257023003346,
        "parent_cell_rmsd_A": 0.0019109140437251469,
        "energy_eV": -84.67088212650613,
        "reduced_polarization": [
          2.9687486897283406e-15,
          -6.480388021382984e-16,
          0.49999216134877283
        ],
        "cartesian_polarization_e_A2": [
          9.366080152594542e-17,
          -4.8079342197430987e-17,
          0.02138902806248366
        ],
        "ranking_score": 0.5174306628363889
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "target_residual": 0.3572145314574332,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.06227762298492781,
            "max_log_strain_component": 0.001024748701066923,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0002077159203362,
              0.9994772502586273,
              0.9989757761745792
            ],
            "cell_volume_ratio": 0.9986609565464583,
            "cell_rmsd_from_input_A": 0.00493459271010781
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.945784463072265e-16,
              -3.0578544396109407e-15,
              0.9612259391693468
            ],
            "branch_aligned_reduced_polarization": [
              9.945784463072265e-16,
              -3.0578544396109407e-15,
              0.9612259391693468
            ],
            "target_residual": 0.038774060830653156,
            "energy_eV": -84.63126324146579,
            "max_atomic_step_A": 0.0083278282253381,
            "max_log_strain_component": 0.00018183612332754942,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0002445784957328,
              0.9993845196910089,
              0.9987941428063961
            ],
            "cell_volume_ratio": 0.9984235378960308,
            "cell_rmsd_from_input_A": 0.005809268915788399
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.93813993658165e-15,
              2.238336109290934e-15,
              0.9994027267209536
            ],
            "branch_aligned_reduced_polarization": [
              -1.93813993658165e-15,
              2.238336109290934e-15,
              0.9994027267209536
            ],
            "target_residual": 0.0005972732790463509,
            "energy_eV": -84.58373152812192
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmma",
        "spacegroup_number": 51,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.1871313801108217e-15,
        "parent_symmetrization_rmsd_A": 0.16837188129760133,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -84.57442636149172,
        "reduced_polarization": [
          1.139837763538066e-17,
          -9.289043293388198e-16,
          7.391128043585113e-16
        ],
        "cartesian_polarization_e_A2": [
          3.3572634889114617e-19,
          -3.9747168110428935e-17,
          3.162829777240285e-17
        ],
        "ranking_score": 0.16837188129760372
      },
      "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": [
          -84.71738652150118,
          -84.6943161862773,
          -84.66953501099107,
          -84.64482173766169,
          -84.62186244243452,
          -84.60219171489823,
          -84.58712024342856,
          -84.57765399397165,
          -84.57442636149172
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.434091501141371e-17,
            7.337938728079188e-18,
            0.027506234613920284
          ],
          [
            2.648334434863479e-17,
            -2.5275122285606093e-17,
            0.024297605132686778
          ],
          [
            2.6021374000388218e-17,
            -1.1210739723454315e-17,
            0.02100540453194977
          ],
          [
            1.492186635132744e-17,
            3.261306101368528e-17,
            0.01763633431077666
          ],
          [
            4.05570587408009e-17,
            9.172423410098985e-18,
            0.014198717691380014
          ],
          [
            7.648780439213553e-17,
            -2.2217647815573096e-17,
            0.010703001462341745
          ],
          [
            5.117651389629416e-17,
            -4.097015789844213e-17,
            0.007161687093529565
          ],
          [
            5.095158306377287e-17,
            3.8524178322415734e-17,
            0.003588891836495941
          ],
          [
            4.138430551190471e-17,
            -3.139007122567208e-17,
            -1.3981268439352453e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.62177911252365e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.335962395804013e-16,
            -3.2672433398282975e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.621779112523649e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.3359623958040135e-16,
            -3.3306690738754696e-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": [
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.35721453145743354
          ],
          [
            8.881784197001252e-16,
            -6.106226635438361e-16,
            -0.43219609230802014
          ],
          [
            8.881784197001252e-16,
            -2.7755575615628914e-16,
            0.4908693968298533
          ],
          [
            5.551115123125783e-16,
            7.771561172376096e-16,
            0.4121385414050396
          ],
          [
            1.3322676295501878e-15,
            2.220446049250313e-16,
            0.33180584445893224
          ],
          [
            2.55351295663786e-15,
            -4.996003610813204e-16,
            0.2501154340587728
          ],
          [
            1.7763568394002505e-15,
            -9.43689570931383e-16,
            0.16735945354148773
          ],
          [
            1.7763568394002505e-15,
            8.881784197001252e-16,
            0.08386780499222424
          ],
          [
