{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 10,
  "input_formula": "I2O6Tl2",
  "input_spacegroup": "R3m",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -42.61158551432618,
  "input_cartesian_polarization_e_A2": [
    0.010204494953960147,
    -5.311206460678069e-18,
    -0.0069472838287706834
  ],
  "input_reduced_polarization": [
    0.29271818889423495,
    -1.6020002998223994e-16,
    -0.29271818979222924
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "R-3m",
      "spacegroup_number": 166,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.437309062474395e-16,
      "parent_symmetrization_rmsd_A": 0.4170189183450961,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -37.17648944835422,
      "reduced_polarization": [
        -5.456299636148911e-17,
        7.297595463486411e-16,
        4.199472896664618e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.2121038911878327e-18,
        2.419415038647676e-17,
        9.966900302665574e-18
      ],
      "ranking_score": 0.41701891834509774
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00017952919126689018,
      "parent_symmetrization_rmsd_A": 0.12340473463237972,
      "parent_cell_rmsd_A": 0.10006294730724526,
      "energy_eV": -41.138177773371524,
      "reduced_polarization": [
        0.499879225012855,
        -1.5802093444298557e-16,
        -0.49986716878003623
      ],
      "cartesian_polarization_e_A2": [
        0.017759252642044483,
        3.026843232985284e-17,
        -0.012059258981293503
      ],
      "ranking_score": 0.6487795298417248
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.707106781186547,
      "parent_symmetrization_rmsd_A": 0.4170189183450965,
      "parent_cell_rmsd_A": 0.10006294730724526,
      "energy_eV": -38.04750947350618,
      "reduced_polarization": [
        -5.379764582308229e-16,
        3.7575121056047016e-16,
        5.859811180270472e-17
      ],
      "cartesian_polarization_e_A2": [
        -1.8774651117017685e-17,
        1.281668448488809e-17,
        1.3015151526108064e-18
      ],
      "ranking_score": 1.856248217545002
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0004672276011610835,
      "parent_symmetrization_rmsd_A": 0.09219326674197831,
      "parent_cell_rmsd_A": 0.06964370900533469,
      "energy_eV": -41.433883013568405,
      "reduced_polarization": [
        -0.00021741598397700742,
        -1.7400661627567961e-15,
        -0.4995864399424533
      ],
      "cartesian_polarization_e_A2": [
        0.0004306162951913606,
        -9.987528610194371e-17,
        -0.011625183403520707
      ],
      "ranking_score": 0.6105386491956342
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0003746230733140657,
      "parent_symmetrization_rmsd_A": 0.09085127178231366,
      "parent_cell_rmsd_A": 0.06312019362601322,
      "energy_eV": -41.348894466161696,
      "reduced_polarization": [
        0.4996751744750147,
        -8.497793687070539e-16,
        0.00018663018345727505
      ],
      "cartesian_polarization_e_A2": [
        0.017002930758667163,
        1.0416285842354027e-16,
        1.0571388409130597e-05
      ],
      "ranking_score": 0.6073805663354451
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00011846530371955115,
      "parent_symmetrization_rmsd_A": 0.1488453803744784,
      "parent_cell_rmsd_A": 0.12543046030350166,
      "energy_eV": -40.28829715648513,
      "reduced_polarization": [
        8.21211991917161e-05,
        -3.5584768065905915e-16,
        -8.5382298099079e-05
      ],
      "cartesian_polarization_e_A2": [
        2.8014137251644816e-06,
        -1.1406379363620278e-17,
        -1.9860722362825706e-06
      ],
      "ranking_score": 0.6804399260577929
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 0.00020831485992665785,
      "parent_symmetrization_rmsd_A": 0.2159526070558771,
      "parent_cell_rmsd_A": 0.25797458921801253,
      "energy_eV": -33.98838645592882,
      "reduced_polarization": [
        0.49988568224736185,
        -0.49990874457039347,
        -0.4998516794725422
      ],
      "cartesian_polarization_e_A2": [
        0.01726547767359761,
        -0.016536040775681646,
        -0.012048472633710545
      ],
      "ranking_score": 0.7808628840802335
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.11977450372564019,
      "parent_symmetrization_rmsd_A": 0.28199233643291965,
      "parent_cell_rmsd_A": 0.417848721685655,
      "energy_eV": -37.984731141758246,
      "reduced_polarization": [
        0.06860813609862376,
        -0.4048369967988174,
        -0.47585754309255524
      ],
      "cartesian_polarization_e_A2": [
        0.0020710579394870223,
        -0.013103377601265063,
        -0.010838202321169168
      ],
      "ranking_score": 1.126003524305614
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0001919749680887857,
      "parent_symmetrization_rmsd_A": 0.1831767715078854,
      "parent_cell_rmsd_A": 0.23050180658749697,
      "energy_eV": -33.146308837966096,
      "reduced_polarization": [
        0.5000146562555107,
        -0.4998644352144521,
        -0.0001351361219898409
      ],
      "cartesian_polarization_e_A2": [
        0.016489507393015156,
        -0.01609222872694801,
        4.4967648998989354e-05
      ],
      "ranking_score": 0.7411861730909373
    },
    {
      "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": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.07698822545637025,
      "parent_symmetrization_rmsd_A": 0.29946755799091895,
      "parent_cell_rmsd_A": 0.4166182433519301,
      "energy_eV": -38.98220337822677,
      "reduced_polarization": [
        0.041992088156679624,
        -0.43736698451236244,
        0.015522782034413074
      ],
      "cartesian_polarization_e_A2": [
        0.0006698560169034479,
        -0.013831783683563768,
        0.0003552876091743878
      ],
      "ranking_score": 1.057598569741642
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.29314074786405314,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.11565632466250682,
            "max_log_strain_component": 0.011579941992136716,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              0.9945282120796797,
              0.9921246038920003,
              0.9844444104582954
            ],
            "cell_volume_ratio": 0.9713472719143487,
            "cell_rmsd_from_input_A": 0.07474711963901193
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.46804840369001277,
              4.681069720158051e-15,
              -0.46900350362896986
            ],
            "branch_aligned_reduced_polarization": [
              0.46804840369001277,
              4.681069720158051e-15,
              -0.46900350362896986
            ],
            "target_residual": 0.04451614644188863,
            "energy_eV": -41.5488220569124,
            "max_atomic_step_A": 0.022653873100464378,
            "max_log_strain_component": 0.004194737208183226,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              0.9925686420567528,
              0.989285281947913,
              0.978897812842518
            ],
            "cell_volume_ratio": 0.9612126033844672,
            "cell_rmsd_from_input_A": 0.10130149108208854
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5012310041322829,
              4.686963030101453e-15,
              -0.5014720969539735
            ],
            "branch_aligned_reduced_polarization": [
