{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 16,
  "input_formula": "As2Na6O8",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -81.45033966399319,
  "input_cartesian_polarization_e_A2": [
    3.21452701866371e-18,
    1.8893858181927518e-18,
    0.0003424683405147691
  ],
  "input_reduced_polarization": [
    1.1081674232186611e-16,
    7.646976539290786e-17,
    0.014861129595128296
  ],
  "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": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        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": "Pmmn",
      "spacegroup_number": 59,
      "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": 2.7104755324278027e-16,
      "parent_symmetrization_rmsd_A": 0.49803412593369933,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -74.71815742999611,
      "reduced_polarization": [
        1.4607704654343645e-16,
        -1.483741716578809e-17,
        2.2783354371973604e-16
      ],
      "cartesian_polarization_e_A2": [
        4.237343591608346e-18,
        -3.665972483060563e-19,
        5.2503260355710195e-18
      ],
      "ranking_score": 0.4980341259336999
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "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": 3.803617823224496e-16,
      "parent_symmetrization_rmsd_A": 0.5719027000492292,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -68.43560159332438,
      "reduced_polarization": [
        -1.7207089336113034e-16,
        1.3011273514614172e-16,
        3.1326884502325318e-16
      ],
      "cartesian_polarization_e_A2": [
        -4.9913625346286126e-18,
        3.214775869760801e-18,
        7.219145812796185e-18
      ],
      "ranking_score": 0.5719027000492299
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Immm",
      "spacegroup_number": 71,
      "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": 3.3910307477102816e-16,
      "parent_symmetrization_rmsd_A": 0.7270164687257876,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -53.51318711690972,
      "reduced_polarization": [
        3.3869962172512306e-16,
        -1.222600054910029e-17,
        1.1134921328750089e-17
      ],
      "cartesian_polarization_e_A2": [
        9.824860959044405e-18,
        -3.0207536183744124e-19,
        2.565994734659758e-19
      ],
      "ranking_score": 0.7270164687257883
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.170280530597971e-05,
      "parent_symmetrization_rmsd_A": 0.003013040932954388,
      "parent_cell_rmsd_A": 0.0033186497473049227,
      "energy_eV": -81.44652174435106,
      "reduced_polarization": [
        1.3318482502071263e-15,
        6.347678185004271e-16,
        2.170280530597971e-05
      ],
      "cartesian_polarization_e_A2": [
        3.861452574769301e-17,
        1.56758522964782e-17,
        5.004261098605098e-07
      ],
      "ranking_score": 0.5038861089803925
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4406708108461315e-15,
      "parent_symmetrization_rmsd_A": 0.49803417971598135,
      "parent_cell_rmsd_A": 0.0033186497473049227,
      "energy_eV": -74.69322833165151,
      "reduced_polarization": [
        3.5786083074989656e-16,
        1.3620269028225342e-15,
        -3.0389262417291214e-16
      ],
      "cartesian_polarization_e_A2": [
        1.0375551686554956e-17,
        3.363541688794693e-17,
        -7.007195686736918e-18
      ],
      "ranking_score": 0.4988638421528105
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "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": 7.510158748978639e-16,
      "parent_symmetrization_rmsd_A": 0.5719028047486469,
      "parent_cell_rmsd_A": 0.0033186497473049227,
      "energy_eV": -68.50180540137688,
      "reduced_polarization": [
        5.037198884168054e-16,
        3.4136298737966286e-16,
        -4.4018453994796e-16
      ],
      "cartesian_polarization_e_A2": [
        1.4604481096359185e-17,
        8.429999706199608e-18,
        -1.0149832422180129e-17
      ],
      "ranking_score": 0.5727324671854747
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00034296209311862613,
      "parent_symmetrization_rmsd_A": 0.10747616158341586,
      "parent_cell_rmsd_A": 0.11749900777285868,
      "energy_eV": -76.06409558210144,
      "reduced_polarization": [
        2.0101576445315216e-16,
        1.47338131171445e-16,
        0.4996570379068814
      ],
      "cartesian_polarization_e_A2": [
        9.124518035065626e-17,
        -1.4544201158397618e-16,
        0.011273449494556312
      ],
      "ranking_score": 0.6375368377128678
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0002524986868598124,
      "parent_symmetrization_rmsd_A": 0.1391379853105489,
      "parent_cell_rmsd_A": 0.11494777330949223,
      "energy_eV": -76.93037434665911,
      "reduced_polarization": [
        2.0311323696652054e-15,
        0.4997827140425634,
        0.00012861725998790266
      ],
      "cartesian_polarization_e_A2": [
        -1.2731088346397783e-16,
        0.01234116191642757,
        0.0002785491831203299
      ],
      "ranking_score": 0.6683799260116416
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0007257634336531905,
      "parent_symmetrization_rmsd_A": 0.1535808602301102,
      "parent_cell_rmsd_A": 0.15341973737802628,
      "energy_eV": -75.46083960315576,
      "reduced_polarization": [
        0.49927544393988466,
        -1.130757864523936e-16,
        -4.18458764778386e-05
      ],
      "cartesian_polarization_e_A2": [
        0.01447845840179443,
        -1.9066595955356107e-16,
        0.00036678722011456756
      ],
      "ranking_score": 0.6933873214419232
