{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "Nb4O24Te4Tl4",
  "input_spacegroup": "Ima2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -233.35537262564068,
  "input_cartesian_polarization_e_A2": [
    -7.188230307750294e-08,
    0.014920737682917256,
    -1.0276957108376799e-07
  ],
  "input_reduced_polarization": [
    -5.633395557960735e-06,
    1.1345241804065724,
    -5.685700715026168e-06
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        1.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        1.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1269061115872193e-15,
      "parent_symmetrization_rmsd_A": 0.19891763388980607,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -232.81012885527286,
      "reduced_polarization": [
        1.2103856785886333e-15,
        1.2827840120729428e-15,
        1.1887646087197592e-15
      ],
      "cartesian_polarization_e_A2": [
        1.544455902196095e-17,
        1.6870582468433087e-17,
        2.148703125277509e-17
      ],
      "ranking_score": 0.19891763388981032
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00098280539784964,
      "parent_symmetrization_rmsd_A": 0.013954240831592026,
      "parent_cell_rmsd_A": 0.005210785573983001,
      "energy_eV": -233.30570731770356,
      "reduced_polarization": [
        3.927504467470482e-08,
        0.9990171946030845,
        1.7133727157563297e-08
      ],
      "cartesian_polarization_e_A2": [
        1.6936664077726055e-10,
        0.013129361011376182,
        3.053705158731317e-10
      ],
      "ranking_score": 0.517222548020787
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.638381040298983e-15,
      "parent_symmetrization_rmsd_A": 0.19891786554576943,
      "parent_cell_rmsd_A": 0.005210785573983001,
      "energy_eV": -232.79196220092058,
      "reduced_polarization": [
        3.0635961153891583e-15,
        3.2157327043748816e-15,
        -1.5701628666543308e-15
      ],
      "cartesian_polarization_e_A2": [
        3.9043836502770313e-17,
        4.226204998662168e-17,
        -2.833958190652992e-17
      ],
      "ranking_score": 0.20022056193927446
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.0808328798168e-05,
      "parent_symmetrization_rmsd_A": 0.03892050696175068,
      "parent_cell_rmsd_A": 0.014456896868107758,
      "energy_eV": -233.26145410958821,
      "reduced_polarization": [
        -4.5694679521320787e-10,
        1.4999891916712136,
        -2.1270390594045883e-10
      ],
      "cartesian_polarization_e_A2": [
        -4.466990992348734e-10,
        0.019765871964676725,
        1.6981894140306595e-10
      ],
      "ranking_score": 0.542556347836374
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.4441329338016806e-06,
      "parent_symmetrization_rmsd_A": 0.0715340452382679,
      "parent_cell_rmsd_A": 0.005380577229883295,
      "energy_eV": -232.8150124265808,
      "reduced_polarization": [
        -9.402541053204177e-11,
        1.0000002374956043,
        -0.49999556221751745
      ],
      "cartesian_polarization_e_A2": [
        -1.5738221445148356e-10,
        0.013144092670533838,
        -0.009026960894613434
      ],
      "ranking_score": 0.5728880778116063
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.1041944594094144e-05,
      "parent_symmetrization_rmsd_A": 0.05083045003893194,
      "parent_cell_rmsd_A": 0.01414954536773956,
      "energy_eV": -233.13200096783737,
      "reduced_polarization": [
        -0.4999891500080588,
        1.0000020499305577,
        -6.241149537664419e-11
      ],
      "cartesian_polarization_e_A2": [
        -0.006343954749236981,
        0.013128791524710672,
        1.1145640203647925e-10
      ],
      "ranking_score": 0.5543899202700551
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 6.418581871523064e-05,
      "parent_symmetrization_rmsd_A": 0.08153919924879674,
      "parent_cell_rmsd_A": 0.014909332759711246,
      "energy_eV": -232.70312438142855,
      "reduced_polarization": [
        -9.34087919281127e-10,
        1.4999608974683678,
        -0.49994909998680526
      ],
      "cartesian_polarization_e_A2": [
        -2.061614788427084e-10,
        0.019768183279516825,
        -0.009077938841141943
      ],
      "ranking_score": 0.585394904076155
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 8.332690482158537e-05,
      "parent_symmetrization_rmsd_A": 0.06409788370960919,
      "parent_cell_rmsd_A": 0.01989354735280378,
      "energy_eV": -233.0600521471088,
      "reduced_polarization": [
        -0.49992944309699644,
        1.4999556705909625,
        -2.731171531008159e-10
      ],
      "cartesian_polarization_e_A2": [
        -0.006357314532213287,
        0.01975181183502581,
        3.146401598569978e-10
      ],
      "ranking_score": 0.5692379243574534
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        1.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.8698028831512244e-05,
      "parent_symmetrization_rmsd_A": 0.08710438423448702,
      "parent_cell_rmsd_A": 0.014345886420766642,
      "energy_eV": -232.61292995668296,
      "reduced_polarization": [
        -0.4999847448111963,
        0.9999935588429973,
        -0.49999131627998983
      ],
      "cartesian_polarization_e_A2": [
        -0.006343684690704143,
        0.013130305610124078,
        -0.009027072723495176
      ],
      "ranking_score": 0.5907282518973417
    },
    {