              0.5012310041322829,
              4.686963030101453e-15,
              -0.5014720969539735
            ],
            "target_residual": 0.0019189686333017197,
            "energy_eV": -41.1219890590299,
            "max_atomic_step_A": 0.0011078730468157526,
            "max_log_strain_component": 0.00019532190535376769,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              0.9926623553330036,
              0.9894169983703853,
              0.9791601578542313
            ],
            "cell_volume_ratio": 0.9616890109995924,
            "cell_rmsd_from_input_A": 0.10006294730724526
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499879225012855,
              -1.5802093444298557e-16,
              -0.49986716878003623
            ],
            "branch_aligned_reduced_polarization": [
              0.499879225012855,
              -1.5802093444298557e-16,
              -0.49986716878003623
            ],
            "target_residual": 0.00017952919126689018,
            "energy_eV": -41.138177773371524
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00017952919126689018,
        "parent_symmetrization_rmsd_A": 0.12340473463237972,
        "parent_cell_rmsd_A": 0.10006294730724526,
        "energy_eV": -41.138177773371524,
        "reduced_polarization": [
          0.499879225012855,
          -1.5802093444298557e-16,
          -0.49986716878003623
        ],
        "cartesian_polarization_e_A2": [
          0.017759252642044483,
          3.026843232985284e-17,
          -0.012059258981293503
        ],
        "ranking_score": 0.6487795298417248
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.3586776922984357,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011758205972699493,
            "step_scale": 0.9779497973349891,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0120404891440287,
              1.0086043787225494,
              0.996792250137787
            ],
            "cell_volume_ratio": 1.017474163035046,
            "cell_rmsd_from_input_A": 0.07142048320201026
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0004362477170987838,
              -4.004952829348159e-15,
              -0.4714590161652987
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004362477170987838,
              -4.004952829348159e-15,
              -0.4714590161652987
            ],
            "target_residual": 0.02854431765384055,
            "energy_eV": -41.49662424962208,
            "max_atomic_step_A": 0.008188640131099607,
            "max_log_strain_component": 0.0013554943896798826,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0115976401000346,
              1.0084147611738172,
              0.9955373739187992
            ],
            "cell_volume_ratio": 1.0155576231866006,
            "cell_rmsd_from_input_A": 0.06964370900533469
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00021741598397700742,
              -1.7400661627567961e-15,
              -0.4995864399424533
            ],
            "branch_aligned_reduced_polarization": [
              -0.00021741598397700742,
              -1.7400661627567961e-15,
              -0.4995864399424533
            ],
            "target_residual": 0.0004672276011610835,
            "energy_eV": -41.433883013568405
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0004672276011610835,
        "parent_symmetrization_rmsd_A": 0.09219326674197831,
        "parent_cell_rmsd_A": 0.06964370900533469,
        "energy_eV": -41.433883013568405,
        "reduced_polarization": [
          -0.00021741598397700742,
          -1.7400661627567961e-15,
          -0.4995864399424533
        ],
        "cartesian_polarization_e_A2": [
          0.0004306162951913606,
          -9.987528610194371e-17,
          -0.011625183403520707
        ],
        "ranking_score": 0.6105386491956342
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.358677693550248,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.10293220513093936,
            "max_log_strain_component": 0.007250360216074139,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0070497475450642,
              0.9945132499221293,
              0.9927716893607498
            ],
            "cell_volume_ratio": 0.9942849883863524,
            "cell_rmsd_from_input_A": 0.04631303992190002
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4600390002876767,
              -2.860383504347565e-17,
              -0.004899500581440551
            ],
            "branch_aligned_reduced_polarization": [
              0.4600390002876767,
              -2.860383504347565e-17,
              -0.004899500581440551
            ],
            "target_residual": 0.04026023601465644,
            "energy_eV": -41.68100533066462,
            "max_atomic_step_A": 0.01794668118507966,
            "max_log_strain_component": 0.003015016271460555,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0072532193836605,
              0.9923548172069936,
              0.9897798752146867
            ],
            "cell_volume_ratio": 0.9893370322605509,
            "cell_rmsd_from_input_A": 0.06312019362601322
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4996751744750147,
              -8.497793687070539e-16,
              0.00018663018345727505
            ],
            "branch_aligned_reduced_polarization": [
              0.4996751744750147,
              -8.497793687070539e-16,
              0.00018663018345727505
            ],
            "target_residual": 0.0003746230733140657,
            "energy_eV": -41.348894466161696
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0003746230733140657,
        "parent_symmetrization_rmsd_A": 0.09085127178231366,
        "parent_cell_rmsd_A": 0.06312019362601322,
        "energy_eV": -41.348894466161696,
        "reduced_polarization": [
          0.4996751744750147,
          -8.497793687070539e-16,
          0.00018663018345727505
        ],
        "cartesian_polarization_e_A2": [
          0.017002930758667163,
          1.0416285842354027e-16,
          1.0571388409130597e-05
        ],
        "ranking_score": 0.6073805663354451
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.41396603332249443,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012014846929370803,
            "step_scale": 0.7347225054597774,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.01639967854177,
              1.008237256930153,
              1.0057091150750264
            ],
            "cell_volume_ratio": 1.0306225652474001,
            "cell_rmsd_from_input_A": 0.07964739378106803
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0846032210810396,
              -6.8863278434447035e-15,
              -0.08562904676605594
            ],
            "branch_aligned_reduced_polarization": [
              0.0846032210810396,
              -6.8863278434447035e-15,
              -0.08562904676605594
            ],
            "target_residual": 0.12037457649915391,
            "energy_eV": -41.439434481441694,
            "max_atomic_step_A": 0.050038332460688076,
            "max_log_strain_component": 0.005751754315480577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0243763059304671,
              1.0122026189554205,
              1.00846956038409
            ],
            "cell_volume_ratio": 1.0456582667670538,
            "cell_rmsd_from_input_A": 0.11860300434176081
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.010440362764177747,