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.749287254225151e-07,
      "parent_symmetrization_rmsd_A": 0.19750116557650058,
      "parent_cell_rmsd_A": 0.2153756929950862,
      "energy_eV": -72.9065068825265,
      "reduced_polarization": [
        0.49999928682556205,
        2.5470350469176765e-15,
        0.5000003031447683
      ],
      "cartesian_polarization_e_A2": [
        0.015134305396403439,
        -2.636088943446476e-16,
        0.011677377972351525
      ],
      "ranking_score": 0.751346638682723
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00026755451172146466,
      "parent_symmetrization_rmsd_A": 0.17793191336057362,
      "parent_cell_rmsd_A": 0.17148077418735627,
      "energy_eV": -73.66157291611327,
      "reduced_polarization": [
        -1.974439300453612e-16,
        0.49982149245646573,
        0.49980070004103394
      ],
      "cartesian_polarization_e_A2": [
        -7.753992600947421e-17,
        0.012863516978804,
        0.011552714459766314
      ],
      "ranking_score": 0.7213372159308556
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.105917739557321e-06,
      "parent_symmetrization_rmsd_A": 0.22884416009439787,
      "parent_cell_rmsd_A": 0.2264377457722005,
      "energy_eV": -72.02306047161959,
      "reduced_polarization": [
        0.4999998148252426,
        0.49999957873706574,
        -1.005635071038932e-06
      ],
      "cartesian_polarization_e_A2": [
        0.014513656567047182,
        0.012362295764008376,
        0.0007599999963127219
      ],
      "ranking_score": 0.7854558083729271
    },
    {
      "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": 0.000415151606602708,
      "parent_symmetrization_rmsd_A": 0.2716328526688566,
      "parent_cell_rmsd_A": 0.28978184820936514,
      "energy_eV": -69.89759570732696,
      "reduced_polarization": [
        0.49981646149880093,
        0.49969749194174157,
        0.4997828517793508
      ],
      "cartesian_polarization_e_A2": [
        0.015272424781405822,
        0.013018512638879163,
        0.012084112934736496
      ],
      "ranking_score": 0.8449086179344033
    }
  ],
  "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": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "target_residual": 0.014861129595128296,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.004923684530240236,
            "max_log_strain_component": 0.0007942906708172347,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.000794606203188,
              0.9997117772091856,
              0.9997000478366956
            ],
            "cell_volume_ratio": 1.000206050403348,
            "cell_rmsd_from_input_A": 0.0033186497473049227
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3318482502071263e-15,
              6.347678185004271e-16,
              2.170280530597971e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.3318482502071263e-15,
              6.347678185004271e-16,
              2.170280530597971e-05
            ],
            "target_residual": 2.170280530597971e-05,
            "energy_eV": -81.44652174435106
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "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": 2.7104755324278027e-16,
        "parent_symmetrization_rmsd_A": 0.49803412593369933,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -74.71815742999611,
        "reduced_polarization": [
          1.4607704654343645e-16,
          -1.483741716578809e-17,
          2.2783354371973604e-16
        ],
        "cartesian_polarization_e_A2": [
          4.237343591608346e-18,
          -3.665972483060563e-19,
          5.2503260355710195e-18
        ],
        "ranking_score": 0.4980341259336999
      },
      "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": [
          -81.45033966399318,
          -81.06876881713644,
          -80.23324599254275,
          -79.19228913628882,
          -78.05400293135267,
          -76.86477549109867,
          -75.74216075237514,
          -74.97421195644932,
          -74.7181574299961
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.599155799314648e-18,
            5.8373561845656654e-18,
            0.00034246834051477763
          ],
          [
            2.6880528177474615e-18,
            1.5862380936319744e-17,
            -0.004177519790509938
          ],
          [
            6.9178792003279315e-18,
            4.624765286322556e-18,
            -0.00859732929090779
          ],
          [
            -7.183268902333534e-18,
            1.2323307500749738e-17,
            -0.01249064954751805
          ],
          [
            -2.0566928478907328e-18,
            1.7554368236193848e-17,
            -0.014440919466950091
          ],
          [
            1.3790910149029058e-18,
            -3.257075552257654e-18,
            -0.013155191862816287
          ],
          [
            1.1477950979541631e-18,
            5.428459253762757e-18,
            -0.009390648947626503
          ],
          [
            1.360530911976824e-17,
            -7.529343484439771e-18,
            -0.004554908261516678
          ],
          [
            -5.243810037889739e-18,
            2.3462223891587603e-17,
            4.630979503254176e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714134e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.871797242453267e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911727e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.1970790803186213e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.047377217896477e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343766e-16,