            1.4432899320127035e-15,
            -7.216449660063518e-16,
            -3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -84.57442636149172,
          -84.57765399397167,
          -84.58712024342856,
          -84.60219171489821,
          -84.62186244243453,
          -84.6448217376617,
          -84.66953501099107,
          -84.6943161862773,
          -84.7173865215012
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.244293957964645e-17,
            -1.487970908749391e-17,
            -1.112401126758274e-17
          ],
          [
            4.2589662539953313e-17,
            6.726443834072589e-18,
            -0.003588891836496011
          ],
          [
            2.3595620260013513e-17,
            2.6498112073619288e-17,
            -0.00716168709352959
          ],
          [
            4.883398391442458e-17,
            -4.423146399981066e-17,
            -0.01070300146234191
          ],
          [
            1.0391804180156826e-17,
            -4.13778211611132e-17,
            -0.01419871769138009
          ],
          [
            2.033775158776989e-17,
            4.973491804587005e-17,
            -0.017636334310776845
          ],
          [
            3.848574939615935e-17,
            -8.560928516092386e-18,
            -0.021005404531949854
          ],
          [
            9.908619876710669e-17,
            -1.222989788013198e-17,
            -0.024297605132686816
          ],
          [
            4.870374987188038e-17,
            -1.0538095340047056e-16,
            -0.027506234613920467
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1014830326902602e-15,
            -3.4774367200889147e-16,
            -2.5995389391055834e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580028e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598565e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037458e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1014830326902602e-15,
            -3.4774367200889147e-16,
            -2.5995389391055834e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580025e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925466e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598563e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037457e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.983701743143326e-15,
          -1.6386825091925845e-15,
          -0.6427854685425671
        ],
        "actual_opposite_endpoint_branch_residual": 3.769761743235434e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.62177911252365e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.335962395804013e-16,
            -3.2672433398282975e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580028e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598565e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037458e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.621779112523649e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.3359623958040135e-16,
            -3.3306690738754696e-16
          ],
          [
            1.4459784243840022e-15,
            1.571991941958003e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598563e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037457e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "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": [
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.35721453145743354
          ],
          [
            8.881784197001252e-16,
            -6.106226635438361e-16,
            -0.43219609230802014
          ],
          [
            8.881784197001252e-16,
            -2.7755575615628914e-16,
            0.4908693968298533
          ],
          [
            5.551115123125783e-16,
            7.771561172376096e-16,
            0.4121385414050396
          ],
          [
            1.3322676295501878e-15,
            2.220446049250313e-16,
            0.33180584445893224
          ],
          [
            2.55351295663786e-15,
            -4.996003610813204e-16,
            0.2501154340587728
          ],
          [
            1.7763568394002505e-15,
            -9.43689570931383e-16,
            0.16735945354148773
          ],
          [
            1.7763568394002505e-15,
            8.881784197001252e-16,
            0.08386780499222424
          ],
          [
            1.4432899320127035e-15,
            -7.216449660063518e-16,
            -3.3306690738754696e-16
          ],
          [
            1.4432899320127035e-15,
            1.1102230246251565e-16,
            -0.0838678049922259
          ],
          [
            7.771561172376096e-16,
            6.661338147750939e-16,
            -0.1673594535414883
          ],
          [
            1.6653345369377348e-15,
            -1.0547118733938987e-15,
            -0.2501154340587766
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            -0.33180584445893396
          ],
          [
            6.661338147750939e-16,
            1.1102230246251565e-15,
            -0.41213854140504386
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-16,
            -0.49086939682985525
          ],
          [
            3.3306690738754696e-15,
            -2.7755575615628914e-16,
            0.43219609230801903
          ],
          [
            1.6653345369377348e-15,
            -2.4424906541753444e-15,
            0.3572145314574292
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "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": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              1.586416829572304e-17,
              -3.885780586188048e-16,
              0.6427854685425668
            ],