              -3.3106902084983888e-15,
              -0.010670639909480308
            ],
            "branch_aligned_reduced_polarization": [
              0.010440362764177747,
              -3.3106902084983888e-15,
              -0.010670639909480308
            ],
            "target_residual": 0.014928621193044691,
            "energy_eV": -40.45098378767492,
            "max_atomic_step_A": 0.006411823713952591,
            "max_log_strain_component": 0.0009147308814501751,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0256514772142051,
              1.0128346327560065,
              1.0089096935352184
            ],
            "cell_volume_ratio": 1.0480708635545755,
            "cell_rmsd_from_input_A": 0.12484690650267372
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0009436653118023384,
              -1.4663128663668698e-15,
              -0.0009765347966705519
            ],
            "branch_aligned_reduced_polarization": [
              0.0009436653118023384,
              -1.4663128663668698e-15,
              -0.0009765347966705519
            ],
            "target_residual": 0.0013579854306314926,
            "energy_eV": -40.30207943922484,
            "max_atomic_step_A": 0.0005832611597417952,
            "max_log_strain_component": 8.533618475807781e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.025770746790035,
              1.0128935997000454,
              1.0089508794959887
            ],
            "cell_volume_ratio": 1.0482965577629653,
            "cell_rmsd_from_input_A": 0.12543046030350166
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              8.21211991917161e-05,
              -3.5584768065905915e-16,
              -8.5382298099079e-05
            ],
            "branch_aligned_reduced_polarization": [
              8.21211991917161e-05,
              -3.5584768065905915e-16,
              -8.5382298099079e-05
            ],
            "target_residual": 0.00011846530371955115,
            "energy_eV": -40.28829715648513
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "R-3m",
        "spacegroup_number": 166,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 8.437309062474395e-16,
        "parent_symmetrization_rmsd_A": 0.4170189183450961,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -37.17648944835422,
        "reduced_polarization": [
          -5.456299636148911e-17,
          7.297595463486411e-16,
          4.199472896664618e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.2121038911878327e-18,
          2.419415038647676e-17,
          9.966900302665574e-18
        ],
        "ranking_score": 0.41701891834509774
      },
      "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": [
          -42.61158551432618,
          -42.369226629583366,
          -41.81116798052377,
          -41.02224065954514,
          -40.060796030836954,
          -39.02064921889034,
          -38.07311296858512,
          -37.41261170667839,
          -37.17648944835422
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.010204494953960155,
            -4.051124536464542e-17,
            -0.006947283828770674
          ],
          [
            0.007384027730329527,
            3.625664499151904e-17,
            -0.005027091353604735
          ],
          [
            0.004655352035855963,
            -3.061703257026167e-17,
            -0.003169391235611239
          ],
          [
            0.0024582083066761232,
            -7.647711326304807e-18,
            -0.001673561752889497
          ],
          [
            0.001062121029266719,
            -2.9053906136301913e-17,
            -0.0007230969361646929
          ],
          [
            0.00044103792162857757,
            -1.7850558480029794e-17,
            -0.00030026010793320805
          ],
          [
            0.0002981460531243556,
            5.733434316595293e-18,
            -0.0002029789657988807
          ],
          [
            0.00022445242119737584,
            -4.240679924814094e-18,
            -0.00015280831908579166
          ],
          [
            7.131224944448119e-18,
            -1.2936348824086568e-17,
            5.830310604900787e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.234906554728332e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208902,
            -8.763426292305216e-16,
            -0.030467105046417798
          ],
          [
            0.012651271400966864,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086919e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.709346892765145e-16,
            -3.9019448496732017e-16,
            2.4565542566798857e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.23490655472833e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208906,
            -8.763426292305216e-16,
            -0.030467105046417794
          ],
          [
            0.012651271400966863,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086916e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.706168622523819e-16,
            -3.9019448496732017e-16,
            2.456368441983159e-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": [
          [
            0.2927181888942352,
            -1.2212453270876722e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.1102230246251565e-15,
            -0.21181243162304053
          ],
          [
            0.13353980168152058,
            -9.43689570931383e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479723,
            -2.220446049250313e-16,
            -0.07051417199662735
          ],
          [
            0.030467177804208934,
            -8.881784197001252e-16,
            -0.03046710504641781
          ],
          [
            0.01265127140096689,
            -5.551115123125783e-16,
            -0.012651216997503933
          ],
          [
            0.008552386069998863,
            2.220446049250313e-16,
            -0.008552354689827124
          ],
          [
            0.00643846752120425,
            -1.1102230246251565e-16,
            -0.006438455035153112
          ],
          [
            2.220446049250313e-16,
            -3.885780586188048e-16,
            2.4424906541753444e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -37.17648944835422,
          -37.41261170667838,
          -38.07311296858511,
          -39.02064921889031,
          -40.06079603083694,
          -41.02224065954513,
          -41.81116798052376,
          -42.36922662958334,
          -42.611585514326194
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.636168564662448e-18,
            -1.274577714873853e-17,
            5.895629896632697e-17
          ],
          [
            -0.00022445242119739045,
            -1.898055200891625e-18,
            0.00015280831908581787
          ],
          [
            -0.00029814605312438163,
            6.403059217079107e-18,
            0.00020297896579890426
          ],
          [
            -0.0004410379216286019,
            -1.0875143021711337e-18,
            0.0003002601079332345
          ],
          [
            -0.0010621210292667447,
            7.035797780433431e-18,
            0.0007230969361647557
          ],
          [
            -0.0024582083066761362,
            1.805356901590989e-18,
            0.001673561752889496
          ],
          [
            -0.004655352035856029,
            1.6591497272763575e-17,
            0.003169391235611205