            9.495946986104377e-16,
            2.0095751463272914e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714131e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.8717972424532672e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911732e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.197079080318621e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.0473772178964773e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343764e-16,
            9.495946986104377e-16,
            1.942890293094024e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            0.014861129595128642
          ],
          [
            1.1102230246251565e-16,
            6.661338147750939e-16,
            -0.181280006495386
          ],
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.3730739739974976
          ],
          [
            -2.220446049250313e-16,
            4.440892098500626e-16,
            0.4579786225670365
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            0.37334827695729367
          ],
          [
            0.0,
            -1.1102230246251565e-16,
            0.42914135996270575
          ],
          [
            0.0,
            2.220446049250313e-16,
            -0.40749942252549387
          ],
          [
            4.440892098500626e-16,
            -2.7755575615628914e-16,
            -0.19765646619063365
          ],
          [
            -1.6653345369377348e-16,
            9.992007221626409e-16,
            2.220446049250313e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -74.71815742999613,
          -74.97421195644932,
          -75.74216075237513,
          -76.86477549109865,
          -78.05400293135267,
          -79.19228913628882,
          -80.23324599254275,
          -81.06876881713643,
          -81.45033966399319
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.4434108617693464e-18,
            9.587928032619933e-19,
            2.2771803813786217e-18
          ],
          [
            1.429174151656162e-18,
            6.683349834502718e-18,
            0.004554908261516611
          ],
          [
            -9.540266174152854e-19,
            7.331944966121126e-18,
            0.009390648947626501
          ],
          [
            3.4545380262311542e-18,
            2.81997883312351e-20,
            0.013155191862816286
          ],
          [
            -2.105488041422025e-18,
            9.89812570426352e-18,
            0.014440919466950093
          ],
          [
            -4.386988653565702e-18,
            1.1082516814175394e-17,
            0.012490649547518067
          ],
          [
            9.77349938062897e-18,
            2.6789798914673346e-19,
            0.00859732929090779
          ],
          [
            -7.541554909944026e-18,
            2.4280017753193422e-17,
            0.0041775197905099745
          ],
          [
            2.5487103667055196e-18,
            9.3200300434732e-18,
            -0.00034246834051474386
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.22128417959117e-16,
            3.880555258744577e-17,
            9.881635396803036e-17
          ],
          [
            4.926896640706729e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.288885774376234e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819836993e-18,
            0.5708586400372941
          ],
          [
            -7.25840300589629e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845144e-17,
            0.3730739739974976
          ],
          [
            -2.59985541359328e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.7721279794561264e-16,
            -0.0148611295951272
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.22128417959117e-16,
            3.880555258744577e-17,
            9.881635396803036e-17
          ],
          [
            4.9268966407067283e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.2888857743762345e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819837049e-18,
            0.5708586400372941
          ],
          [
            -7.258403005896289e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845147e-17,
            0.3730739739974976
          ],
          [
            -2.5998554135932806e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.772127979456127e-16,
            -0.014861129595127198
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.0299733821113758e-16,
          1.66293206235025e-15,
          -0.014861129595128263
        ],
        "actual_opposite_endpoint_branch_residual": 1.6947433901315731e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714134e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.871797242453267e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911727e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.1970790803186213e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.047377217896477e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343766e-16,
            9.495946986104377e-16,
            2.0095751463272914e-16
          ],
          [
            4.926896640706729e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.288885774376234e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819836993e-18,
            0.5708586400372941
          ],
          [
            -7.25840300589629e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845144e-17,
            0.3730739739974976
          ],
          [
            -2.59985541359328e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.7721279794561264e-16,
            -0.0148611295951272