            "target_residual": 0.5199881633527055,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.09781776905393377,
            "max_log_strain_component": 0.003590006884190326,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0039083351437985,
              0.999916984048648,
              0.9967232820605094
            ],
            "cell_volume_ratio": 1.0005357433699191,
            "cell_rmsd_from_input_A": 0.021828381223828172
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.859115036569998e-15,
              -0.4957788301713327,
              0.48166197728482973
            ],
            "branch_aligned_reduced_polarization": [
              1.859115036569998e-15,
              -0.4957788301713327,
              0.48166197728482973
            ],
            "target_residual": 0.018817580923821,
            "energy_eV": -84.4592447647461,
            "max_atomic_step_A": 0.0036435327173520724,
            "max_log_strain_component": 5.461940590333831e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0039167860425555,
              0.9999280533606228,
              0.9966326766883798
            ],
            "cell_volume_ratio": 1.0004642884235242,
            "cell_rmsd_from_input_A": 0.022105419176172814
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.901914112187932e-15,
              -0.49997350682273,
              0.4999725962437175
            ],
            "branch_aligned_reduced_polarization": [
              -2.901914112187932e-15,
              -0.49997350682273,
              0.4999725962437175
            ],
            "target_residual": 3.811632590178266e-05,
            "energy_eV": -84.4527347747352
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.811632590178266e-05,
        "parent_symmetrization_rmsd_A": 0.06861962976026625,
        "parent_cell_rmsd_A": 0.022105419176172814,
        "energy_eV": -84.4527347747352,
        "reduced_polarization": [
          -2.901914112187932e-15,
          -0.49997350682273,
          0.4999725962437175
        ],
        "cartesian_polarization_e_A2": [
          -3.4795074845095175e-18,
          -0.021313461322891587,
          0.02131117862832413
        ],
        "ranking_score": 0.574222217206113
      },
      "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
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "target_residual": 0.5199881633527058,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.07143875032627033,
            "max_log_strain_component": 0.0008090848390538607,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.000885540631747,
              1.0004096955237023,
              0.9992411276067226
            ],
            "cell_volume_ratio": 1.0005357433699227,
            "cell_rmsd_from_input_A": 0.00390637954106096
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49541838663809606,
              8.309583351900728e-16,
              0.4868464972661635
            ],
            "branch_aligned_reduced_polarization": [
              0.49541838663809606,
              8.309583351900728e-16,
              0.4868464972661635
            ],
            "target_residual": 0.013928597027950098,
            "energy_eV": -84.5546211507092,
            "max_atomic_step_A": 0.0023130916790021984,
            "max_log_strain_component": 3.473132304285132e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.000888068046735,
              1.0003749505747643,
              0.9992279298854596
            ],
            "cell_volume_ratio": 1.0004903060925663,
            "cell_rmsd_from_input_A": 0.0038614953470997374
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999672595339237,
              -5.926456613019139e-16,
              0.4999570350599361
            ],
            "branch_aligned_reduced_polarization": [
              0.4999672595339237,
              -5.926456613019139e-16,
              0.4999570350599361
            ],
            "target_residual": 5.4017813669091354e-05,
            "energy_eV": -84.55669481035797
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 5.4017813669091354e-05,
        "parent_symmetrization_rmsd_A": 0.052338955603260136,
        "parent_cell_rmsd_A": 0.0038614953470997374,
        "energy_eV": -84.55669481035797,
        "reduced_polarization": [
          0.4999672595339237,
          -5.926456613019139e-16,
          0.4999570350599361
        ],
        "cartesian_polarization_e_A2": [
          0.0147351600328167,
          -2.770751669738588e-17,
          0.02139995639788308
        ],
        "ranking_score": 0.5534123650673732
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              1.586416829572304e-17,
              -3.885780586188048e-16,
              0.6427854685425668
            ],
            "target_residual": 0.6144934674057595,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.11461945660803881,
            "max_log_strain_component": 0.0035900068841937817,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0028289422454861,
              1.0002077159203335,
              0.9956369623818955
            ],
            "cell_volume_ratio": 0.9986609565464541,
            "cell_rmsd_from_input_A": 0.022223094832595065
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.922503658845531e-15,
              -0.4512674518120691,
              0.9300175843648292
            ],
            "branch_aligned_reduced_polarization": [
              2.922503658845531e-15,
              -0.4512674518120691,
              0.9300175843648292
            ],
            "target_residual": 0.08527836625441887,
            "energy_eV": -84.04089723487701,
            "max_atomic_step_A": 0.02250260982981254,
            "max_log_strain_component": 0.0006865486319883724,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0032137345915608,