          ],
          [
            -0.007384027730329532,
            2.071109932975417e-17,
            0.005027091353604701
          ],
          [
            -0.01020449495396018,
            5.235576922011363e-17,
            0.006947283828770657
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.5706614104238755e-16,
            -3.844463393566102e-16,
            2.484076012384026e-15
          ],
          [
            -0.006438467521204683,
            -5.725036342344807e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.280230680237728e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237388e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.445433761703107e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.5706614104238755e-16,
            -3.844463393566102e-16,
            2.484076012384026e-15
          ],
          [
            -0.006438467521204683,
            -5.72503634234481e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.2802306802377307e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237385e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.4454337617031075e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.2927181888942347,
          4.4153730427115e-16,
          0.29271818979223374
        ],
        "actual_opposite_endpoint_branch_residual": 5.8085485538035926e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.234906554728332e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208902,
            -8.763426292305216e-16,
            -0.030467105046417798
          ],
          [
            0.012651271400966864,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086919e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.709346892765145e-16,
            -3.9019448496732017e-16,
            2.4565542566798857e-15
          ],
          [
            -0.006438467521204683,
            -5.725036342344807e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.280230680237728e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237388e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.445433761703107e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.23490655472833e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208906,
            -8.763426292305216e-16,
            -0.030467105046417794
          ],
          [
            0.012651271400966863,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086916e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.706168622523819e-16,
            -3.9019448496732017e-16,
            2.456368441983159e-15
          ],
          [
            -0.006438467521204683,
            -5.72503634234481e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.2802306802377307e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237385e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.4454337617031075e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "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": [
          [
            0.2927181888942352,
            -1.2212453270876722e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.1102230246251565e-15,
            -0.21181243162304053
          ],
          [
            0.13353980168152058,
            -9.43689570931383e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479723,
            -2.220446049250313e-16,
            -0.07051417199662735
          ],
          [
            0.030467177804208934,
            -8.881784197001252e-16,
            -0.03046710504641781
          ],
          [
            0.01265127140096689,
            -5.551115123125783e-16,
            -0.012651216997503933
          ],
          [
            0.008552386069998863,
            2.220446049250313e-16,
            -0.008552354689827124
          ],
          [
            0.00643846752120425,
            -1.1102230246251565e-16,
            -0.006438455035153112
          ],
          [
            2.220446049250313e-16,
            -3.885780586188048e-16,
            2.4424906541753444e-15
          ],
          [
            -0.006438467521204694,
            -5.551115123125783e-17,
            0.006438455035154167
          ],
          [
            -0.00855238606999964,
            2.220446049250313e-16,
            0.008552354689828179
          ],
          [
            -0.012651271400967556,
            -5.551115123125783e-17,
            0.012651216997505044
          ],
          [
            -0.0304671778042096,
            2.220446049250313e-16,
            0.030467105046420473
          ],
          [
            -0.07051424945479767,
            0.0,
            0.07051417199662735
          ],
          [
            -0.13353980168152257,
            5.551115123125783e-16,
            0.1335397384211423
          ],
          [
            -0.21181246521477254,
            6.661338147750939e-16,
            0.2118124316230391
          ],
          [
            -0.29271818889423595,
            1.5543122344752192e-15,
            0.2927181897922282
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_03_000",
        "incoming_03_001",
        "incoming_03_002",
        "incoming_03_003",
        "incoming_03_004",
        "incoming_03_005",
        "incoming_03_006",
        "incoming_03_007",
        "incoming_03_008"
      ],
      "reflected_structure_ids": [
        "reflected_03_001",
        "reflected_03_002",
        "reflected_03_003",
        "reflected_03_004",
        "reflected_03_005",
        "reflected_03_006",
        "reflected_03_007",
        "reflected_03_008"
      ]
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6653345369377348e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.5795959782972068,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015078133596272494,
            "step_scale": 0.6023175449705926,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.009413939069284,
              0.9946462590105539,
              0.9787178375187238
            ],
            "cell_volume_ratio": 0.9826422986284045,
            "cell_rmsd_from_input_A": 0.10931930374986457
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.38640868147099866,
              -0.2851478571384643,
              -0.3758082208018678
            ],
            "branch_aligned_reduced_polarization": [
              0.38640868147099866,
              -0.2851478571384643,
              -0.3758082208018678
            ],
            "target_residual": 0.2729249511454539,
            "energy_eV": -40.58220297781869,
            "max_atomic_step_A": 0.09767267856952894,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9906371415969994,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.020756310398901,
              0.9844049428538342,
              0.9493703909308051
            ],
            "cell_volume_ratio": 0.9539630246964145,
            "cell_rmsd_from_input_A": 0.2539612826249188
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4953305247814205,
              -0.49766459617454395,
              -0.48952403984524095
            ],
            "branch_aligned_reduced_polarization": [
              0.4953305247814205,
              -0.49766459617454395,
              -0.48952403984524095
            ],
            "target_residual": 0.01170486441651428,
            "energy_eV": -34.09007773760506,
            "max_atomic_step_A": 0.005638043878012393,
            "max_log_strain_component": 0.0011005000243859684,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0206622183771212,