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714131e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.8717972424532672e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911732e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.197079080318621e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.0473772178964773e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343764e-16,
            9.495946986104377e-16,
            1.942890293094024e-16
          ],
          [
            4.9268966407067283e-17,
            2.704975283301367e-16,
            0.1976564661906308
          ],
          [
            -3.2888857743762345e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819837049e-18,
            0.5708586400372941
          ],
          [
            -7.258403005896289e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845147e-17,
            0.3730739739974976
          ],
          [
            -2.5998554135932806e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.772127979456127e-16,
            -0.014861129595127198
          ]
        ],
        "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": [
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            0.014861129595128642
          ],
          [
            1.1102230246251565e-16,
            6.661338147750939e-16,
            -0.181280006495386
          ],
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.3730739739974976
          ],
          [
            -2.220446049250313e-16,
            4.440892098500626e-16,
            0.4579786225670365
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            0.37334827695729367
          ],
          [
            0.0,
            -1.1102230246251565e-16,
            0.42914135996270575
          ],
          [
            0.0,
            2.220446049250313e-16,
            -0.40749942252549387
          ],
          [
            4.440892098500626e-16,
            -2.7755575615628914e-16,
            -0.19765646619063365
          ],
          [
            -1.6653345369377348e-16,
            9.992007221626409e-16,
            2.220446049250313e-16
          ],
          [
            0.0,
            2.220446049250313e-16,
            0.19765646619063082
          ],
          [
            -5.551115123125783e-17,
            3.3306690738754696e-16,
            0.40749942252549376
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.42914135996270586
          ],
          [
            -5.551115123125783e-17,
            4.440892098500626e-16,
            -0.37334827695729356
          ],
          [
            -1.6653345369377348e-16,
            4.440892098500626e-16,
            -0.4579786225670357
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.37307397399749753
          ],
          [
            -2.7755575615628914e-16,
            9.992007221626409e-16,
            0.18128000649538756
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.014861129595127198
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128308
            ],
            "target_residual": 0.4851388704048717,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.019358445877810448,
            "step_scale": 0.746580729259814,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.007338322821123,
              1.00705031332401,
              0.9808277255701401
            ],
            "cell_volume_ratio": 0.9949912443845171,
            "cell_rmsd_from_input_A": 0.08003509221435363
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0699065104362353e-14,
              -8.068428660421493e-15,
              0.36990280794443386
            ],
            "branch_aligned_reduced_polarization": [
              -1.0699065104362353e-14,
              -8.068428660421493e-15,
              0.36990280794443386
            ],
            "target_residual": 0.13009719205556614,
            "energy_eV": -78.99065893756512,
            "max_atomic_step_A": 0.04299745602785426,
            "max_log_strain_component": 0.008482338880220803,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0105707184955905,
              1.0101552080551683,
              0.972543198175785
            ],
            "cell_volume_ratio": 0.9928044574857084,
            "cell_rmsd_from_input_A": 0.11461039896470555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.493303882114682e-15,
              -4.306696634789495e-15,
              0.49094046468551034
            ],
            "branch_aligned_reduced_polarization": [
              -5.493303882114682e-15,
              -4.306696634789495e-15,
              0.49094046468551034
            ],
            "target_residual": 0.009059535314489664,
            "energy_eV": -76.27045714377618,
            "max_atomic_step_A": 0.002608188775894475,
            "max_log_strain_component": 0.0007118924677665789,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0108424732644103,
              1.0104162258163527,
              0.9718510983779715
            ],
            "cell_volume_ratio": 0.9926211470088309,
            "cell_rmsd_from_input_A": 0.11749900777285868
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.0101576445315216e-16,
              1.47338131171445e-16,
              0.4996570379068814
            ],
            "branch_aligned_reduced_polarization": [
              2.0101576445315216e-16,
              1.47338131171445e-16,
              0.4996570379068814
            ],
            "target_residual": 0.00034296209311862613,
            "energy_eV": -76.06409558210144
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmn2_1",
