{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "H6O6Pr2",
  "input_spacegroup": "Pm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -83.5294686968296,
  "input_cartesian_polarization_e_A2": [
    0.00010367360157102934,
    -4.849460144126527e-19,
    2.299142582540429e-05
  ],
  "input_reduced_polarization": [
    0.0025699974520093627,
    -1.814557286212175e-17,
    0.0017462048005844578
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.019187630808462e-16,
      "parent_symmetrization_rmsd_A": 0.014741069069691566,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -83.53192073059222,
      "reduced_polarization": [
        -6.972914079519284e-16,
        1.574607770918802e-17,
        -7.890946329901613e-17
      ],
      "cartesian_polarization_e_A2": [
        -2.8186329895129025e-17,
        4.2081876861779996e-19,
        1.2220646527958039e-17
      ],
      "ranking_score": 0.01474106906969297
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.1230491691671203e-17,
      "parent_symmetrization_rmsd_A": 0.03749342704967845,
      "parent_cell_rmsd_A": 1.0243445467652204e-15,
      "energy_eV": -83.5359708760629,
      "reduced_polarization": [
        3.0974975146563767e-17,
        -1.2638382005769733e-17,
        3.8799297595657384e-17
      ],
      "cartesian_polarization_e_A2": [
        5.420448056755585e-19,
        -3.377646453431382e-19,
        1.5768576165107155e-18
      ],
      "ranking_score": 0.03749342704967881
    },
    {
      "candidate_id": "symmetry_projection_01",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.6845197900150783e-16,
      "parent_symmetrization_rmsd_A": 1.6594979748736012,
      "parent_cell_rmsd_A": 3.424338219191669,
      "energy_eV": -83.53167877370812,
      "reduced_polarization": [
        -9.556530232281484e-17,
        3.1592401253364613e-16,
        1.6375638041529001e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1842596040028834e-17,
        1.2780134893197785e-17,
        4.382421171556631e-18
      ],
      "ranking_score": 2.5155825296715193
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4032670427728465e-08,
      "parent_symmetrization_rmsd_A": 0.001395361733942713,
      "parent_cell_rmsd_A": 5.1928372491436165e-06,
      "energy_eV": -83.52953620850509,
      "reduced_polarization": [
        1.3995882383916607e-08,
        -2.85297018378751e-16,
        1.0154386386275333e-09
      ],
      "cartesian_polarization_e_A2": [
        5.658316807546794e-10,
        -7.624650304268189e-18,
        -2.7186100390827303e-10
      ],
      "ranking_score": 0.5013966880085958
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.764987966405355e-16,
      "parent_symmetrization_rmsd_A": 0.014741069383876577,
      "parent_cell_rmsd_A": 5.1928372491436165e-06,
      "energy_eV": -83.53192311596644,
      "reduced_polarization": [
        -6.260010810800225e-16,
        1.8845108851608663e-16,
        -5.838312891889678e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.522969060303302e-17,
        5.036413116477216e-18,
        -1.3009059217188902e-17
      ],
      "ranking_score": 0.014742367593190617
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.7876507916797143e-16,
      "parent_symmetrization_rmsd_A": 0.03748950021538773,
      "parent_cell_rmsd_A": 5.1928372488631224e-06,
      "energy_eV": -83.53607681598524,
      "reduced_polarization": [
        3.530237290117863e-16,
        -1.3412849742944226e-16,
        2.909945238406831e-17
      ],
      "cartesian_polarization_e_A2": [
        1.571927988743659e-17,
        -3.5846252153081004e-18,
        1.1826417470171729e-18
      ],
      "ranking_score": 0.037490798424700704
    },
    {
      "candidate_id": "symmetry_parent_00_01",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0573343679353835e-15,
      "parent_symmetrization_rmsd_A": 1.6594624552080355,
      "parent_cell_rmsd_A": 3.424335921855122,
      "energy_eV": -83.53093666868122,
      "reduced_polarization": [
        -9.39655781279493e-16,
        2.7567123197471357e-16,
        3.987585111152941e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.0331003892237304e-17,
        1.1151771450632971e-17,
        1.0671515980784065e-17
      ],
      "ranking_score": 2.5155464356718182
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.125960088937343e-07,
      "parent_symmetrization_rmsd_A": 0.3076882847534145,
      "parent_cell_rmsd_A": 0.0011772235867836833,
      "energy_eV": -80.88478562755073,
      "reduced_polarization": [
        0.4999995663540288,
        -3.510073218486525e-15,
        -2.733236908992306e-07
      ],
      "cartesian_polarization_e_A2": [
        0.020224502723156717,
        -2.937836909149287e-17,
        -0.011406455607487714
      ],
      "ranking_score": 0.8079836158421282
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.4769578184956326e-07,
      "parent_symmetrization_rmsd_A": 0.31144420710438586,
      "parent_cell_rmsd_A": 0.0013833763968721282,
      "energy_eV": -80.87957673925739,
      "reduced_polarization": [
        3.71907401702052e-07,
        1.1818077027661011e-15,
        0.49999975076838554
      ],
      "cartesian_polarization_e_A2": [
        -7.707978582488768e-05,
        -1.466579258129304e-16,
        0.023379606099852564
      ],
      "ranking_score": 0.8117909465951676
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.371766334489826e-05,
      "parent_symmetrization_rmsd_A": 0.1502861892694768,
      "parent_cell_rmsd_A": 0.0010607539635322744,
      "energy_eV": -83.29755021492099,
      "reduced_polarization": [
        6.8405380187797595e-06,
        0.4999378840736814,
        1.2440231482124862e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.3328972052813468e-06,
        0.01336099351806665,
        -3.0729212068466686e-06
      ],
      "ranking_score": 0.6506788130870497
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.976683421769172e-07,
      "parent_symmetrization_rmsd_A": 0.31677021853057014,
      "parent_cell_rmsd_A": 0.0012892643290462974,
      "energy_eV": -80.85663114599082,
      "reduced_polarization": [
        0.49999968109820936,
        -1.1977698118305284e-15,
        0.49999976242525745
      ],
      "cartesian_polarization_e_A2": [
        0.02015402656132422,
        -3.9068429759283555e-17,
        0.011964680583608629
      ],
      "ranking_score": 0.817093329949516
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.836835003686647e-06,
      "parent_symmetrization_rmsd_A": 0.34401825288069376,
      "parent_cell_rmsd_A": 0.0016039310123295099,
      "energy_eV": -80.52932027934247,
      "reduced_polarization": [
        0.499995222199481,
        0.499995214457572,
        -1.006736677659175e-06
      ],
      "cartesian_polarization_e_A2": [
        0.020222762083659505,
        0.013362947419942948,
        -0.011409938586604818
      ],
      "ranking_score": 0.8444329093037835
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.837332473925589e-06,
      "parent_symmetrization_rmsd_A": 0.34772249401282695,
      "parent_cell_rmsd_A": 0.0017660094003159685,
      "energy_eV": -80.5048778124214,
      "reduced_polarization": [
        2.3907767807745253e-06,