              0.9834252842676727,
              0.948167044618531
            ],
            "cell_volume_ratio": 0.9517179607778709,
            "cell_rmsd_from_input_A": 0.25874946075947025
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5007700352683704,
              -0.5006811806562924,
              -0.5010168161448951
            ],
            "branch_aligned_reduced_polarization": [
              0.5007700352683704,
              -0.5006811806562924,
              -0.5010168161448951
            ],
            "target_residual": 0.001445986332425241,
            "energy_eV": -33.957492185659014,
            "max_atomic_step_A": 0.0007626479908686796,
            "max_log_strain_component": 0.00013665321693637434,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0206543471875489,
              0.9835470529296447,
              0.9483509356899408
            ],
            "cell_volume_ratio": 0.9520130641783754,
            "cell_rmsd_from_input_A": 0.25797458921801253
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49988568224736185,
              -0.49990874457039347,
              -0.4998516794725422
            ],
            "branch_aligned_reduced_polarization": [
              0.49988568224736185,
              -0.49990874457039347,
              -0.4998516794725422
            ],
            "target_residual": 0.00020831485992665785,
            "energy_eV": -33.98838645592882
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 0.00020831485992665785,
        "parent_symmetrization_rmsd_A": 0.2159526070558771,
        "parent_cell_rmsd_A": 0.25797458921801253,
        "energy_eV": -33.98838645592882,
        "reduced_polarization": [
          0.49988568224736185,
          -0.49990874457039347,
          -0.4998516794725422
        ],
        "cartesian_polarization_e_A2": [
          0.01726547767359761,
          -0.016536040775681646,
          -0.012048472633710545
        ],
        "ranking_score": 0.7808628840802335
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6653345369377348e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.6153451770774929,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01476877313305747,
            "step_scale": 0.589959700180214,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0212435672112097,
              0.9981005853590528,
              0.9913680746747634
            ],
            "cell_volume_ratio": 1.0105052479231165,
            "cell_rmsd_from_input_A": 0.10984066412800977
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.12651021090501105,
              -0.24826387128802918,
              -0.3748323648067633
            ],
            "branch_aligned_reduced_polarization": [
              0.12651021090501105,
              -0.24826387128802918,
              -0.3748323648067633
            ],
            "target_residual": 0.3082902023451078,
            "energy_eV": -41.616017248312914,
            "max_atomic_step_A": 0.09633409644271268,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7615859254536913,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.048048456175104,
              0.9932277309553984,
              0.9774084064747082
            ],
            "cell_volume_ratio": 1.0174340529292822,
            "cell_rmsd_from_input_A": 0.25695186905409784
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.11278894246201761,
              -0.3277552047924422,
              -0.4411919827519601
            ],
            "branch_aligned_reduced_polarization": [
              0.11278894246201761,
              -0.3277552047924422,
              -0.4411919827519601
            ],
            "target_residual": 0.2141214559787029,
            "energy_eV": -39.86610651612861,
            "max_atomic_step_A": 0.07520786564408014,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7640976158114848,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0771407753060196,
              0.9894556670455684,
              0.9650093360872004
            ],
            "cell_volume_ratio": 1.0284905880242028,
            "cell_rmsd_from_input_A": 0.4145350974923869
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.10408186933887537,
              -0.37614075017297166,
              -0.48249544694537927
            ],
            "branch_aligned_reduced_polarization": [
              0.10408186933887537,
              -0.37614075017297166,
              -0.48249544694537927
            ],
            "target_residual": 0.16272848143589055,
            "energy_eV": -39.37096908576024,
            "max_atomic_step_A": 0.03876809988214738,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5864636609614508,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.1097309135824862,
              0.9879430088575626,
              0.9549981450322024
            ],
            "cell_volume_ratio": 1.047013073690911,
            "cell_rmsd_from_input_A": 0.5884625677212704
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.09434118623215391,
              -0.38143492004464036,
              -0.4786028263407523
            ],
            "branch_aligned_reduced_polarization": [
              0.09434118623215391,
              -0.38143492004464036,
              -0.4786028263407523
            ],
            "target_residual": 0.15302214429655198,
            "energy_eV": -37.87061317914355,
            "max_atomic_step_A": 0.10169450253610653,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8797564334338547,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.646202099028224,
            "cell_principal_stretches": [
              1.0779254857116605,
              0.9879374242107855,
              0.9650686927786256
            ],
            "cell_volume_ratio": 1.0277237778854937,
            "cell_rmsd_from_input_A": 0.417848721685655
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.06860813609862376,
              -0.4048369967988174,
              -0.47585754309255524
            ],
            "branch_aligned_reduced_polarization": [
              0.06860813609862376,
              -0.4048369967988174,
              -0.47585754309255524
            ],
            "target_residual": 0.11977450372564019,
            "energy_eV": -37.984731141758246
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.11977450372564019,
        "parent_symmetrization_rmsd_A": 0.28199233643291965,
        "parent_cell_rmsd_A": 0.417848721685655,
        "energy_eV": -37.984731141758246,
        "reduced_polarization": [
          0.06860813609862376,
          -0.4048369967988174,
          -0.47585754309255524
        ],
        "cartesian_polarization_e_A2": [
          0.0020710579394870223,
          -0.013103377601265063,
          -0.010838202321169168
        ],
        "ranking_score": 1.126003524305614
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6653345369377348e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.61534517780716,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01563590028079757,
            "step_scale": 0.6245983304499717,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.011826705053751,
              1.0043146933579674,
              0.9805491042724482
            ],
            "cell_volume_ratio": 0.996426574080416,
            "cell_rmsd_from_input_A": 0.10781233417957953
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.38340080008262156,