      "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,
        1.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00017161582992437335,
      "parent_symmetrization_rmsd_A": 0.09656600875268176,
      "parent_cell_rmsd_A": 0.02033037124695524,
      "energy_eV": -232.47076156362778,
      "reduced_polarization": [
        -0.49987133785364624,
        1.49990824220186,
        -0.49993307801813486
      ],
      "cartesian_polarization_e_A2": [
        -0.006356668428902175,
        0.01975375890713966,
        -0.009078170428100387
      ],
      "ranking_score": 0.6019918332242693
    }
  ],
  "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,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "target_residual": 0.13452418064467958,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.0125789282796097,
            "max_log_strain_component": 0.0009862548957086297,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0009867414062263,
              1.0004686571537442,
              1.0002358683390196
            ],
            "cell_volume_ratio": 1.0016920727339265,
            "cell_rmsd_from_input_A": 0.005210785573983001
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.927504467470482e-08,
              0.9990171946030845,
              1.7133727157563297e-08
            ],
            "branch_aligned_reduced_polarization": [
              3.927504467470482e-08,
              0.9990171946030845,
              1.7133727157563297e-08
            ],
            "target_residual": 0.00098280539784964,
            "energy_eV": -233.30570731770356
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.1269061115872193e-15,
        "parent_symmetrization_rmsd_A": 0.19891763388980607,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -232.81012885527286,
        "reduced_polarization": [
          1.2103856785886333e-15,
          1.2827840120729428e-15,
          1.1887646087197592e-15
        ],
        "cartesian_polarization_e_A2": [
          1.544455902196095e-17,
          1.6870582468433087e-17,
          2.148703125277509e-17
        ],
        "ranking_score": 0.19891763388981032
      },
      "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": [
          -233.35537262564065,
          -233.27347450175168,
          -233.1797006879503,
          -233.0843044959904,
          -232.9954004703281,
          -232.91915508686796,
          -232.86035199880476,
          -232.8229958896945,
          -232.81012885527284
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.188230310011388e-08,
            0.014920737682917275,
            -1.027695710984512e-07
          ],
          [
            -6.327590454116498e-08,
            0.013081463534774088,
            -9.022697486092792e-08
          ],
          [
            -5.4582140010516526e-08,
            0.011231162703266736,
            -7.755529657670188e-08
          ],
          [
            -4.5777528764236446e-08,
            0.009371092377654922,
            -6.47710450828072e-08
          ],
          [
            -3.6839504634566205e-08,
            0.007503455399215169,
            -5.18997714406988e-08
          ],
          [
            -2.7768680706364177e-08,
            0.005630837784744824,
            -3.8962550459025695e-08
          ],
          [
            -1.8588668267410514e-08,
            0.0037553162869022843,
            -2.5984185492586646e-08
          ],
          [
            -9.321496099492019e-09,
            0.001878126752388782,
            -1.2991536307974606e-08
          ],
          [
            6.480551467548168e-18,
            -9.450426568993319e-18,
            -2.389193520063912e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789672481648e-16,
            -7.185795826941555e-16,
            -1.3218153157699463e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789434704288e-16,
            -7.216449660063518e-16,
            -1.3218153488601882e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -5.633395559756504e-06,
            0.134524180406574,
            -5.685700715851727e-06
          ],
          [
            -4.958914563202299e-06,
            -0.005328220983352505,
            -4.991784728403115e-06
          ],
          [
            -4.27758672044698e-06,
            -0.14601905537653836,
            -4.290727309175235e-06
          ],
          [
            -3.5875718522593303e-06,
            -0.28745273020612827,
            -3.5834418053437567e-06
          ],
          [
            -2.8871014544629148e-06,
            -0.42946174861325925,
            -2.871341823029727e-06
          ],
          [
            -2.1762235744571257e-06,
            0.4281505216765502,
            -2.1555933207295652e-06
          ],
          [
            -1.4567886220118176e-06,
            0.2855419901552929,
            -1.4375685378209546e-06
          ],
          [
            -7.305229864917884e-07,
            0.14280662657135712,
            -7.187534841190946e-07
          ],
          [
            5.551115123125783e-16,
            -7.216449660063518e-16,
            -1.3322676295501878e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -232.81012885527286,
          -232.8229958896945,
          -232.86035199880476,
          -232.91915508686796,
          -232.99540047032818,
          -233.0843044959904,
          -233.1797006879502,
          -233.27347450175176,
          -233.35537262564068