              1.0002905480164008,
              0.9946411236748143
            ],
            "cell_volume_ratio": 0.9981275560060622,
            "cell_rmsd_from_input_A": 0.026695420421438423
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.0753648182005924e-16,
              -0.499661375576362,
              0.9981134043741523
            ],
            "branch_aligned_reduced_polarization": [
              -4.0753648182005924e-16,
              -0.499661375576362,
              0.9981134043741523
            ],
            "target_residual": 0.001916744520209162,
            "energy_eV": -83.66950033521914,
            "max_atomic_step_A": 0.0004879841753057784,
            "max_log_strain_component": 1.128448899247369e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0032157141083649,
              1.0002928358048642,
              0.9946222100916681
            ],
            "cell_volume_ratio": 0.9981128283726735,
            "cell_rmsd_from_input_A": 0.026768844980782722
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.312739508581288e-15,
              -0.5000169772792288,
              1.000016051490345
            ],
            "branch_aligned_reduced_polarization": [
              -1.312739508581288e-15,
              -0.5000169772792288,
              1.000016051490345
            ],
            "target_residual": 2.3364039725701565e-05,
            "energy_eV": -83.66122889029364
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          1.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.3364039725701565e-05,
        "parent_symmetrization_rmsd_A": 0.09608035057775602,
        "parent_cell_rmsd_A": 0.026768844980782722,
        "energy_eV": -83.66122889029364,
        "reduced_polarization": [
          -1.312739508581288e-15,
          -0.5000169772792288,
          1.000016051490345
        ],
        "cartesian_polarization_e_A2": [
          -1.2369580942580451e-18,
          -0.021221497230884172,
          0.04275084934779322
        ],
        "ranking_score": 0.6028192899024031
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "target_residual": 0.6144934674057597,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.09144565759734571,
            "max_log_strain_component": 0.001024748701066915,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0007303953855575,
              0.9989757761745792,
              0.9989552253085757
            ],
            "cell_volume_ratio": 0.9986609565464583,
            "cell_rmsd_from_input_A": 0.005973568025169395
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4658764493321443,
              -4.596888198368916e-15,
              0.9468312558405724
            ],
            "branch_aligned_reduced_polarization": [
              0.4658764493321443,
              -4.596888198368916e-15,
              0.9468312558405724
            ],
            "target_residual": 0.06317699000168009,
            "energy_eV": -84.4983578224313,
            "max_atomic_step_A": 0.013109371437312509,
            "max_log_strain_component": 0.00027593445446840484,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.000815788819882,
              0.9987852182444822,
              0.998700162366175
            ],
            "cell_volume_ratio": 0.9983006983393445,
            "cell_rmsd_from_input_A": 0.007303104698642419
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49915889356434656,
              -9.273970101406259e-16,
              0.9985664584955726
            ],
            "branch_aligned_reduced_polarization": [
              0.49915889356434656,
              -9.273970101406259e-16,
              0.9985664584955726
            ],
            "target_residual": 0.0016620773992247417,
            "energy_eV": -84.397911960345,
            "max_atomic_step_A": 0.00036325659423729723,
            "max_log_strain_component": 8.33287297028828e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.000818207268419,
              0.998780244807601,
              0.9986918403592601
            ],
            "cell_volume_ratio": 0.9982898210170639,
            "cell_rmsd_from_input_A": 0.007343089231130739
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999501906939103,
              8.740901499705626e-16,
              1.0000038882917488
            ],
            "branch_aligned_reduced_polarization": [
              0.49999501906939103,
              8.740901499705626e-16,
              1.0000038882917488
            ],
            "target_residual": 6.318898832480227e-06,
            "energy_eV": -84.39477253777814
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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,
          1.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.318898832480227e-06,
        "parent_symmetrization_rmsd_A": 0.0761224515167413,
        "parent_cell_rmsd_A": 0.007343089231130739,
        "energy_eV": -84.39477253777814,
        "reduced_polarization": [
          0.49999501906939103,
          8.740901499705626e-16,
          1.0000038882917488
        ],
        "cartesian_polarization_e_A2": [
          0.014794772494255442,
          1.927466913212713e-16,
          0.042850480466270276
        ],
        "ranking_score": 0.5779708616221889
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -3.885780586188048e-16,
              0.6427854685425668
            ],
            "target_residual": 0.7213790196747615,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.1185416463165872,
            "max_log_strain_component": 0.003590006884190308,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.003987860748225,
              0.999941017577573,