        "spacegroup_number": 31,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00034296209311862613,
        "parent_symmetrization_rmsd_A": 0.10747616158341586,
        "parent_cell_rmsd_A": 0.11749900777285868,
        "energy_eV": -76.06409558210144,
        "reduced_polarization": [
          2.0101576445315216e-16,
          1.47338131171445e-16,
          0.4996570379068814
        ],
        "cartesian_polarization_e_A2": [
          9.124518035065626e-17,
          -1.4544201158397618e-16,
          0.011273449494556312
        ],
        "ranking_score": 0.6375368377128678
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1081674232186611e-16,
              5.551115123125783e-17,
              0.014861129595128296
            ],
            "target_residual": 0.500220804418252,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012859203378762705,
            "step_scale": 0.6429368540512678,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0131080813569473,
              0.9998146814089452,
              0.9873752548493441
            ],
            "cell_volume_ratio": 1.000132472525173,
            "cell_rmsd_from_input_A": 0.06614271573040284
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.8968594885109696e-15,
              0.31195763661082593,
              0.006075536727124553
            ],
            "branch_aligned_reduced_polarization": [
              -4.8968594885109696e-15,
              0.31195763661082593,
              0.006075536727124553
            ],
            "target_residual": 0.18814048627424357,
            "energy_eV": -79.85219576347853,
            "max_atomic_step_A": 0.07248739661789991,
            "max_log_strain_component": 0.00881516499813406,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.022308684577343,
              0.9995646167050731,
              0.978908834801228
            ],
            "cell_volume_ratio": 1.00031129469913,
            "cell_rmsd_from_input_A": 0.11164354649515258
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.208588762050081e-15,
              0.48903340304365,
              0.001602928339658922
            ],
            "branch_aligned_reduced_polarization": [
              -5.208588762050081e-15,
              0.48903340304365,
              0.001602928339658922
            ],
            "target_residual": 0.011083123569874453,
            "energy_eV": -77.11079493943265,
            "max_atomic_step_A": 0.004232013873724529,
            "max_log_strain_component": 0.0006350218881598183,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.02300077460654,
              0.9995193406386788,
              0.9783225590843493
            ],
            "cell_volume_ratio": 1.0003436799800574,
            "cell_rmsd_from_input_A": 0.11494777330949223
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.0311323696652054e-15,
              0.4997827140425634,
              0.00012861725998790266
            ],
            "branch_aligned_reduced_polarization": [
              2.0311323696652054e-15,
              0.4997827140425634,
              0.00012861725998790266
            ],
            "target_residual": 0.0002524986868598124,
            "energy_eV": -76.93037434665911
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0002524986868598124,
        "parent_symmetrization_rmsd_A": 0.1391379853105489,
        "parent_cell_rmsd_A": 0.11494777330949223,
        "energy_eV": -76.93037434665911,
        "reduced_polarization": [
          2.0311323696652054e-15,
          0.4997827140425634,
          0.00012861725998790266
        ],
        "cartesian_polarization_e_A2": [
          -1.2731088346397783e-16,
          0.01234116191642757,
          0.0002785491831203299
        ],
        "ranking_score": 0.6683799260116416
      },
      "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,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "target_residual": 0.500220804418252,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012582965303154938,
            "step_scale": 0.5623282220363632,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0128102801226526,
              0.9998313173600673,
              0.9876327413043263
            ],
            "cell_volume_ratio": 1.000115862732843,
            "cell_rmsd_from_input_A": 0.0759590053312312
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2753548021284094,
              -2.9896270204544894e-15,
              0.007657366060485962
            ],
            "branch_aligned_reduced_polarization": [
              0.2753548021284094,
              -2.9896270204544894e-15,
              0.007657366060485962
            ],
            "target_residual": 0.2247756663470278,
            "energy_eV": -79.93447333547076,
            "max_atomic_step_A": 0.09651326766121196,
            "max_log_strain_component": 0.011371497508081153,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.024609071432203,
              0.9995906671031792,
              0.9766562276212927
            ],
            "cell_volume_ratio": 1.000281214815064,
            "cell_rmsd_from_input_A": 0.14476679641156634
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48007916879466267,
              -3.2999969326143148e-15,
              -0.0011066731697869222
            ],
            "branch_aligned_reduced_polarization": [
              0.48007916879466267,
              -3.2999969326143148e-15,
              -0.0011066731697869222
            ],
            "target_residual": 0.01995154734390964,
            "energy_eV": -75.85765442530956,
            "max_atomic_step_A": 0.007919059137287137,