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.423206289754915e-18,
            -1.0489731792693351e-17,
            -5.9820475085060015e-18
          ],
          [
            9.321496121973036e-09,
            -0.0018781267523887517,
            1.2991536231682352e-08
          ],
          [
            1.8588668310402703e-08,
            -0.0037553162869022895,
            2.598418548734178e-08
          ],
          [
            2.7768680730796915e-08,
            -0.00563083778474481,
            3.896255043175602e-08
          ],
          [
            3.683950462885607e-08,
            -0.007503455399215175,
            5.18997713773465e-08
          ],
          [
            4.5777528785814114e-08,
            -0.00937109237765493,
            6.477104507228121e-08
          ],
          [
            5.458214003539942e-08,
            -0.011231162703266694,
            7.755529652900259e-08
          ],
          [
            6.327590454874828e-08,
            -0.013081463534774098,
            9.022697476636927e-08
          ],
          [
            7.188230311043442e-08,
            -0.014920737682917266,
            1.0276957105199667e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.60124270716962e-16,
            -7.976049587960703e-16,
            -3.3095527633086664e-16
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.60124270716962e-16,
            -7.976049587960703e-16,
            -3.3095527633086664e-16
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          5.633395560748505e-06,
          -1.1345241804065755,
          5.685700713194882e-06
        ],
        "actual_opposite_endpoint_branch_residual": 2.231280846742284e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789672481648e-16,
            -7.185795826941555e-16,
            -1.3218153157699463e-15
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789434704288e-16,
            -7.216449660063518e-16,
            -1.3218153488601882e-15
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "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": [
          [
            -5.633395559756504e-06,
            0.134524180406574,
            -5.685700715851727e-06
          ],
          [
            -4.958914563202299e-06,
            -0.005328220983352505,
            -4.991784728403115e-06
          ],
          [
            -4.27758672044698e-06,
            -0.14601905537653836,
            -4.290727309175235e-06
          ],
          [
            -3.5875718522593303e-06,
            -0.28745273020612827,
            -3.5834418053437567e-06
          ],
          [
            -2.8871014544629148e-06,
            -0.42946174861325925,
            -2.871341823029727e-06
          ],
          [
            -2.1762235744571257e-06,
            0.4281505216765502,
            -2.1555933207295652e-06
          ],
          [
            -1.4567886220118176e-06,
            0.2855419901552929,
            -1.4375685378209546e-06
          ],
          [
            -7.305229864917884e-07,
            0.14280662657135712,
            -7.187534841190946e-07
          ],
          [
            5.551115123125783e-16,
            -7.216449660063518e-16,
            -1.3322676295501878e-15
          ],
          [
            7.305229882126341e-07,
            -0.1428066265713548,
            7.187534798447359e-07
          ],
          [
            1.4567886253979978e-06,
            -0.28554199015529336,
            1.4375685375433989e-06
          ],
          [
            2.176223576344505e-06,
            -0.42815052167654893,
            2.1555933192862753e-06
          ],
          [
            2.8871014540188256e-06,
            0.4294617486132588,
            2.8713418195325247e-06
          ],
          [
            3.587571853924665e-06,
            0.2874527302061278,
            3.583441804733134e-06
          ],
          [
            4.27758672238987e-06,
            0.14601905537654147,
            4.290727306566211e-06
          ],
          [
            4.9589145637574106e-06,
            0.005328220983351728,
            4.991784723129555e-06
          ],
          [
            5.633395560589172e-06,
            -0.13452418040657332,
            5.685700713242703e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "target_residual": 0.36547581968106996,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.034174154955463526,
            "max_log_strain_component": 0.002679461159072782,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              0.9993594727591679,
              0.9987278585321756,
              0.9973241253925458
            ],
            "cell_volume_ratio": 0.9954173874063705,
            "cell_rmsd_from_input_A": 0.014114488096800801
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0300701687710425e-07,
              1.4919227905899481,
              -3.8507141360169266e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.0300701687710425e-07,
              1.4919227905899481,
              -3.8507141360169266e-08
            ],
            "target_residual": 0.008077209410800458,
            "energy_eV": -233.26816134503127,
            "max_atomic_step_A": 0.0007823045535865264,
            "max_log_strain_component": 6.514752768637605e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              0.9993439043027973,
              0.9986969482681453,
              0.9972591543078457
            ],