              0.9966203775881181
            ],
            "cell_volume_ratio": 1.000535743369919,
            "cell_rmsd_from_input_A": 0.02208706803736339
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48474967481541753,
              -0.4878874868936115,
              0.4747696759065327
            ],
            "branch_aligned_reduced_polarization": [
              0.48474967481541753,
              -0.4878874868936115,
              0.4747696759065327
            ],
            "target_residual": 0.031872474736821754,
            "energy_eV": -84.33667025685585,
            "max_atomic_step_A": 0.0065319506095198945,
            "max_log_strain_component": 0.0001308798937641203,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.004062368469813,
              0.9999530897041832,
              0.9964265800896567
            ],
            "cell_volume_ratio": 1.0004274994595337,
            "cell_rmsd_from_input_A": 0.02285420714827744
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49983703287533393,
              -0.4998712458565875,
              0.4999084382391587
            ],
            "branch_aligned_reduced_polarization": [
              0.49983703287533393,
              -0.4998712458565875,
              0.4999084382391587
            ],
            "target_residual": 0.00022697900611328532,
            "energy_eV": -84.30948557086322
          }
        ],
        "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": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00022697900611328532,
        "parent_symmetrization_rmsd_A": 0.08642435549799056,
        "parent_cell_rmsd_A": 0.02285420714827744,
        "energy_eV": -84.30948557086322,
        "reduced_polarization": [
          0.49983703287533393,
          -0.4998712458565875,
          0.4999084382391587
        ],
        "cartesian_polarization_e_A2": [
          0.014732887819063024,
          -0.021307534618510857,
          0.02131963116752387
        ],
        "ranking_score": 0.5925918652972865
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.586416829572304e-17,
              -3.810889556261825e-16,
              0.6427854685425668
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -3.885780586188048e-16,
              0.6427854685425668
            ],
            "target_residual": 0.7922134948890691,
            "energy_eV": -84.7173865215012,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003245308629948654,
            "step_scale": 0.9039839573114019,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0026742823165975,
              1.000130615507406,
              0.9959954350143344
            ],
            "cell_volume_ratio": 0.9987894483466593,
            "cell_rmsd_from_input_A": 0.020322820133900566
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.41670625243450476,
              -0.40802184970954536,
              0.8979071385854324
            ],
            "branch_aligned_reduced_polarization": [
              0.41670625243450476,
              -0.40802184970954536,
              0.8979071385854324
            ],
            "target_residual": 0.16068845903229023,
            "energy_eV": -84.10439261447058,
            "max_atomic_step_A": 0.03983509422575198,
            "max_log_strain_component": 0.0011984140973488897,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0034529820801863,
              1.0002234299372261,
              0.9943081477540732
            ],
            "cell_volume_ratio": 0.9979644012857944,
            "cell_rmsd_from_input_A": 0.02810690411944167
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4950795099110935,
              -0.4974141111935463,
              0.9937913566958461
            ],
            "branch_aligned_reduced_polarization": [
              0.4950795099110935,
              -0.4974141111935463,
              0.9937913566958461
            ],
            "target_residual": 0.0083333843852654,
            "energy_eV": -83.4637927104983,
            "max_atomic_step_A": 0.0021211267957992413,
            "max_log_strain_component": 5.655216141707456e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5844726234285609,
            "cell_principal_stretches": [
              1.0034807981120013,
              1.0002288990889043,
              0.9942157308316851
            ],
            "cell_volume_ratio": 0.9979047622883386,
            "cell_rmsd_from_input_A": 0.028497860401312972
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999602078326303,
              -0.5000785598433481,
              1.0000645901489
            ],
            "branch_aligned_reduced_polarization": [
              0.4999602078326303,
              -0.5000785598433481,
              1.0000645901489
            ],
            "target_residual": 0.00010921058971452001,
            "energy_eV": -83.42330100244462
          }
        ],
        "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,
          1.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00010921058971452001,
        "parent_symmetrization_rmsd_A": 0.11510649995318221,
        "parent_cell_rmsd_A": 0.028497860401312972,
        "energy_eV": -83.42330100244462,
        "reduced_polarization": [
          0.4999602078326303,
          -0.5000785598433481,
          1.0000645901489
        ],
        "cartesian_polarization_e_A2": [
          0.014803509168842767,
          -0.02121600640546323,
          0.042768317743862215
        ],
        "ranking_score": 0.6224493862329394
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "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
        ],
        "endpoint_rmsd_A": 0.16837188129760133,
        "minimum_distance_A_by_image": [