        0.49999899465074576,
        0.49999591671153054
      ],
      "cartesian_polarization_e_A2": [
        -7.867555079550578e-05,
        0.013356778262233469,
        0.023375903456788038
      ],
      "ranking_score": 0.8481736710278538
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 7.83524305147848e-06,
      "parent_symmetrization_rmsd_A": 0.3524125991231098,
      "parent_cell_rmsd_A": 0.0016897223538411216,
      "energy_eV": -80.47863139032724,
      "reduced_polarization": [
        0.49999438760377424,
        0.4999983524738909,
        0.49999478677642906
      ],
      "cartesian_polarization_e_A2": [
        0.020152266869507614,
        0.013357194651410623,
        0.011961020502262294
      ],
      "ranking_score": 0.8528507001976731
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "target_residual": 0.0031071076757844783,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.0012528502235254057,
            "max_log_strain_component": 1.2049337321987502e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0000012049344582,
              1.0000008045448947,
              0.9999992295827311
            ],
            "cell_volume_ratio": 1.0000012390615052,
            "cell_rmsd_from_input_A": 5.1928372491436165e-06
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3995882383916607e-08,
              -2.85297018378751e-16,
              1.0154386386275333e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.3995882383916607e-08,
              -2.85297018378751e-16,
              1.0154386386275333e-09
            ],
            "target_residual": 1.4032670427728465e-08,
            "energy_eV": -83.52953620850509
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.019187630808462e-16,
        "parent_symmetrization_rmsd_A": 0.014741069069691566,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.53192073059222,
        "reduced_polarization": [
          -6.972914079519284e-16,
          1.574607770918802e-17,
          -7.890946329901613e-17
        ],
        "cartesian_polarization_e_A2": [
          -2.8186329895129025e-17,
          4.2081876861779996e-19,
          1.2220646527958039e-17
        ],
        "ranking_score": 0.01474106906969297
      },
      "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": [
          -83.52946869682958,
          -83.5300438759358,
          -83.53054212407594,
          -83.53096354499854,
          -83.5313082259168,
          -83.53157623782555,
          -83.53176763573462,
          -83.53188245883234,
          -83.53192073059222
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00010367360157101928,
            -1.9657575918196836e-20,
            2.299142582537413e-05
          ],
          [
            9.069929067664639e-05,
            1.442216343871893e-18,
            2.013643282546753e-05
          ],
          [
            7.773105054196226e-05,
            -7.149895716265719e-18,
            1.72740051450896e-05
          ],
          [
            6.476799631289399e-05,
            -4.214110920506916e-18,
            1.4405107432494352e-05
          ],
          [
            5.180924988797046e-05,
            2.0920167624310242e-18,
            1.1530747054096462e-05
          ],
          [
            3.885393987510663e-05,
            -6.650097105430121e-18,
            8.651968803745969e-06
          ],
          [
            2.5901201033733363e-05,
            1.046964215836207e-17,
            5.769848680050355e-06
          ],
          [
            1.2950173233300705e-05,
            5.028711548941028e-18,
            2.8854868560900857e-06
          ],
          [
            -5.4204480567555813e-17,
            5.913478252061289e-20,
            2.7003686682745988e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634293e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.488314533586129e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.917501102777263e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406741763343878e-15,
            2.212688573620141e-18,
            -7.669201653482282e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634296e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.4883145335861295e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.9175011027772636e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406701963869505e-15,
            2.2126885736201428e-18,
            -7.66801986490373e-17
          ]
        ],
        "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": [
          [
            0.002569997452009143,
            0.0,
            0.0017462048005837394
          ],
          [
            0.0022483749100391526,
            0.0,
            0.0015281522791602553
          ],
          [
            0.0019269021790162544,
            -2.7755575615628914e-16,
            0.0013100138340063072
          ],
          [
            0.0016055574137842088,
            -1.6653345369377348e-16,
            0.0010917994387894536
          ],
          [
            0.001284318939766771,
            1.1102230246251565e-16,
            0.0008735200642671082
          ],
          [
            0.0009631652514879852,
            -2.220446049250313e-16,
            0.0006551875643843186
          ],
          [
            0.0006420749982710694,
            4.440892098500626e-16,
            0.0004368145361774989
          ],
          [
            0.0003210269578951541,
            2.220446049250313e-16,
            0.000218414156523683
          ],
          [
            -1.3322676295501878e-15,
            0.0,
            -5.551115123125783e-17
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.53192073059222,
          -83.53188245883233,
          -83.5317676357346,
          -83.53157623782553,
          -83.5313082259168,
          -83.53096354499854,
          -83.53054212407596,
          -83.53004387593582,
          -83.52946869682958
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.395490606023617e-17,
            1.2586077949998382e-18,
            2.049914901463929e-17
          ],
          [
            -1.2950173233449718e-05,
            1.051526884651501e-17,
            -2.885486856120046e-06
          ],
          [
            -2.5901201033809745e-05,
            -1.3980010271045655e-17,
            -5.7698486800895794e-06
          ],
          [
            -3.8853939875092246e-05,
            -7.496079165217531e-18,
            -8.65196880382501e-06
          ],
          [
            -5.1809249887852196e-05,
            -2.126150237659883e-18,
            -1.1530747054161704e-05
          ],
          [
            -6.476799631279444e-05,
            1.4229204300966006e-19,
            -1.4405107432389294e-05
          ],
          [
            -7.773105054192018e-05,
            5.012295499311189e-18,
            -1.7274005145063186e-05
          ],
          [
            -9.069929067668877e-05,
            1.4475559778243369e-18,
            -2.0136432825540262e-05
          ],
          [
            -0.00010367360157099475,
            -1.5410174170134077e-18,
            -2.299142582542952e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0872730127351366e-15,
            4.7094230636506264e-17,