            "cell_volume_ratio": 0.9953062291829916,
            "cell_rmsd_from_input_A": 0.014456896868107758
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.5694679521320787e-10,
              1.4999891916712136,
              -2.1270390594045883e-10
            ],
            "branch_aligned_reduced_polarization": [
              -4.5694679521320787e-10,
              1.4999891916712136,
              -2.1270390594045883e-10
            ],
            "target_residual": 1.0808328798168e-05,
            "energy_eV": -233.26145410958821
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ima2",
        "spacegroup_number": 46,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.0808328798168e-05,
        "parent_symmetrization_rmsd_A": 0.03892050696175068,
        "parent_cell_rmsd_A": 0.014456896868107758,
        "energy_eV": -233.26145410958821,
        "reduced_polarization": [
          -4.5694679521320787e-10,
          1.4999891916712136,
          -2.1270390594045883e-10
        ],
        "cartesian_polarization_e_A2": [
          -4.466990992348734e-10,
          0.019765871964676725,
          1.6981894140306595e-10
        ],
        "ranking_score": 0.542556347836374
      },
      "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,
        1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.68570071501906e-06
            ],
            "target_residual": 0.517775114772241,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.06509827783176127,
            "max_log_strain_component": 0.0009862587551619883,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0010297527202758,
              1.000468665002416,
              1.000192923425482
            ],
            "cell_volume_ratio": 1.0016921129302214,
            "cell_rmsd_from_input_A": 0.00545144853746096
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.455108061682476e-08,
              0.9980674399345649,
              -0.497374013136074
            ],
            "branch_aligned_reduced_polarization": [
              3.455108061682476e-08,
              0.9980674399345649,
              -0.497374013136074
            ],
            "target_residual": 0.003260459387451431,
            "energy_eV": -232.81948884844545,
            "max_atomic_step_A": 0.0004238845915519813,
            "max_log_strain_component": 1.4550019060556301e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0010162200800972,
              1.0004617494352375,
              1.000188412200892
            ],
            "cell_volume_ratio": 1.0016671295111739,
            "cell_rmsd_from_input_A": 0.005380577229883295
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.402541053204177e-11,
              1.0000002374956043,
              -0.49999556221751745
            ],
            "branch_aligned_reduced_polarization": [
              -9.402541053204177e-11,
              1.0000002374956043,
              -0.49999556221751745
            ],
            "target_residual": 4.4441329338016806e-06,
            "energy_eV": -232.8150124265808
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.4441329338016806e-06,
        "parent_symmetrization_rmsd_A": 0.0715340452382679,
        "parent_cell_rmsd_A": 0.005380577229883295,
        "energy_eV": -232.8150124265808,
        "reduced_polarization": [
          -9.402541053204177e-11,
          1.0000002374956043,
          -0.49999556221751745
        ],
        "cartesian_polarization_e_A2": [
          -1.5738221445148356e-10,
          0.013144092670533838,
          -0.009026960894613434
        ],
        "ranking_score": 0.5728880778116063
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.6333955579801476e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "target_residual": 0.5177751652817701,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.04415011098824714,
            "max_log_strain_component": 0.0021590858959397155,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0029061655714848,
              1.0002358679623176,
              0.9985539030293364
            ],
            "cell_volume_ratio": 1.0016920773580575,
            "cell_rmsd_from_input_A": 0.0142173602013204
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5012480051394288,
              0.9972008280085956,
              1.5233985907652476e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.5012480051394288,
              0.9972008280085956,
              1.5233985907652476e-08
            ],
            "target_residual": 0.0030647806880323286,
            "energy_eV": -233.1298195348027,
            "max_atomic_step_A": 0.0002802011475980549,
            "max_log_strain_component": 1.9807705744265754e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0028858070480438,
              1.0002311302925402,
              0.9985449977889922
            ],
            "cell_volume_ratio": 1.0016580660057979,
            "cell_rmsd_from_input_A": 0.01414954536773956
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999891500080588,
              1.0000020499305577,
              -6.241149537664419e-11
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999891500080588,
              1.0000020499305577,
              -6.241149537664419e-11
            ],
            "target_residual": 1.1041944594094144e-05,
            "energy_eV": -233.13200096783737
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.1041944594094144e-05,