              -0.2932945962844006,
              -0.08987802499320867
            ],
            "branch_aligned_reduced_polarization": [
              0.38340080008262156,
              -0.2932945962844006,
              -0.08987802499320867
            ],
            "target_residual": 0.2537726477051488,
            "energy_eV": -40.39084662285881,
            "max_atomic_step_A": 0.08758917691677809,
            "max_log_strain_component": 0.016240734845095948,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0210208936258656,
              1.0064434660187063,
              0.9577435374129903
            ],
            "cell_volume_ratio": 0.984177074256954,
            "cell_rmsd_from_input_A": 0.22119123327344972
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5035997909273697,
              -0.484340179983946,
              -0.020985550978116184
            ],
            "branch_aligned_reduced_polarization": [
              0.5035997909273697,
              -0.484340179983946,
              -0.020985550978116184
            ],
            "target_residual": 0.02643069820324638,
            "energy_eV": -33.89039582747548,
            "max_atomic_step_A": 0.009494305277736986,
            "max_log_strain_component": 0.0014279403124226634,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0227913384111431,
              1.0074945322655553,
              0.9566654968859023
            ],
            "cell_volume_ratio": 0.9858023528418205,
            "cell_rmsd_from_input_A": 0.22965637821642493
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5002110878320645,
              -0.49850654006695655,
              -0.0017117988675753122
            ],
            "branch_aligned_reduced_polarization": [
              0.5002110878320645,
              -0.49850654006695655,
              -0.0017117988675753122
            ],
            "target_residual": 0.0022814986319268193,
            "energy_eV": -33.21193231127744,
            "max_atomic_step_A": 0.000832684470583152,
            "max_log_strain_component": 0.0001400059121768516,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0229594973948715,
              1.0075865468677467,
              0.956553955227656
            ],
            "cell_volume_ratio": 0.9859395104110863,
            "cell_rmsd_from_input_A": 0.23050180658749697
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000146562555107,
              -0.4998644352144521,
              -0.0001351361219898409
            ],
            "branch_aligned_reduced_polarization": [
              0.5000146562555107,
              -0.4998644352144521,
              -0.0001351361219898409
            ],
            "target_residual": 0.0001919749680887857,
            "energy_eV": -33.146308837966096
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0001919749680887857,
        "parent_symmetrization_rmsd_A": 0.1831767715078854,
        "parent_cell_rmsd_A": 0.23050180658749697,
        "energy_eV": -33.146308837966096,
        "reduced_polarization": [
          0.5000146562555107,
          -0.4998644352144521,
          -0.0001351361219898409
        ],
        "cartesian_polarization_e_A2": [
          0.016489507393015156,
          -0.01609222872694801,
          4.4967648998989354e-05
        ],
        "ranking_score": 0.7411861730909373
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.29271818889423495,
              -1.6020002998223994e-16,
              -0.29271818979222924
            ],
            "branch_aligned_reduced_polarization": [
              0.29271818889423495,
              -1.6653345369377348e-16,
              -0.29271818979222924
            ],
            "target_residual": 0.6491285517867477,
            "energy_eV": -42.61158551432618,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013049618054936771,
            "step_scale": 0.5212855994058939,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0212979050746236,
              1.0065572565419911,
              0.9938097977072302
            ],
            "cell_volume_ratio": 1.0216313215680992,
            "cell_rmsd_from_input_A": 0.10586583284541558
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.14895874011489815,
              -0.23654014076203578,
              -0.12233328977769468
            ],
            "branch_aligned_reduced_polarization": [
              0.14895874011489815,
              -0.23654014076203578,
              -0.12233328977769468
            ],
            "target_residual": 0.32644331433518303,
            "energy_eV": -41.539494169577615,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01762900479548585,
            "step_scale": 0.9170359841618365,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0496739546503695,
              1.0105837144955852,
              0.9853189670735965
            ],
            "cell_volume_ratio": 1.0452100080164688,
            "cell_rmsd_from_input_A": 0.2504880534687697
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.13201631519109613,
              -0.3414751461940262,
              0.0074779448155528555
            ],
            "branch_aligned_reduced_polarization": [
              0.13201631519109613,
              -0.3414751461940262,
              0.0074779448155528555
            ],
            "target_residual": 0.20643244999152788,
            "energy_eV": -39.67987767559919,
            "max_atomic_step_A": 0.09322008428983003,
            "max_log_strain_component": 0.019270155030816194,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.0783971757444308,
              1.009499301691005,
              0.9740451282304432
            ],
            "cell_volume_ratio": 1.0603856532179636,
            "cell_rmsd_from_input_A": 0.40423999336167016
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.10019668072640583,
              -0.38851845150239583,
              0.005273473155374241
            ],
            "branch_aligned_reduced_polarization": [
              0.10019668072640583,
              -0.38851845150239583,
              0.005273473155374241
            ],
            "target_residual": 0.14998439919916148,
            "energy_eV": -39.54641035568793,
            "max_atomic_step_A": 0.05253640515232348,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7942598156049065,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.161956552239882,
            "cell_principal_stretches": [
              1.1128868503353866,
              1.0078740765998395,
              0.9654107592845984
            ],
            "cell_volume_ratio": 1.0828527914815627,
            "cell_rmsd_from_input_A": 0.5872439680839867
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.0905493778982996,
              -0.39037121025222793,
              0.01610106536945683
            ],
            "branch_aligned_reduced_polarization": [
              0.0905493778982996,
              -0.39037121025222793,
              0.01610106536945683
            ],
            "target_residual": 0.14309753906116557,
            "energy_eV": -38.22898329198921,
            "max_atomic_step_A": 0.06752065462964238,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9168532285177228,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.4411254735037247,
            "cell_principal_stretches": [
              1.0812995213503085,
              1.0107305395924233,
              0.9760646482924291