            -9.215750184644045e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579176e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.324243436167071e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944323e-17,
            -0.0017462048005845799
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0872730127351366e-15,
            4.7094230636506264e-17,
            -9.215750184644045e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579175e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.3242434361670774e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944324e-17,
            -0.0017462048005845799
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0025699974520117927,
          5.160918765307499e-18,
          -0.0017462048005838433
        ],
        "actual_opposite_endpoint_branch_residual": 3.3664424080525954e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634293e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.488314533586129e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.917501102777263e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406741763343878e-15,
            2.212688573620141e-18,
            -7.669201653482282e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579176e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.324243436167071e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944323e-17,
            -0.0017462048005845799
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634296e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.4883145335861295e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.9175011027772636e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406701963869505e-15,
            2.2126885736201428e-18,
            -7.66801986490373e-17
          ],
          [
            -0.0003210269578988495,
            3.934573567953397e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579175e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.3242434361670774e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944324e-17,
            -0.0017462048005845799
          ]
        ],
        "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": [
          [
            0.002569997452009143,
            0.0,
            0.0017462048005837394
          ],
          [
            0.0022483749100391526,
            0.0,
            0.0015281522791602553
          ],
          [
            0.0019269021790162544,
            -2.7755575615628914e-16,
            0.0013100138340063072
          ],
          [
            0.0016055574137842088,
            -1.6653345369377348e-16,
            0.0010917994387894536
          ],
          [
            0.001284318939766771,
            1.1102230246251565e-16,
            0.0008735200642671082
          ],
          [
            0.0009631652514879852,
            -2.220446049250313e-16,
            0.0006551875643843186
          ],
          [
            0.0006420749982710694,
            4.440892098500626e-16,
            0.0004368145361774989
          ],
          [
            0.0003210269578951541,
            2.220446049250313e-16,
            0.000218414156523683
          ],
          [
            -1.3322676295501878e-15,
            0.0,
            -5.551115123125783e-17
          ],
          [
            -0.00032102695789887337,
            4.440892098500626e-16,
            -0.00021841415652618101
          ],
          [
            -0.0006420749982730123,
            -4.996003610813204e-16,
            -0.00043681453617927524
          ],
          [
            -0.0009631652514876521,
            -2.7755575615628914e-16,
            -0.0006551875643858174
          ],
          [
            -0.0012843189397638843,
            -5.551115123125783e-17,
            -0.0008735200642670526
          ],
          [
            -0.0016055574137817108,
            0.0,
            -0.0010917994387859564
          ],
          [
            -0.0019269021790151997,
            2.220446049250313e-16,
            -0.001310013834005197
          ],
          [
            -0.0022483749100402073,
            0.0,
            -0.0015281522791623092
          ],
          [
            -0.0025699974520085322,
            -5.551115123125783e-17,
            -0.001746204800584572
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.002569997452009365,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "target_residual": 0.497433067523762,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 7.322700109189144e-05,
            "step_scale": 0.44153102108457215,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0000748079976207,
              0.9999592077105742,
              0.9999297340014114
            ],
            "cell_volume_ratio": 0.9999637442680838,
            "cell_rmsd_from_input_A": 0.000496478352691531
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2204884610792942,
              -1.5158328889399365e-15,
              0.00031274403596098267
            ],
            "branch_aligned_reduced_polarization": [
              0.2204884610792942,
              -1.5158328889399365e-15,
              0.00031274403596098267
            ],
            "target_residual": 0.2795117138845048,
            "energy_eV": -83.05121544222688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 7.393935397976543e-05,
            "step_scale": 0.7682122049589206,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001501951764757,
              0.9999168673797274,
              0.9998588410125276
            ],
            "cell_volume_ratio": 0.9999258816178922,
            "cell_rmsd_from_input_A": 0.0009963478227891895
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.42930702125704745,
              -3.2785673246171686e-15,
              -0.001919961961755594
            ],
            "branch_aligned_reduced_polarization": [
              0.42930702125704745,
              -3.2785673246171686e-15,
              -0.001919961961755594
            ],
            "target_residual": 0.07071904621448263,
            "energy_eV": -81.61617662483003,
            "max_atomic_step_A": 0.041006101688727765,
            "max_log_strain_component": 2.669242620842336e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001771781778876,
              0.9998997762882612,
              0.9998333221632786
            ],
            "cell_volume_ratio": 0.9999102460483289,
            "cell_rmsd_from_input_A": 0.001174669601712012
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4988983748807651,
              2.6430010919868317e-15,
              -0.0002919082595115324
            ],
            "branch_aligned_reduced_polarization": [
              0.4988983748807651,
              2.6430010919868317e-15,
              -0.0002919082595115324
            ],
            "target_residual": 0.0011396439511094456,
            "energy_eV": -80.8959639335146,
            "max_atomic_step_A": 0.000563419466922503,
            "max_log_strain_component": 4.069966960504682e-07,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001775715223282,
              0.9998993728212392,
              0.9998329384293023
            ],
            "cell_volume_ratio": 0.9999098520528906,
            "cell_rmsd_from_input_A": 0.0011772235867836833