            "max_log_strain_component": 0.0014342262074478849,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0260481181630408,
              0.9996243169979401,
              0.9752310766229689
            ],
            "cell_volume_ratio": 1.000258089753919,
            "cell_rmsd_from_input_A": 0.15341973737802628
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49927544393988466,
              -1.130757864523936e-16,
              -4.18458764778386e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49927544393988466,
              -1.130757864523936e-16,
              -4.18458764778386e-05
            ],
            "target_residual": 0.0007257634336531905,
            "energy_eV": -75.46083960315576
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0007257634336531905,
        "parent_symmetrization_rmsd_A": 0.1535808602301102,
        "parent_cell_rmsd_A": 0.15341973737802628,
        "energy_eV": -75.46083960315576,
        "reduced_polarization": [
          0.49927544393988466,
          -1.130757864523936e-16,
          -4.18458764778386e-05
        ],
        "cartesian_polarization_e_A2": [
          0.01447845840179443,
          -1.9066595955356107e-16,
          0.00036678722011456756
        ],
        "ranking_score": 0.6933873214419232
      },
      "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": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              7.646976539290786e-17,
              0.014861129595128308
            ],
            "target_residual": 0.696677632465486,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011648737662922489,
            "step_scale": 0.4492469650834018,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0091398700069079,
              1.0044093265376173,
              0.983616172512964
            ],
            "cell_volume_ratio": 0.9969830217508402,
            "cell_rmsd_from_input_A": 0.07720091392004666
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21951849234040283,
              -9.053866196355921e-15,
              0.2314756427159509
            ],
            "branch_aligned_reduced_polarization": [
              0.21951849234040283,
              -9.053866196355921e-15,
              0.2314756427159509
            ],
            "target_residual": 0.388297832332106,
            "energy_eV": -80.06490146493056,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012488069151645095,
            "step_scale": 0.7980438644191478,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.019183000526246,
              1.009157956395978,
              0.9662058306439473
            ],
            "cell_volume_ratio": 0.9937587686895188,
            "cell_rmsd_from_input_A": 0.15972199986144617
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.42003569313982986,
              -1.0366538011484118e-14,
              0.4249095325280095
            ],
            "branch_aligned_reduced_polarization": [
              0.42003569313982986,
              -1.0366538011484118e-14,
              0.4249095325280095
            ],
            "target_residual": 0.10969443320784113,
            "energy_eV": -75.62842524112497,
            "max_atomic_step_A": 0.040695428461214565,
            "max_log_strain_component": 0.006629428861641337,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0249860483708535,
              1.0116879345230494,
              0.9566864875200028
            ],
            "cell_volume_ratio": 0.9920513776209913,
            "cell_rmsd_from_input_A": 0.20556900457467842
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48593127561425475,
              -6.394757403920363e-15,
              0.49151971048517273
            ],
            "branch_aligned_reduced_polarization": [
              0.48593127561425475,
              -6.394757403920363e-15,
              0.49151971048517273
            ],
            "target_residual": 0.016426938731770816,
            "energy_eV": -73.23843363085459,
            "max_atomic_step_A": 0.007472520125564681,
            "max_log_strain_component": 0.0015061843962290988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0263212819771657,
              1.0121052067906804,
              0.9547775046977797
            ],
            "cell_volume_ratio": 0.9917704673214429,
            "cell_rmsd_from_input_A": 0.21525062846002563
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4982735548605887,
              -8.602489598851845e-16,
              0.49877186110154925
            ],
            "branch_aligned_reduced_polarization": [
              0.4982735548605887,
              -8.602489598851845e-16,
              0.49877186110154925
            ],
            "target_residual": 0.002118711394523722,
            "energy_eV": -72.93932625783859,
            "max_atomic_step_A": 0.0010843357156155571,
            "max_log_strain_component": 0.00016893204930895064,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.6589853795310314,
            "cell_principal_stretches": [
              1.0262257650732365,
              1.0121366357461408,
              0.9546333710781173
            ],
            "cell_volume_ratio": 0.9915592517924662,
            "cell_rmsd_from_input_A": 0.2153756929950862
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49999928682556205,
              2.5470350469176765e-15,
              0.5000003031447683
            ],
            "branch_aligned_reduced_polarization": [
              0.49999928682556205,
              2.5470350469176765e-15,
              0.5000003031447683
            ],
            "target_residual": 7.749287254225151e-07,
            "energy_eV": -72.9065068825265