            ],
            "cell_volume_ratio": 1.0667434441843149,
            "cell_rmsd_from_input_A": 0.4166182433519301
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.041992088156679624,
              -0.43736698451236244,
              0.015522782034413074
            ],
            "branch_aligned_reduced_polarization": [
              0.041992088156679624,
              -0.43736698451236244,
              0.015522782034413074
            ],
            "target_residual": 0.07698822545637025,
            "energy_eV": -38.98220337822677
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.07698822545637025,
        "parent_symmetrization_rmsd_A": 0.29946755799091895,
        "parent_cell_rmsd_A": 0.4166182433519301,
        "energy_eV": -38.98220337822677,
        "reduced_polarization": [
          0.041992088156679624,
          -0.43736698451236244,
          0.015522782034413074
        ],
        "cartesian_polarization_e_A2": [
          0.0006698560169034479,
          -0.013831783683563768,
          0.0003552876091743878
        ],
        "ranking_score": 1.057598569741642
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 3,
      "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": 0.4170189183450961,
        "minimum_distance_A_by_image": [
          1.8405630312973134,
          1.8945785397278845,
          1.949541308297161,
          2.005373451718417,
          2.0620043519589264,
          2.119369980130545,
          2.177412266062633,
          2.236078518000196,
          2.295320892482
        ],
        "minimum_distance_A": 1.8405630312973134,
        "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": [
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977,
          193.2995364695977
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.709346892765145e-16,
        -3.9019448496732017e-16,
        2.4565542566798857e-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": [
          -42.61158551432618,
          -42.369226629583366,
          -41.81116798052377,
          -41.02224065954514,
          -40.060796030836954,
          -39.02064921889034,
          -38.07311296858512,
          -37.41261170667839,
          -37.17648944835422
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.010204494953960155,
            -4.051124536464542e-17,
            -0.006947283828770674
          ],
          [
            0.007384027730329527,
            3.625664499151904e-17,
            -0.005027091353604735
          ],
          [
            0.004655352035855963,
            -3.061703257026167e-17,
            -0.003169391235611239
          ],
          [
            0.0024582083066761232,
            -7.647711326304807e-18,
            -0.001673561752889497
          ],
          [
            0.001062121029266719,
            -2.9053906136301913e-17,
            -0.0007230969361646929
          ],
          [
            0.00044103792162857757,
            -1.7850558480029794e-17,
            -0.00030026010793320805
          ],
          [
            0.0002981460531243556,
            5.733434316595293e-18,
            -0.0002029789657988807
          ],
          [
            0.00022445242119737584,
            -4.240679924814094e-18,
            -0.00015280831908579166
          ],
          [
            7.131224944448119e-18,
            -1.2936348824086568e-17,
            5.830310604900787e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.234906554728332e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208902,
            -8.763426292305216e-16,
            -0.030467105046417798
          ],
          [
            0.012651271400966864,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086919e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.709346892765145e-16,
            -3.9019448496732017e-16,
            2.4565542566798857e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.23490655472833e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208906,
            -8.763426292305216e-16,
            -0.030467105046417794
          ],
          [
            0.012651271400966863,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086916e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.706168622523819e-16,
            -3.9019448496732017e-16,
            2.456368441983159e-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": [
          [
            0.2927181888942352,
            -1.2212453270876722e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.1102230246251565e-15,
            -0.21181243162304053
          ],
          [
            0.13353980168152058,
            -9.43689570931383e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479723,
            -2.220446049250313e-16,
            -0.07051417199662735
          ],
          [
            0.030467177804208934,
            -8.881784197001252e-16,
            -0.03046710504641781
          ],
          [
            0.01265127140096689,
            -5.551115123125783e-16,
            -0.012651216997503933
          ],
          [
            0.008552386069998863,
            2.220446049250313e-16,
            -0.008552354689827124
          ],
          [
            0.00643846752120425,
            -1.1102230246251565e-16,
            -0.006438455035153112
          ],
          [
            2.220446049250313e-16,
            -3.885780586188048e-16,
            2.4424906541753444e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -37.17648944835422,
          -37.41261170667838,
          -38.07311296858511,
          -39.02064921889031,
          -40.06079603083694,
          -41.02224065954513,
          -41.81116798052376,
          -42.36922662958334,
          -42.611585514326194
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.636168564662448e-18,
            -1.274577714873853e-17,
            5.895629896632697e-17
          ],
          [
            -0.00022445242119739045,
            -1.898055200891625e-18,
            0.00015280831908581787
          ],
          [
            -0.00029814605312438163,
            6.403059217079107e-18,
            0.00020297896579890426
          ],
          [
            -0.0004410379216286019,
            -1.0875143021711337e-18,
            0.0003002601079332345
          ],
          [
            -0.0010621210292667447,
            7.035797780433431e-18,
            0.0007230969361647557
          ],
          [
            -0.0024582083066761362,
            1.805356901590989e-18,
            0.001673561752889496
          ],
          [
            -0.004655352035856029,
            1.6591497272763575e-17,
            0.003169391235611205
          ],
          [
            -0.007384027730329532,
            2.071109932975417e-17,
            0.005027091353604701
          ],
          [
            -0.01020449495396018,
            5.235576922011363e-17,
            0.006947283828770657
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.5706614104238755e-16,
            -3.844463393566102e-16,
            2.484076012384026e-15
          ],
          [
            -0.006438467521204683,
            -5.725036342344807e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.280230680237728e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237388e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.445433761703107e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.5706614104238755e-16,