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999995663540288,
              -3.510073218486525e-15,
              -2.733236908992306e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4999995663540288,
              -3.510073218486525e-15,
              -2.733236908992306e-07
            ],
            "target_residual": 5.125960088937343e-07,
            "energy_eV": -80.88478562755073
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.125960088937343e-07,
        "parent_symmetrization_rmsd_A": 0.3076882847534145,
        "parent_cell_rmsd_A": 0.0011772235867836833,
        "energy_eV": -80.88478562755073,
        "reduced_polarization": [
          0.4999995663540288,
          -3.510073218486525e-15,
          -2.733236908992306e-07
        ],
        "cartesian_polarization_e_A2": [
          0.020224502723156717,
          -2.937836909149287e-17,
          -0.011406455607487714
        ],
        "ranking_score": 0.8079836158421282
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.001746204800584461
            ],
            "target_residual": 0.4982604231900467,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 9.046213856779538e-05,
            "step_scale": 0.4390078831732064,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.000070263497384,
              0.999918850580673,
              0.999909541953008
            ],
            "cell_volume_ratio": 0.9998986513144581,
            "cell_rmsd_from_input_A": 0.0005722201740693805
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0020408276677028997,
              4.328688988992998e-15,
              0.21882884960631405
            ],
            "branch_aligned_reduced_polarization": [
              0.0020408276677028997,
              4.328688988992998e-15,
              0.21882884960631405
            ],
            "target_residual": 0.28117855677714476,
            "energy_eV": -83.06007420138911,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 9.10193348897275e-05,
            "step_scale": 0.7526275057596549,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001412885120786,
              0.9998368355804618,
              0.9998185349933089
            ],
            "cell_volume_ratio": 0.9997966400064865,
            "cell_rmsd_from_input_A": 0.0011506900754279154
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0015127349705710176,
              7.013330355881977e-15,
              0.4255097046318496
            ],
            "branch_aligned_reduced_polarization": [
              0.0015127349705710176,
              7.013330355881977e-15,
              0.4255097046318496
            ],
            "target_residual": 0.0745056539540824,
            "energy_eV": -81.67083633713374,
            "max_atomic_step_A": 0.04551073329978898,
            "max_log_strain_component": 3.543072944332933e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.000169354339103,
              0.9998044324903019,
              0.9997831113208498
            ],
            "cell_volume_ratio": 0.999756870722572,
            "cell_rmsd_from_input_A": 0.0013793275006524464
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0001475120918046987,
              -2.3903190370938393e-16,
              0.4988283324055181
            ],
            "branch_aligned_reduced_polarization": [
              0.0001475120918046987,
              -2.3903190370938393e-16,
              0.4988283324055181
            ],
            "target_residual": 0.0011809169188336619,
            "energy_eV": -80.89429468769535,
            "max_atomic_step_A": 0.0007617249502920139,
            "max_log_strain_component": 5.754720079117518e-07,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001698507675874,
              0.9998038595634784,
              0.999782535973821
            ],
            "cell_volume_ratio": 0.9997562187145853,
            "cell_rmsd_from_input_A": 0.0013833763968721282
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              3.71907401702052e-07,
              1.1818077027661011e-15,
              0.49999975076838554
            ],
            "branch_aligned_reduced_polarization": [
              3.71907401702052e-07,
              1.1818077027661011e-15,
              0.49999975076838554
            ],
            "target_residual": 4.4769578184956326e-07,
            "energy_eV": -80.87957673925739
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.4769578184956326e-07,
        "parent_symmetrization_rmsd_A": 0.31144420710438586,
        "parent_cell_rmsd_A": 0.0013833763968721282,
        "energy_eV": -80.87957673925739,
        "reduced_polarization": [
          3.71907401702052e-07,
          1.1818077027661011e-15,
          0.49999975076838554
        ],
        "cartesian_polarization_e_A2": [
          -7.707978582488768e-05,
          -1.466579258129304e-16,
          0.023379606099852564
        ],
        "ranking_score": 0.8117909465951676
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.0025699974520093627,
              0.0,
              0.0017462048005844578
            ],
            "target_residual": 0.5000096540249087,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00023042292733583799,
            "step_scale": 0.8810705455382976,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0002544908655089,
              0.9999993553664069,
              0.999747309777072
            ],
            "cell_volume_ratio": 1.0000010917005155,
            "cell_rmsd_from_input_A": 0.0009334928466533892
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0003842771391173637,
              0.44029260408475773,
              0.00036639736637914796
            ],
            "branch_aligned_reduced_polarization": [
              0.0003842771391173637,
              0.44029260408475773,
              0.00036639736637914796
            ],
            "target_residual": 0.05970975668120937,
            "energy_eV": -83.35137665079242,
            "max_atomic_step_A": 0.016305349696602,
            "max_log_strain_component": 3.141249744992112e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0002892750400942,
              0.9999992136309778,
              0.9997129521826696
            ],
            "cell_volume_ratio": 1.0000013578162865,
            "cell_rmsd_from_input_A": 0.0010607539635322744
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.8405380187797595e-06,
              0.4999378840736814,
              1.2440231482124862e-05
            ],
            "branch_aligned_reduced_polarization": [
              6.8405380187797595e-06,
              0.4999378840736814,
              1.2440231482124862e-05
            ],
            "target_residual": 6.371766334489826e-05,
            "energy_eV": -83.29755021492099
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.371766334489826e-05,
        "parent_symmetrization_rmsd_A": 0.1502861892694768,
        "parent_cell_rmsd_A": 0.0010607539635322744,
        "energy_eV": -83.29755021492099,
        "reduced_polarization": [
          6.8405380187797595e-06,
          0.4999378840736814,
          1.2440231482124862e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.3328972052813468e-06,
          0.01336099351806665,