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.749287254225151e-07,
        "parent_symmetrization_rmsd_A": 0.19750116557650058,
        "parent_cell_rmsd_A": 0.2153756929950862,
        "energy_eV": -72.9065068825265,
        "reduced_polarization": [
          0.49999928682556205,
          2.5470350469176765e-15,
          0.5000003031447683
        ],
        "cartesian_polarization_e_A2": [
          0.015134305396403439,
          -2.636088943446476e-16,
          0.011677377972351525
        ],
        "ranking_score": 0.751346638682723
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1081674232186611e-16,
              5.551115123125783e-17,
              0.014861129595128308
            ],
            "target_residual": 0.6966776324654861,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01259476279389384,
            "step_scale": 0.4857315122746958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0091477006302836,
              1.004581359581634,
              0.9831988044989363
            ],
            "cell_volume_ratio": 0.996738404872398,
            "cell_rmsd_from_input_A": 0.0719083804311406
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0037795290999066e-14,
              0.23773844532292052,
              0.24770851638122
            ],
            "branch_aligned_reduced_polarization": [
              -1.0037795290999066e-14,
              0.23773844532292054,
              0.24770851638122
            ],
            "target_residual": 0.3639122363540472,
            "energy_eV": -79.9657681805911,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013386941248295769,
            "step_scale": 0.8989175380890638,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.019043499411947,
              1.0094738877939005,
              0.9655734877236263
            ],
            "cell_volume_ratio": 0.993283325632539,
            "cell_rmsd_from_input_A": 0.14744987918781463
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.3217602149164786e-14,
              0.4526980786257054,
              0.4519915492585402
            ],
            "branch_aligned_reduced_polarization": [
              -1.3217602149164786e-14,
              0.4526980786257054,
              0.4519915492585402
            ],
            "target_residual": 0.06739646213485634,
            "energy_eV": -75.11436412014714,
            "max_atomic_step_A": 0.028498196129696313,
            "max_log_strain_component": 0.004127380733692273,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.021942743167276,
              1.0109871228076133,
              0.9603642945128777
            ],
            "cell_volume_ratio": 0.992220493954509,
            "cell_rmsd_from_input_A": 0.16971969491935554
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.57699675041522e-15,
              0.49644582521745145,
              0.4968116257413105
            ],
            "branch_aligned_reduced_polarization": [
              -3.57699675041522e-15,
              0.49644582521745145,
              0.4968116257413105
            ],
            "target_residual": 0.004774713478144828,
            "energy_eV": -73.75246385797547,
            "max_atomic_step_A": 0.0020457908846124597,
            "max_log_strain_component": 0.00030738234239349174,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0221826600836457,
              1.0110999101115883,
              0.9599552429497846
            ],
            "cell_volume_ratio": 0.9921413861988604,
            "cell_rmsd_from_input_A": 0.17148077418735627
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.974439300453612e-16,
              0.49982149245646573,
              0.49980070004103394
            ],
            "branch_aligned_reduced_polarization": [
              -1.974439300453612e-16,
              0.49982149245646573,
              0.49980070004103394
            ],
            "target_residual": 0.00026755451172146466,
            "energy_eV": -73.66157291611327
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00026755451172146466,
        "parent_symmetrization_rmsd_A": 0.17793191336057362,
        "parent_cell_rmsd_A": 0.17148077418735627,
        "energy_eV": -73.66157291611327,
        "reduced_polarization": [
          -1.974439300453612e-16,
          0.49982149245646573,
          0.49980070004103394
        ],
        "cartesian_polarization_e_A2": [
          -7.753992600947421e-17,
          0.012863516978804,
          0.011552714459766314
        ],
        "ranking_score": 0.7213372159308556
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              5.551115123125783e-17,
              0.014861129595128296
            ],
            "target_residual": 0.707262930721555,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.009472838200577292,
            "step_scale": 0.42333775343334595,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0128958827622836,
              0.9998752135618431,
              0.9874776407450911
            ],
            "cell_volume_ratio": 1.0000872237330634,
            "cell_rmsd_from_input_A": 0.07185912316692808
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.20680882831011327,
              0.2066739346554143,
              0.009474040590464054
            ],
            "branch_aligned_reduced_polarization": [
              0.20680882831011327,
              0.20667393465541428,
              0.009474040590464054
            ],
            "target_residual": 0.4148385242627962,
            "energy_eV": -79.90692758015402,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010404380032230532,