          1.908491471933566,
          1.9188311534755549,
          1.9291729079926847,
          1.9395167023248356,
          1.949862504009065,
          1.9602102812615367,
          1.9705600029600232,
          1.9809116386269272,
          1.9912651584128276
        ],
        "minimum_distance_A": 1.908491471933566,
        "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": [
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267,
          136.16912857818267
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.4050548726981237e-15,
        -7.335962395804013e-16,
        -3.2672433398282975e-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": [
          -84.71738652150118,
          -84.6943161862773,
          -84.66953501099107,
          -84.64482173766169,
          -84.62186244243452,
          -84.60219171489823,
          -84.58712024342856,
          -84.57765399397165,
          -84.57442636149172
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.434091501141371e-17,
            7.337938728079188e-18,
            0.027506234613920284
          ],
          [
            2.648334434863479e-17,
            -2.5275122285606093e-17,
            0.024297605132686778
          ],
          [
            2.6021374000388218e-17,
            -1.1210739723454315e-17,
            0.02100540453194977
          ],
          [
            1.492186635132744e-17,
            3.261306101368528e-17,
            0.01763633431077666
          ],
          [
            4.05570587408009e-17,
            9.172423410098985e-18,
            0.014198717691380014
          ],
          [
            7.648780439213553e-17,
            -2.2217647815573096e-17,
            0.010703001462341745
          ],
          [
            5.117651389629416e-17,
            -4.097015789844213e-17,
            0.007161687093529565
          ],
          [
            5.095158306377287e-17,
            3.8524178322415734e-17,
            0.003588891836495941
          ],
          [
            4.138430551190471e-17,
            -3.139007122567208e-17,
            -1.3981268439352453e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.62177911252365e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.335962395804013e-16,
            -3.2672433398282975e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.621779112523649e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.3359623958040135e-16,
            -3.3306690738754696e-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": [
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.35721453145743354
          ],
          [
            8.881784197001252e-16,
            -6.106226635438361e-16,
            -0.43219609230802014
          ],
          [
            8.881784197001252e-16,
            -2.7755575615628914e-16,
            0.4908693968298533
          ],
          [
            5.551115123125783e-16,
            7.771561172376096e-16,
            0.4121385414050396
          ],
          [
            1.3322676295501878e-15,
            2.220446049250313e-16,
            0.33180584445893224
          ],
          [
            2.55351295663786e-15,
            -4.996003610813204e-16,
            0.2501154340587728
          ],
          [
            1.7763568394002505e-15,
            -9.43689570931383e-16,
            0.16735945354148773
          ],
          [
            1.7763568394002505e-15,
            8.881784197001252e-16,
            0.08386780499222424
          ],
          [
            1.4432899320127035e-15,
            -7.216449660063518e-16,
            -3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -84.57442636149172,
          -84.57765399397167,
          -84.58712024342856,
          -84.60219171489821,
          -84.62186244243453,
          -84.6448217376617,
          -84.66953501099107,
          -84.6943161862773,
          -84.7173865215012
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.244293957964645e-17,
            -1.487970908749391e-17,
            -1.112401126758274e-17
          ],
          [
            4.2589662539953313e-17,
            6.726443834072589e-18,
            -0.003588891836496011
          ],
          [
            2.3595620260013513e-17,
            2.6498112073619288e-17,
            -0.00716168709352959
          ],
          [
            4.883398391442458e-17,
            -4.423146399981066e-17,
            -0.01070300146234191
          ],
          [
            1.0391804180156826e-17,
            -4.13778211611132e-17,
            -0.01419871769138009
          ],
          [
            2.033775158776989e-17,
            4.973491804587005e-17,
            -0.017636334310776845
          ],
          [
            3.848574939615935e-17,
            -8.560928516092386e-18,
            -0.021005404531949854
          ],
          [
            9.908619876710669e-17,
            -1.222989788013198e-17,
            -0.024297605132686816
          ],
          [
            4.870374987188038e-17,
            -1.0538095340047056e-16,
            -0.027506234613920467
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1014830326902602e-15,
            -3.4774367200889147e-16,
            -2.5995389391055834e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580028e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598565e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037458e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1014830326902602e-15,
            -3.4774367200889147e-16,
            -2.5995389391055834e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580025e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925466e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598563e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037457e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.983701743143326e-15,