          -3.0729212068466686e-06
        ],
        "ranking_score": 0.6506788130870497
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.002569997452009365,
              -1.814557286212175e-17,
              0.001746204800584461
            ],
            "target_residual": 0.7040550062782843,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00013069950577405145,
            "step_scale": 0.43616589772962205,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.000073639649928,
              0.9999200118070517,
              0.9998693090350342
            ],
            "cell_volume_ratio": 0.9998629554321784,
            "cell_rmsd_from_input_A": 0.0005226811160968667
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21752150522991512,
              -2.593471411908505e-16,
              0.2166605426819952
            ],
            "branch_aligned_reduced_polarization": [
              0.2175215052299151,
              -2.593471411908505e-16,
              0.2166605426819952
            ],
            "target_residual": 0.40009417401511155,
            "energy_eV": -83.06593226144278,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00013256769011983543,
            "step_scale": 0.7386004279621314,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001483026864684,
              0.9998389060313454,
              0.9997367674558734
            ],
            "cell_volume_ratio": 0.9997239556563894,
            "cell_rmsd_from_input_A": 0.001052779350100729
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4202904266872251,
              -2.5806964012940986e-16,
              0.4192031199039713
            ],
            "branch_aligned_reduced_polarization": [
              0.4202904266872251,
              -2.5806964012940986e-16,
              0.4192031199039713
            ],
            "target_residual": 0.11349780575392933,
            "energy_eV": -81.70581225365483,
            "max_atomic_step_A": 0.050081398888853365,
            "max_log_strain_component": 5.798825943031058e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001808838147925,
              0.9998034744939204,
              0.9996787961416841
            ],
            "cell_volume_ratio": 0.9996631239377034,
            "cell_rmsd_from_input_A": 0.0012845472373685626
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49856398279454645,
              2.6173013584833554e-16,
              0.4984470203848938
            ],
            "branch_aligned_reduced_polarization": [
              0.49856398279454645,
              2.6173013584833554e-16,
              0.4984470203848938
            ],
            "target_residual": 0.0021151574644205644,
            "energy_eV": -80.87446928740704,
            "max_atomic_step_A": 0.0009550543135466496,
            "max_log_strain_component": 1.1825608274774017e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001815411384598,
              0.9998027558441851,
              0.9996776139613985
            ],
            "cell_volume_ratio": 0.9996618802100925,
            "cell_rmsd_from_input_A": 0.0012892643290462974
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999968109820936,
              -1.1977698118305284e-15,
              0.49999976242525745
            ],
            "branch_aligned_reduced_polarization": [
              0.49999968109820936,
              -1.1977698118305284e-15,
              0.49999976242525745
            ],
            "target_residual": 3.976683421769172e-07,
            "energy_eV": -80.85663114599082
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.976683421769172e-07,
        "parent_symmetrization_rmsd_A": 0.31677021853057014,
        "parent_cell_rmsd_A": 0.0012892643290462974,
        "energy_eV": -80.85663114599082,
        "reduced_polarization": [
          0.49999968109820936,
          -1.1977698118305284e-15,
          0.49999976242525745
        ],
        "cartesian_polarization_e_A2": [
          0.02015402656132422,
          -3.9068429759283555e-17,
          0.011964680583608629
        ],
        "ranking_score": 0.817093329949516
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.002569997452009365,
              0.0,
              0.0017462048005844578
            ],
            "target_residual": 0.7052940214308494,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00010345309645819758,
            "step_scale": 0.3955746816835796,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001062125880196,
              1.0000167335663952,
              0.9998445890261428
            ],
            "cell_volume_ratio": 0.999967517850416,
            "cell_rmsd_from_input_A": 0.0006110862452919304
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19805583337514152,
              0.1985202003827505,
              0.0005363190034892599
            ],
            "branch_aligned_reduced_polarization": [
              0.19805583337514154,
              0.19852020038275053,
              0.0005363190034892599
            ],
            "target_residual": 0.42668564186542607,
            "energy_eV": -83.1099711882523,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.00010072582674077817,
            "step_scale": 0.6455690676529552,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0002101576700395,
              1.0000326849785106,
              0.9996907785862029
            ],
            "cell_volume_ratio": 0.9999335530094805,
            "cell_rmsd_from_input_A": 0.001218964126327362
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.38769898117684143,
              0.3920611866088172,
              -0.001610112843393146
            ],
            "branch_aligned_reduced_polarization": [
              0.38769898117684143,
              0.3920611866088172,
              -0.001610112843393146
            ],
            "target_residual": 0.15577194461257923,
            "energy_eV": -81.82042169323267,
            "max_atomic_step_A": 0.07060831488824898,
            "max_log_strain_component": 5.950140310933569e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.000271450790296,
              1.0000418268309714,
              0.9995965159221463
            ],
            "cell_volume_ratio": 0.9999096784902266,
            "cell_rmsd_from_input_A": 0.0015910756009274308
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4962586227733034,
              0.49665749382890156,
              -0.0008393357840435401
            ],
            "branch_aligned_reduced_polarization": [
              0.4962586227733034,
              0.49665749382890156,
              -0.0008393357840435401
            ],
            "target_residual": 0.005086721499615546,
            "energy_eV": -80.57608098165224,
            "max_atomic_step_A": 0.0021518462185110354,
            "max_log_strain_component": 2.134976032075686e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.00027335415072,
              1.0000422278856953,
              0.9995928853624376
            ],
            "cell_volume_ratio": 0.9999083504592556,
            "cell_rmsd_from_input_A": 0.0016039310123295099
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.499995222199481,
              0.499995214457572,