            -3.844463393566102e-16,
            2.484076012384026e-15
          ],
          [
            -0.006438467521204683,
            -5.72503634234481e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.2802306802377307e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237385e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.4454337617031075e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.2927181888942347,
          4.4153730427115e-16,
          0.29271818979223374
        ],
        "actual_opposite_endpoint_branch_residual": 5.8085485538035926e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.234906554728332e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208902,
            -8.763426292305216e-16,
            -0.030467105046417798
          ],
          [
            0.012651271400966864,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086919e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.709346892765145e-16,
            -3.9019448496732017e-16,
            2.4565542566798857e-15
          ],
          [
            -0.006438467521204683,
            -5.725036342344807e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.280230680237728e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237388e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.445433761703107e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.29271818889423523,
            -1.2219262742057904e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.0935962775499498e-15,
            -0.2118124316230405
          ],
          [
            0.13353980168152055,
            -9.23490655472833e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479726,
            -2.306751945796384e-16,
            -0.07051417199662734
          ],
          [
            0.030467177804208906,
            -8.763426292305216e-16,
            -0.030467105046417794
          ],
          [
            0.012651271400966863,
            -5.384200416369079e-16,
            -0.012651216997503954
          ],
          [
            0.00855238606999888,
            1.7293553851086916e-16,
            -0.008552354689827135
          ],
          [
            0.006438467521204282,
            -1.2791011912829482e-16,
            -0.0064384550351530975
          ],
          [
            2.706168622523819e-16,
            -3.9019448496732017e-16,
            2.456368441983159e-15
          ],
          [
            -0.006438467521204683,
            -5.72503634234481e-17,
            0.006438455035154202
          ],
          [
            -0.008552386069999623,
            1.9313319603530782e-16,
            0.008552354689828129
          ],
          [
            -0.012651271400967555,
            -3.2802306802377307e-17,
            0.012651216997505071
          ],
          [
            -0.030467177804209593,
            2.1221826410237385e-16,
            0.030467105046420445
          ],
          [
            -0.07051424945479765,
            5.4454337617031075e-17,
            0.0705141719966273
          ],
          [
            -0.13353980168152255,
            5.004434265972108e-16,
            0.13353973842114225
          ],
          [
            -0.21181246521477254,
            6.247015170952659e-16,
            0.21181243162303906
          ],
          [
            -0.29271818889423595,
            1.579188431273041e-15,
            0.2927181897922282
          ]
        ],
        "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": [
          [
            0.2927181888942352,
            -1.2212453270876722e-15,
            -0.29271818979222886
          ],
          [
            0.21181246521477237,
            1.1102230246251565e-15,
            -0.21181243162304053
          ],
          [
            0.13353980168152058,
            -9.43689570931383e-16,
            -0.1335397384211437
          ],
          [
            0.07051424945479723,
            -2.220446049250313e-16,
            -0.07051417199662735
          ],
          [
            0.030467177804208934,
            -8.881784197001252e-16,
            -0.03046710504641781
          ],
          [
            0.01265127140096689,
            -5.551115123125783e-16,
            -0.012651216997503933
          ],
          [
            0.008552386069998863,
            2.220446049250313e-16,
            -0.008552354689827124
          ],
          [
            0.00643846752120425,
            -1.1102230246251565e-16,
            -0.006438455035153112
          ],
          [
            2.220446049250313e-16,
            -3.885780586188048e-16,
            2.4424906541753444e-15
          ],
          [
            -0.006438467521204694,
            -5.551115123125783e-17,
            0.006438455035154167
          ],
          [
            -0.00855238606999964,
            2.220446049250313e-16,
            0.008552354689828179
          ],
          [
            -0.012651271400967556,
            -5.551115123125783e-17,
            0.012651216997505044
          ],
          [
            -0.0304671778042096,
            2.220446049250313e-16,
            0.030467105046420473
          ],
          [
            -0.07051424945479767,
            0.0,
            0.07051417199662735
          ],
          [
            -0.13353980168152257,
            5.551115123125783e-16,
            0.1335397384211423
          ],
          [
            -0.21181246521477254,
            6.661338147750939e-16,
            0.2118124316230391
          ],
          [
            -0.29271818889423595,
            1.5543122344752192e-15,
            0.2927181897922282
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_03_000",
        "incoming_03_001",
        "incoming_03_002",
        "incoming_03_003",
        "incoming_03_004",
        "incoming_03_005",
        "incoming_03_006",
        "incoming_03_007",
        "incoming_03_008"
      ],
      "reflected_structure_ids": [
        "reflected_03_001",
        "reflected_03_002",
        "reflected_03_003",
        "reflected_03_004",
        "reflected_03_005",
        "reflected_03_006",
        "reflected_03_007",
        "reflected_03_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_03_000",
        "extension_plus_03_001",
        "extension_plus_03_002",
        "extension_plus_03_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_03_000",
        "extension_minus_03_001",
        "extension_minus_03_002",
        "extension_minus_03_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": "R-3m",
        "spacegroup_number": 166,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 8.437309062474395e-16,
        "parent_symmetrization_rmsd_A": 0.4170189183450961,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -37.17648944835422,
        "reduced_polarization": [
          -5.456299636148911e-17,
          7.297595463486411e-16,
          4.199472896664618e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.2121038911878327e-18,
          2.419415038647676e-17,
          9.966900302665574e-18
        ],
        "ranking_score": 0.41701891834509774
      }
    }
  ],
  "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": 86,
      "full_response": 30,
      "energy_polarization": 56
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 111,
      "full_response": 55,
      "energy_polarization": 56
    },
    "elapsed_seconds": 162.03448532300536
  }
}