        "parent_symmetrization_rmsd_A": 0.05083045003893194,
        "parent_cell_rmsd_A": 0.01414954536773956,
        "energy_eV": -233.13200096783737,
        "reduced_polarization": [
          -0.4999891500080588,
          1.0000020499305577,
          -6.241149537664419e-11
        ],
        "cartesian_polarization_e_A2": [
          -0.006343954749236981,
          0.013128791524710672,
          1.1145640203647925e-10
        ],
        "ranking_score": 0.5543899202700551
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.68570071501906e-06
            ],
            "target_residual": 0.6193277719195506,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.07684529414914493,
            "max_log_strain_component": 0.0026794572996194236,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              0.9993760731209551,
              0.9987278663658531,
              0.997307591312914
            ],
            "cell_volume_ratio": 0.9954174273508729,
            "cell_rmsd_from_input_A": 0.014203789627403832
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.4124370820292653e-07,
              1.4843856996724811,
              -0.4911369513058788
            ],
            "branch_aligned_reduced_polarization": [
              -1.4124370820292653e-07,
              1.4843856996724811,
              -0.4911369513058788
            ],
            "target_residual": 0.01795438684255937,
            "energy_eV": -232.73931941680348,
            "max_atomic_step_A": 0.002196426299583826,
            "max_log_strain_component": 0.0001344090503975034,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              0.9993438052057894,
              0.9986640950569131,
              0.9971737009853221
            ],
            "cell_volume_ratio": 0.9951881056538459,
            "cell_rmsd_from_input_A": 0.014909332759711246
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.34087919281127e-10,
              1.4999608974683678,
              -0.49994909998680526
            ],
            "branch_aligned_reduced_polarization": [
              -9.34087919281127e-10,
              1.4999608974683678,
              -0.49994909998680526
            ],
            "target_residual": 6.418581871523064e-05,
            "energy_eV": -232.70312438142855
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 6.418581871523064e-05,
        "parent_symmetrization_rmsd_A": 0.08153919924879674,
        "parent_cell_rmsd_A": 0.014909332759711246,
        "energy_eV": -232.70312438142855,
        "reduced_polarization": [
          -9.34087919281127e-10,
          1.4999608974683678,
          -0.49994909998680526
        ],
        "cartesian_polarization_e_A2": [
          -2.061614788427084e-10,
          0.019768183279516825,
          -0.009077938841141943
        ],
        "ranking_score": 0.585394904076155
      },
      "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,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.6333955579801476e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "target_residual": 0.619327814146912,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.054395545685403446,
            "max_log_strain_component": 0.0026794617936683612,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0002945748201442,
              0.9993594723827349,
              0.9957620665574082
            ],
            "cell_volume_ratio": 0.9954173920015355,
            "cell_rmsd_from_input_A": 0.019270724190307984
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48812721099074236,
              1.4881104588085283,
              -4.447846695528104e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.48812721099074236,
              1.4881104588085283,
              -4.447846695528104e-08
            ],
            "target_residual": 0.01680250899729053,
            "energy_eV": -233.08010308973712,
            "max_atomic_step_A": 0.00156172923736253,
            "max_log_strain_component": 0.0001010993290631511,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.000282337475863,
              0.9993353125386225,
              0.9956257606813144
            ],
            "cell_volume_ratio": 0.995244896340857,
            "cell_rmsd_from_input_A": 0.01989354735280378
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49992944309699644,
              1.4999556705909625,
              -2.731171531008159e-10
            ],
            "branch_aligned_reduced_polarization": [
              -0.49992944309699644,
              1.4999556705909625,
              -2.731171531008159e-10
            ],
            "target_residual": 8.332690482158537e-05,
            "energy_eV": -233.0600521471088
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 8.332690482158537e-05,
        "parent_symmetrization_rmsd_A": 0.06409788370960919,
        "parent_cell_rmsd_A": 0.01989354735280378,
        "energy_eV": -233.0600521471088,
        "reduced_polarization": [
          -0.49992944309699644,
          1.4999556705909625,
          -2.731171531008159e-10
        ],
        "cartesian_polarization_e_A2": [
          -0.006357314532213287,
          0.01975181183502581,
          3.146401598569978e-10
        ],
        "ranking_score": 0.5692379243574534
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.6333955579801476e-06,
              1.1345241804065724,
              -5.68570071501906e-06
            ],
            "target_residual": 0.7197815196862514,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.08337596363376108,