          -1.6386825091925845e-15,
          -0.6427854685425671
        ],
        "actual_opposite_endpoint_branch_residual": 3.769761743235434e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.62177911252365e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.335962395804013e-16,
            -3.2672433398282975e-16
          ],
          [
            1.4459784243840022e-15,
            1.5719919419580028e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598565e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037458e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.264080022529214e-16,
            1.714900300317821e-16,
            0.6427854685425665
          ],
          [
            8.991464653596167e-16,
            -5.906878812205829e-16,
            0.56780390769198
          ],
          [
            8.83461927928895e-16,
            -2.6199865699300044e-16,
            0.4908693968298533
          ],
          [
            5.066181676203711e-16,
            7.621779112523649e-16,
            0.4121385414050395
          ],
          [
            1.376968691420324e-15,
            2.1436253753972766e-16,
            0.3318058444589322
          ],
          [
            2.5968676031602367e-15,
            -5.192337020406736e-16,
            0.2501154340587728
          ],
          [
            1.73751400025323e-15,
            -9.574860010107835e-16,
            0.16735945354148768
          ],
          [
            1.7298772848765958e-15,
            9.00322657666856e-16,
            0.08386780499222427
          ],
          [
            1.4050548726981237e-15,
            -7.3359623958040135e-16,
            -3.3306690738754696e-16
          ],
          [
            1.4459784243840022e-15,
            1.571991941958003e-16,
            -0.0838678049922259
          ],
          [
            8.011042063066551e-16,
            6.192695528925465e-16,
            -0.1673594535414883
          ],
          [
            1.6579818412679717e-15,
            -1.0337037921360199e-15,
            -0.2501154340587766
          ],
          [
            3.528162408151057e-16,
            -9.670132249014379e-16,
            -0.33180584445893396
          ],
          [
            6.904950225611479e-16,
            1.1623213146598563e-15,
            -0.41213854140504386
          ],
          [
            1.3066448512216144e-15,
            -2.000717017037457e-16,
            -0.49086939682985525
          ],
          [
            3.3641146002754415e-15,
            -2.8581671671963683e-16,
            -0.567803907691981
          ],
          [
            1.6535602139432058e-15,
            -2.4627873757342043e-15,
            -0.6427854685425708
          ]
        ],
        "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": [
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.35721453145743354
          ],
          [
            8.881784197001252e-16,
            -6.106226635438361e-16,
            -0.43219609230802014
          ],
          [
            8.881784197001252e-16,
            -2.7755575615628914e-16,
            0.4908693968298533
          ],
          [
            5.551115123125783e-16,
            7.771561172376096e-16,
            0.4121385414050396
          ],
          [
            1.3322676295501878e-15,
            2.220446049250313e-16,
            0.33180584445893224
          ],
          [
            2.55351295663786e-15,
            -4.996003610813204e-16,
            0.2501154340587728
          ],
          [
            1.7763568394002505e-15,
            -9.43689570931383e-16,
            0.16735945354148773
          ],
          [
            1.7763568394002505e-15,
            8.881784197001252e-16,
            0.08386780499222424
          ],
          [
            1.4432899320127035e-15,
            -7.216449660063518e-16,
            -3.3306690738754696e-16
          ],
          [
            1.4432899320127035e-15,
            1.1102230246251565e-16,
            -0.0838678049922259
          ],
          [
            7.771561172376096e-16,
            6.661338147750939e-16,
            -0.1673594535414883
          ],
          [
            1.6653345369377348e-15,
            -1.0547118733938987e-15,
            -0.2501154340587766
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            -0.33180584445893396
          ],
          [
            6.661338147750939e-16,
            1.1102230246251565e-15,
            -0.41213854140504386
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-16,
            -0.49086939682985525
          ],
          [
            3.3306690738754696e-15,
            -2.7755575615628914e-16,
            0.43219609230801903
          ],
          [
            1.6653345369377348e-15,
            -2.4424906541753444e-15,
            0.3572145314574292
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": "Pmma",
        "spacegroup_number": 51,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.1871313801108217e-15,
        "parent_symmetrization_rmsd_A": 0.16837188129760133,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -84.57442636149172,
        "reduced_polarization": [
          1.139837763538066e-17,
          -9.289043293388198e-16,
          7.391128043585113e-16
        ],
        "cartesian_polarization_e_A2": [
          3.3572634889114617e-19,
          -3.9747168110428935e-17,
          3.162829777240285e-17
        ],
        "ranking_score": 0.16837188129760372
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 134.21141111798352
  }
}