              -1.006736677659175e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.499995222199481,
              0.499995214457572,
              -1.006736677659175e-06
            ],
            "target_residual": 6.836835003686647e-06,
            "energy_eV": -80.52932027934247
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.836835003686647e-06,
        "parent_symmetrization_rmsd_A": 0.34401825288069376,
        "parent_cell_rmsd_A": 0.0016039310123295099,
        "energy_eV": -80.52932027934247,
        "reduced_polarization": [
          0.499995222199481,
          0.499995214457572,
          -1.006736677659175e-06
        ],
        "cartesian_polarization_e_A2": [
          0.020222762083659505,
          0.013362947419942948,
          -0.011409938586604818
        ],
        "ranking_score": 0.8444329093037835
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.0025699974520093627,
              0.0,
              0.001746204800584461
            ],
            "target_residual": 0.7058777863890636,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000102977770249283,
            "step_scale": 0.3937571719028612,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0000891053338081,
              1.0000032704684783,
              0.9998167381846365
            ],
            "cell_volume_ratio": 0.9999090973493286,
            "cell_rmsd_from_input_A": 0.0006613814200968189
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0020795315041731897,
              0.19777137799525185,
              0.1967200641299405
            ],
            "branch_aligned_reduced_polarization": [
              0.0020795315041731897,
              0.19777137799525185,
              0.19672006412994048
            ],
            "target_residual": 0.4281649027086564,
            "energy_eV": -83.1150877418186,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 9.94293111344987e-05,
            "step_scale": 0.6365576254038792,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001769027154948,
              1.0000038751196598,
              0.999636109981102
            ],
            "cell_volume_ratio": 0.9998168227182764,
            "cell_rmsd_from_input_A": 0.0013216150056210372
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.001915323792140054,
              0.389249141447932,
              0.3854300498958664
            ],
            "branch_aligned_reduced_polarization": [
              0.001915323792140054,
              0.389249141447932,
              0.3854300498958664
            ],
            "target_residual": 0.15936026669817224,
            "energy_eV": -81.85506326770019,
            "max_atomic_step_A": 0.0747188344282479,
            "max_log_strain_component": 6.11134930796057e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0002329677919906,
              1.0000014968705917,
              0.999521700986384
            ],
            "cell_volume_ratio": 0.9997560538533052,
            "cell_rmsd_from_input_A": 0.001749341757561959
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0005943414952318638,
              0.49649715943405065,
              0.49633065671804005
            ],
            "branch_aligned_reduced_polarization": [
              0.0005943414952318638,
              0.49649715943405065,
              0.49633065671804005
            ],
            "target_residual": 0.00510756438669934,
            "energy_eV": -80.56119946720165,
            "max_atomic_step_A": 0.0026160642077519697,
            "max_log_strain_component": 2.313076214479273e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0002352414890832,
              1.0000013062749165,
              0.999517447867159
            ],
            "cell_volume_ratio": 0.9997538817916732,
            "cell_rmsd_from_input_A": 0.0017660094003159685
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              2.3907767807745253e-06,
              0.49999899465074576,
              0.49999591671153054
            ],
            "branch_aligned_reduced_polarization": [
              2.3907767807745253e-06,
              0.49999899465074576,
              0.49999591671153054
            ],
            "target_residual": 4.837332473925589e-06,
            "energy_eV": -80.5048778124214
          }
        ],
        "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": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.837332473925589e-06,
        "parent_symmetrization_rmsd_A": 0.34772249401282695,
        "parent_cell_rmsd_A": 0.0017660094003159685,
        "energy_eV": -80.5048778124214,
        "reduced_polarization": [
          2.3907767807745253e-06,
          0.49999899465074576,
          0.49999591671153054
        ],
        "cartesian_polarization_e_A2": [
          -7.867555079550578e-05,
          0.013356778262233469,
          0.023375903456788038
        ],
        "ranking_score": 0.8481736710278538
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0025699974520093627,
              -1.814557286212175e-17,
              0.0017462048005844578
            ],
            "branch_aligned_reduced_polarization": [
              0.002569997452009365,
              0.0,
              0.001746204800584461
            ],
            "target_residual": 0.8635354375273288,
            "energy_eV": -83.5294686968296,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00011718782900905174,
            "step_scale": 0.3910751945082022,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0000660291127388,
              1.0000203744030263,
              0.9997907354095341
            ],
            "cell_volume_ratio": 0.9998771221891251,
            "cell_rmsd_from_input_A": 0.0006254675830492385
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1956258876795148,
              0.19645963986025453,
              0.19477504224643438
            ],
            "branch_aligned_reduced_polarization": [
              0.19562588767951483,
              0.1964596398602545,
              0.19477504224643438
            ],
            "target_residual": 0.5272026416097663,
            "energy_eV": -83.12048542511911,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00011983946232910701,
            "step_scale": 0.6259695757925707,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.000133516771246,
              1.000034250255911,
              0.999583760760154
            ],
            "cell_volume_ratio": 0.9997514625271715,
            "cell_rmsd_from_input_A": 0.0012476963930855933
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3810512521648007,
              0.3859076142711883,
              0.3797637962657568
            ],
            "branch_aligned_reduced_polarization": [
              0.3810512521648007,
              0.3859076142711883,
              0.3797637962657568
            ],
            "target_residual": 0.20401622921051216,
            "energy_eV": -81.885856610812,
            "max_atomic_step_A": 0.07933802991874686,
            "max_log_strain_component": 8.557839679139374e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001815941412309,
              1.0000360513195157,
              0.9994441539879887
            ],
            "cell_volume_ratio": 0.999661685014443,