            "max_log_strain_component": 0.0021591000288547347,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0029133493360207,
              1.0002376496105547,
              0.9985450119247055
            ],
            "cell_volume_ratio": 1.001692117554353,
            "cell_rmsd_from_input_A": 0.014307393601689838
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4966021554990699,
              0.9963736955149772,
              -0.4958466326503325
            ],
            "branch_aligned_reduced_polarization": [
              -0.4966021554990699,
              0.9963736955149772,
              -0.4958466326503325
            ],
            "target_residual": 0.006476564815693666,
            "energy_eV": -232.6230892116176,
            "max_atomic_step_A": 0.0007794431034406685,
            "max_log_strain_component": 2.819931222852146e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.002907708161159,
              1.0002308551565258,
              0.9985091434464776
            ],
            "cell_volume_ratio": 1.001643697875143,
            "cell_rmsd_from_input_A": 0.014345886420766642
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999847448111963,
              0.9999935588429973,
              -0.49999131627998983
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999847448111963,
              0.9999935588429973,
              -0.49999131627998983
            ],
            "target_residual": 1.8698028831512244e-05,
            "energy_eV": -232.61292995668296
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          1.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.8698028831512244e-05,
        "parent_symmetrization_rmsd_A": 0.08710438423448702,
        "parent_cell_rmsd_A": 0.014345886420766642,
        "energy_eV": -232.61292995668296,
        "reduced_polarization": [
          -0.4999847448111963,
          0.9999935588429973,
          -0.49999131627998983
        ],
        "cartesian_polarization_e_A2": [
          -0.006343684690704143,
          0.013130305610124078,
          -0.009027072723495176
        ],
        "ranking_score": 0.5907282518973417
      },
      "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,
        1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.633395557960735e-06,
              1.1345241804065724,
              -5.685700715026168e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.6333955579801476e-06,
              1.1345241804065724,
              -5.68570071501906e-06
            ],
            "target_residual": 0.795965612118562,
            "energy_eV": -233.35537262564068,
            "max_atomic_step_A": 0.08772791798779468,
            "max_log_strain_component": 0.0026794579342150028,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.000307074792408,
              0.9993532108758808,
              0.995755902266628
            ],
            "cell_volume_ratio": 0.995417431946038,
            "cell_rmsd_from_input_A": 0.019336282376040258
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4839117159763197,
              1.480787967960575,
              -0.4896593847214465
            ],
            "branch_aligned_reduced_polarization": [
              -0.4839117159763197,
              1.480787967960575,
              -0.4896593847214465
            ],
            "target_residual": 0.027108363695537756,
            "energy_eV": -232.53093517017038,
            "max_atomic_step_A": 0.00306111487455389,
            "max_log_strain_component": 0.00017244394492864826,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9019307141986697,
            "cell_principal_stretches": [
              1.0002707584474293,
              0.9993116347605322,
              0.9955391563093943
            ],
            "cell_volume_ratio": 0.9951232268466907,
            "cell_rmsd_from_input_A": 0.02033037124695524
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49987133785364624,
              1.49990824220186,
              -0.49993307801813486
            ],
            "branch_aligned_reduced_polarization": [
              -0.49987133785364624,
              1.49990824220186,
              -0.49993307801813486
            ],
            "target_residual": 0.00017161582992437335,
            "energy_eV": -232.47076156362778
          }
        ],
        "iterations": 2
      },
      "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,
          1.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00017161582992437335,
        "parent_symmetrization_rmsd_A": 0.09656600875268176,
        "parent_cell_rmsd_A": 0.02033037124695524,
        "energy_eV": -232.47076156362778,
        "reduced_polarization": [
          -0.49987133785364624,
          1.49990824220186,
          -0.49993307801813486
        ],
        "cartesian_polarization_e_A2": [
          -0.006356668428902175,
          0.01975375890713966,
          -0.009078170428100387
        ],
        "ranking_score": 0.6019918332242693
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35
        ],
        "endpoint_rmsd_A": 0.19891763388980607,
        "minimum_distance_A_by_image": [
          1.8432298063180157,
          1.8641821396024951,
          1.8851608822440482,
          1.9061651622799685,
          1.9271941447225596,
          1.9279137827603532,
          1.9283300719053735,
          1.9287463888820768,
          1.9291627336724437
        ],
        "minimum_distance_A": 1.8432298063180157,
        "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": [
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249,
          574.1767308852249
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.078789672481648e-16,
        -7.185795826941555e-16,
        -1.3218153157699463e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -233.35537262564065,
          -233.27347450175168,
          -233.1797006879503,
          -233.0843044959904,
          -232.9954004703281,
          -232.91915508686796,
          -232.86035199880476,
          -232.8229958896945,
          -232.81012885527284
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.188230310011388e-08,
            0.014920737682917275,
            -1.027695710984512e-07
          ],
          [
            -6.327590454116498e-08,
            0.013081463534774088,
            -9.022697486092792e-08
          ],
          [
            -5.4582140010516526e-08,
            0.011231162703266736,
            -7.755529657670188e-08
          ],
          [
            -4.5777528764236446e-08,
            0.009371092377654922,
            -6.47710450828072e-08
          ],
          [
            -3.6839504634566205e-08,
            0.007503455399215169,
            -5.18997714406988e-08
          ],
          [
            -2.7768680706364177e-08,
            0.005630837784744824,
            -3.8962550459025695e-08
          ],
          [
            -1.8588668267410514e-08,
            0.0037553162869022843,
            -2.5984185492586646e-08
          ],
          [
            -9.321496099492019e-09,
            0.001878126752388782,
            -1.2991536307974606e-08
          ],
          [
            6.480551467548168e-18,
            -9.450426568993319e-18,
            -2.389193520063912e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789672481648e-16,
            -7.185795826941555e-16,
            -1.3218153157699463e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789434704288e-16,
            -7.216449660063518e-16,
            -1.3218153488601882e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -5.633395559756504e-06,
            0.134524180406574,
            -5.685700715851727e-06
          ],
          [
            -4.958914563202299e-06,
            -0.005328220983352505,
            -4.991784728403115e-06
          ],
          [
            -4.27758672044698e-06,
            -0.14601905537653836,
            -4.290727309175235e-06
          ],
          [
            -3.5875718522593303e-06,
            -0.28745273020612827,
            -3.5834418053437567e-06
          ],
          [
            -2.8871014544629148e-06,
            -0.42946174861325925,
            -2.871341823029727e-06
          ],
          [
            -2.1762235744571257e-06,
            0.4281505216765502,
            -2.1555933207295652e-06
          ],
          [
            -1.4567886220118176e-06,
            0.2855419901552929,
            -1.4375685378209546e-06
          ],
          [
            -7.305229864917884e-07,
            0.14280662657135712,
            -7.187534841190946e-07
          ],
          [
            5.551115123125783e-16,
            -7.216449660063518e-16,
            -1.3322676295501878e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -232.81012885527286,
          -232.8229958896945,
          -232.86035199880476,
          -232.91915508686796,
          -232.99540047032818,
          -233.0843044959904,
          -233.1797006879502,
          -233.27347450175176,
          -233.35537262564068
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.423206289754915e-18,
            -1.0489731792693351e-17,
            -5.9820475085060015e-18
          ],
          [
            9.321496121973036e-09,
            -0.0018781267523887517,
            1.2991536231682352e-08
          ],
          [
            1.8588668310402703e-08,
            -0.0037553162869022895,
            2.598418548734178e-08
          ],
          [
            2.7768680730796915e-08,
            -0.00563083778474481,
            3.896255043175602e-08
          ],
          [
            3.683950462885607e-08,
            -0.007503455399215175,
            5.18997713773465e-08
          ],
          [
            4.5777528785814114e-08,
            -0.00937109237765493,
            6.477104507228121e-08
          ],
          [
            5.458214003539942e-08,
            -0.011231162703266694,
            7.755529652900259e-08
          ],
          [
            6.327590454874828e-08,
            -0.013081463534774098,
            9.022697476636927e-08
          ],
          [
            7.188230311043442e-08,
            -0.014920737682917266,
            1.0276957105199667e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.60124270716962e-16,
            -7.976049587960703e-16,
            -3.3095527633086664e-16
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.60124270716962e-16,
            -7.976049587960703e-16,
            -3.3095527633086664e-16
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          5.633395560748505e-06,
          -1.1345241804065755,
          5.685700713194882e-06
        ],
        "actual_opposite_endpoint_branch_residual": 2.231280846742284e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789672481648e-16,
            -7.185795826941555e-16,