            "cell_rmsd_from_input_A": 0.001672222003658745
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49585241794797535,
              0.4965405078948856,
              0.4953039654485645
            ],
            "branch_aligned_reduced_polarization": [
              0.49585241794797535,
              0.4965405078948856,
              0.4953039654485645
            ],
            "target_residual": 0.007157042895770728,
            "energy_eV": -80.5413434636654,
            "max_atomic_step_A": 0.002995072111389819,
            "max_log_strain_component": 3.756601291402058e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.06687260116312042,
            "cell_principal_stretches": [
              1.0001836669710464,
              1.000035681035599,
              0.9994384959462843
            ],
            "cell_volume_ratio": 0.9996577273378832,
            "cell_rmsd_from_input_A": 0.0016897223538411216
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999438760377424,
              0.4999983524738909,
              0.49999478677642906
            ],
            "branch_aligned_reduced_polarization": [
              0.49999438760377424,
              0.4999983524738909,
              0.49999478677642906
            ],
            "target_residual": 7.83524305147848e-06,
            "energy_eV": -80.47863139032724
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 7.83524305147848e-06,
        "parent_symmetrization_rmsd_A": 0.3524125991231098,
        "parent_cell_rmsd_A": 0.0016897223538411216,
        "energy_eV": -80.47863139032724,
        "reduced_polarization": [
          0.49999438760377424,
          0.4999983524738909,
          0.49999478677642906
        ],
        "cartesian_polarization_e_A2": [
          0.020152266869507614,
          0.013357194651410623,
          0.011961020502262294
        ],
        "ranking_score": 0.8528507001976731
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13
        ],
        "endpoint_rmsd_A": 0.014741069069691566,
        "minimum_distance_A_by_image": [
          0.9700844822524298,
          0.9702121784078533,
          0.9703399314969942,
          0.9704677414973677,
          0.9705956083864878,
          0.9707235321418785,
          0.9708515127410593,
          0.9709795501615516,
          0.9711076443808804
        ],
        "minimum_distance_A": 0.9700844822524298,
        "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": [
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921,
          140.8146192782921
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.3406741763343878e-15,
        2.212688573620141e-18,
        -7.669201653482282e-17
      ],
      "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": [
          -83.52946869682958,
          -83.5300438759358,
          -83.53054212407594,
          -83.53096354499854,
          -83.5313082259168,
          -83.53157623782555,
          -83.53176763573462,
          -83.53188245883234,
          -83.53192073059222
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00010367360157101928,
            -1.9657575918196836e-20,
            2.299142582537413e-05
          ],
          [
            9.069929067664639e-05,
            1.442216343871893e-18,
            2.013643282546753e-05
          ],
          [
            7.773105054196226e-05,
            -7.149895716265719e-18,
            1.72740051450896e-05
          ],
          [
            6.476799631289399e-05,
            -4.214110920506916e-18,
            1.4405107432494352e-05
          ],
          [
            5.180924988797046e-05,
            2.0920167624310242e-18,
            1.1530747054096462e-05
          ],
          [
            3.885393987510663e-05,
            -6.650097105430121e-18,
            8.651968803745969e-06
          ],
          [
            2.5901201033733363e-05,
            1.046964215836207e-17,
            5.769848680050355e-06
          ],
          [
            1.2950173233300705e-05,
            5.028711548941028e-18,
            2.8854868560900857e-06
          ],
          [
            -5.4204480567555813e-17,
            5.913478252061289e-20,
            2.7003686682745988e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634293e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.488314533586129e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.917501102777263e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406741763343878e-15,
            2.212688573620141e-18,
            -7.669201653482282e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634296e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.4883145335861295e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.9175011027772636e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406701963869505e-15,
            2.2126885736201428e-18,
            -7.66801986490373e-17
          ]
        ],
        "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": [
          [
            0.002569997452009143,
            0.0,
            0.0017462048005837394
          ],
          [
            0.0022483749100391526,
            0.0,
            0.0015281522791602553
          ],
          [
            0.0019269021790162544,
            -2.7755575615628914e-16,
            0.0013100138340063072
          ],
          [
            0.0016055574137842088,
            -1.6653345369377348e-16,
            0.0010917994387894536
          ],
          [
            0.001284318939766771,
            1.1102230246251565e-16,
            0.0008735200642671082
          ],
          [
            0.0009631652514879852,
            -2.220446049250313e-16,
            0.0006551875643843186
          ],
          [
            0.0006420749982710694,
            4.440892098500626e-16,
            0.0004368145361774989
          ],
          [
            0.0003210269578951541,
            2.220446049250313e-16,
            0.000218414156523683
          ],
          [
            -1.3322676295501878e-15,
            0.0,
            -5.551115123125783e-17
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.53192073059222,
          -83.53188245883233,
          -83.5317676357346,
          -83.53157623782553,
          -83.5313082259168,
          -83.53096354499854,
          -83.53054212407596,
          -83.53004387593582,
          -83.52946869682958
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.395490606023617e-17,
            1.2586077949998382e-18,
            2.049914901463929e-17
          ],
          [
            -1.2950173233449718e-05,
            1.051526884651501e-17,
            -2.885486856120046e-06
          ],
          [
            -2.5901201033809745e-05,
            -1.3980010271045655e-17,
            -5.7698486800895794e-06
          ],
          [
            -3.8853939875092246e-05,
            -7.496079165217531e-18,
            -8.65196880382501e-06
          ],
          [
            -5.1809249887852196e-05,
            -2.126150237659883e-18,
            -1.1530747054161704e-05
          ],
          [
            -6.476799631279444e-05,
            1.4229204300966006e-19,
            -1.4405107432389294e-05
          ],
          [
            -7.773105054192018e-05,
            5.012295499311189e-18,
            -1.7274005145063186e-05
          ],
          [
            -9.069929067668877e-05,
            1.4475559778243369e-18,
            -2.0136432825540262e-05
          ],
          [
            -0.00010367360157099475,
            -1.5410174170134077e-18,
            -2.299142582542952e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0872730127351366e-15,
            4.7094230636506264e-17,
            -9.215750184644045e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579176e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.324243436167071e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944323e-17,
            -0.0017462048005845799
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0872730127351366e-15,
            4.7094230636506264e-17,
            -9.215750184644045e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579175e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.3242434361670774e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944324e-17,
            -0.0017462048005845799
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0025699974520117927,
          5.160918765307499e-18,
          -0.0017462048005838433
        ],
        "actual_opposite_endpoint_branch_residual": 3.3664424080525954e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634293e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.488314533586129e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.917501102777263e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406741763343878e-15,
            2.212688573620141e-18,
            -7.669201653482282e-17
          ],
          [
            -0.0003210269578988495,
            3.9345735679533966e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579176e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.324243436167071e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944323e-17,
            -0.0017462048005845799
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.002569997452009111,
            -7.35541618067217e-19,
            0.00174620480058369
          ],
          [
            0.0022483749100391456,
            5.396444340792478e-17,
            0.0015281522791602122
          ],
          [
            0.0019269021790162327,
            -2.6753277647452453e-16,
            0.001310013834006269
          ],
          [
            0.0016055574137842075,
            -1.5768241099936771e-16,
            0.0010917994387894246
          ],
          [
            0.0012843189397668065,
            7.827849175634296e-17,
            0.0008735200642670753
          ],
          [
            0.0009631652514879944,
            -2.4883145335861295e-16,
            0.0006551875643843113
          ],
          [
            0.0006420749982711219,
            3.9175011027772636e-16,
            0.0004368145361775358
          ],
          [
            0.0003210269578951558,
            1.8816290700815332e-16,
            0.00021841415652371884
          ],
          [
            -1.3406701963869505e-15,
            2.2126885736201428e-18,
            -7.66801986490373e-17
          ],
          [
            -0.0003210269578988495,
            3.934573567953397e-16,
            -0.0002184141565261626
          ],
          [
            -0.0006420749982730171,
            -5.231000718579175e-16,
            -0.0004368145361792999
          ],
          [
            -0.000963165251487644,
            -2.8048617089353806e-16,
            -0.0006551875643858311
          ],
          [
            -0.001284318939763882,
            -7.955568848215341e-17,
            -0.0008735200642670434
          ],
          [
            -0.0016055574137817333,
            5.3242434361670774e-18,
            -0.0010917994387859696
          ],
          [
            -0.0019269021790151882,
            1.875486559042913e-16,
            -0.0013100138340051942
          ],
          [
            -0.0022483749100402016,
            5.4164240321522426e-17,
            -0.0015281522791622832
          ],
          [
            -0.0025699974520085084,
            -5.766135402944324e-17,
            -0.0017462048005845799
          ]
        ],
        "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": [
          [
            0.002569997452009143,
            0.0,
            0.0017462048005837394
          ],
          [
            0.0022483749100391526,
            0.0,
            0.0015281522791602553
          ],
          [
            0.0019269021790162544,
            -2.7755575615628914e-16,
            0.0013100138340063072
          ],
          [
            0.0016055574137842088,
            -1.6653345369377348e-16,
            0.0010917994387894536
          ],
          [
            0.001284318939766771,
            1.1102230246251565e-16,
            0.0008735200642671082
          ],
          [
            0.0009631652514879852,
            -2.220446049250313e-16,
            0.0006551875643843186
          ],
          [
            0.0006420749982710694,
            4.440892098500626e-16,
            0.0004368145361774989
          ],
          [
            0.0003210269578951541,
            2.220446049250313e-16,
            0.000218414156523683
          ],
          [
            -1.3322676295501878e-15,
            0.0,
            -5.551115123125783e-17
          ],
          [
            -0.00032102695789887337,
            4.440892098500626e-16,
            -0.00021841415652618101
          ],
          [
            -0.0006420749982730123,
            -4.996003610813204e-16,
            -0.00043681453617927524
          ],
          [
            -0.0009631652514876521,
            -2.7755575615628914e-16,
            -0.0006551875643858174
          ],
          [
            -0.0012843189397638843,
            -5.551115123125783e-17,
            -0.0008735200642670526
          ],
          [
            -0.0016055574137817108,
            0.0,
            -0.0010917994387859564
          ],
          [
            -0.0019269021790151997,
            2.220446049250313e-16,
            -0.001310013834005197
          ],
          [
            -0.0022483749100402073,
            0.0,
            -0.0015281522791623092
          ],
          [
            -0.0025699974520085322,
            -5.551115123125783e-17,
            -0.001746204800584572
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.019187630808462e-16,
        "parent_symmetrization_rmsd_A": 0.014741069069691566,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.53192073059222,
        "reduced_polarization": [
          -6.972914079519284e-16,
          1.574607770918802e-17,
          -7.890946329901613e-17
        ],
        "cartesian_polarization_e_A2": [
          -2.8186329895129025e-17,
          4.2081876861779996e-19,
          1.2220646527958039e-17
        ],
        "ranking_score": 0.01474106906969297
      }
    }
  ],
  "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": 64,
      "full_response": 28,
      "energy_polarization": 36
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 89,
      "full_response": 53,
      "energy_polarization": 36
    },
    "elapsed_seconds": 305.71337374299765
  }
}