            -1.3218153157699463e-15
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.633395559732748e-06,
            1.134524180406574,
            -5.685700715838513e-06
          ],
          [
            -4.958914563210584e-06,
            0.9946717790166475,
            -4.991784728412208e-06
          ],
          [
            -4.277586720443683e-06,
            0.8539809446234617,
            -4.290727309164253e-06
          ],
          [
            -3.5875718522377055e-06,
            0.7125472697938717,
            -3.5834418053582346e-06
          ],
          [
            -2.8871014544717675e-06,
            0.5705382513867407,
            -2.8713418230533365e-06
          ],
          [
            -2.1762235744310832e-06,
            0.42815052167655016,
            -2.1555933207462336e-06
          ],
          [
            -1.4567886219940763e-06,
            0.28554199015529297,
            -1.4375685378131066e-06
          ],
          [
            -7.305229864965369e-07,
            0.14280662657135712,
            -7.187534840962905e-07
          ],
          [
            5.078789434704288e-16,
            -7.216449660063518e-16,
            -1.3218153488601882e-15
          ],
          [
            7.305229882583678e-07,
            -0.14280662657135482,
            7.187534798754407e-07
          ],
          [
            1.4567886253633618e-06,
            -0.28554199015529336,
            1.4375685375229358e-06
          ],
          [
            2.1762235763458702e-06,
            -0.42815052167654893,
            2.1555933192375455e-06
          ],
          [
            2.887101454024266e-06,
            -0.5705382513867412,
            2.8713418195483866e-06
          ],
          [
            3.5875718539287416e-06,
            -0.7125472697938722,
            3.5834418047758876e-06
          ],
          [
            4.277586722393749e-06,
            -0.8539809446234585,
            4.290727306525303e-06
          ],
          [
            4.958914563804885e-06,
            -0.9946717790166483,
            4.991784723180775e-06
          ],
          [
            5.633395560541564e-06,
            -1.1345241804065733,
            5.685700713268427e-06
          ]
        ],
        "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": [
          [
            -5.633395559756504e-06,
            0.134524180406574,
            -5.685700715851727e-06
          ],
          [
            -4.958914563202299e-06,
            -0.005328220983352505,
            -4.991784728403115e-06
          ],
          [
            -4.27758672044698e-06,
            -0.14601905537653836,
            -4.290727309175235e-06
          ],
          [
            -3.5875718522593303e-06,
            -0.28745273020612827,
            -3.5834418053437567e-06
          ],
          [
            -2.8871014544629148e-06,
            -0.42946174861325925,
            -2.871341823029727e-06
          ],
          [
            -2.1762235744571257e-06,
            0.4281505216765502,
            -2.1555933207295652e-06
          ],
          [
            -1.4567886220118176e-06,
            0.2855419901552929,
            -1.4375685378209546e-06
          ],
          [
            -7.305229864917884e-07,
            0.14280662657135712,
            -7.187534841190946e-07
          ],
          [
            5.551115123125783e-16,
            -7.216449660063518e-16,
            -1.3322676295501878e-15
          ],
          [
            7.305229882126341e-07,
            -0.1428066265713548,
            7.187534798447359e-07
          ],
          [
            1.4567886253979978e-06,
            -0.28554199015529336,
            1.4375685375433989e-06
          ],
          [
            2.176223576344505e-06,
            -0.42815052167654893,
            2.1555933192862753e-06
          ],
          [
            2.8871014540188256e-06,
            0.4294617486132588,
            2.8713418195325247e-06
          ],
          [
            3.587571853924665e-06,
            0.2874527302061278,
            3.583441804733134e-06
          ],
          [
            4.27758672238987e-06,
            0.14601905537654147,
            4.290727306566211e-06
          ],
          [
            4.9589145637574106e-06,
            0.005328220983351728,
            4.991784723129555e-06
          ],
          [
            5.633395560589172e-06,
            -0.13452418040657332,
            5.685700713242703e-06
          ]
        ]
      },
      "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": "Imma",
        "spacegroup_number": 74,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.1269061115872193e-15,
        "parent_symmetrization_rmsd_A": 0.19891763388980607,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -232.81012885527286,
        "reduced_polarization": [
          1.2103856785886333e-15,
          1.2827840120729428e-15,
          1.1887646087197592e-15
        ],
        "cartesian_polarization_e_A2": [
          1.544455902196095e-17,
          1.6870582468433087e-17,
          2.148703125277509e-17
        ],
        "ranking_score": 0.19891763388981032
      }
    }
  ],
  "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": 48,
      "full_response": 16,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 41,
      "energy_polarization": 32
    },
    "elapsed_seconds": 640.1345284230192
  }
}