            "step_scale": 0.6972330431465099,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.027407964126052,
              0.9995986348882961,
              0.9739872578148943
            ],
            "cell_volume_ratio": 1.0002806266869895,
            "cell_rmsd_from_input_A": 0.15113439935625636
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.38658374464958706,
              0.3900747434773923,
              0.0013882085631056666
            ],
            "branch_aligned_reduced_polarization": [
              0.38658374464958706,
              0.3900747434773923,
              0.0013882085631056666
            ],
            "target_residual": 0.15795168920364816,
            "energy_eV": -74.55956017805447,
            "max_atomic_step_A": 0.06282940760127835,
            "max_log_strain_component": 0.008900253149259126,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0392931431291539,
              0.9996355234550424,
              0.9627884238357213
            ],
            "cell_volume_ratio": 1.0002547048722454,
            "cell_rmsd_from_input_A": 0.21699790270866487
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48559460054897585,
              0.4875255589503344,
              -0.009842025863775477
            ],
            "branch_aligned_reduced_polarization": [
              0.48559460054897585,
              0.4875255589503344,
              -0.009842025863775477
            ],
            "target_residual": 0.021447440079141723,
            "energy_eV": -72.12496556063417,
            "max_atomic_step_A": 0.009503200665333396,
            "max_log_strain_component": 0.0012797226264968944,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0407482529967083,
              0.9999149726476791,
              0.9609859424685245
            ],
            "cell_volume_ratio": 1.0000594011447743,
            "cell_rmsd_from_input_A": 0.2262498562319768
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4988629169885286,
              0.4990143792506289,
              -0.000691613831519592
            ],
            "branch_aligned_reduced_polarization": [
              0.4988629169885286,
              0.4990143792506289,
              -0.000691613831519592
            ],
            "target_residual": 0.0016561206865796164,
            "energy_eV": -72.03104123562713,
            "max_atomic_step_A": 0.0008060944666699417,
            "max_log_strain_component": 7.33426108367753e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.654626024823714,
            "cell_principal_stretches": [
              1.0407088419725852,
              0.999957585732413,
              0.9608682013787241
            ],
            "cell_volume_ratio": 0.9999416195547677,
            "cell_rmsd_from_input_A": 0.2264377457722005
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999998148252426,
              0.49999957873706574,
              -1.005635071038932e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999998148252426,
              0.49999957873706574,
              -1.005635071038932e-06
            ],
            "target_residual": 1.105917739557321e-06,
            "energy_eV": -72.02306047161959
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.105917739557321e-06,
        "parent_symmetrization_rmsd_A": 0.22884416009439787,
        "parent_cell_rmsd_A": 0.2264377457722005,
        "energy_eV": -72.02306047161959,
        "reduced_polarization": [
          0.4999998148252426,
          0.49999957873706574,
          -1.005635071038932e-06
        ],
        "cartesian_polarization_e_A2": [
          0.014513656567047182,
          0.012362295764008376,
          0.0007599999963127219
        ],
        "ranking_score": 0.7854558083729271
      },
      "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": [
              1.1081674232186611e-16,
              7.646976539290786e-17,
              0.014861129595128296
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              5.551115123125783e-17,
              0.014861129595128308
            ],
            "target_residual": 0.8575311793618438,
            "energy_eV": -81.45033966399319,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.009532382723015589,
            "step_scale": 0.3676273028242008,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.009863219805695,
              1.0035435067465386,
              0.9842998317629414
            ],
            "cell_volume_ratio": 0.9975304721117817,
            "cell_rmsd_from_input_A": 0.07352771051458712
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.17956202817340058,
              0.18044868099329925,
              0.19174093181540364
            ],
            "branch_aligned_reduced_polarization": [
              0.1795620281734006,
              0.18044868099329925,
              0.19174093181540364
            ],
            "target_residual": 0.5475556523179195,
            "energy_eV": -80.12266521493436,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010056493441096692,
            "step_scale": 0.5689519793456501,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.020707854436336,
              1.007296000123315,
              0.9676866170325334
            ],
            "cell_volume_ratio": 0.9949317747721702,
            "cell_rmsd_from_input_A": 0.15198757146236194
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3429426325665585,
              0.34534314447969683,
              0.3511618539795143
            ],
            "branch_aligned_reduced_polarization": [
              0.3429426325665585,
              0.34534314447969683,
              0.3511618539795143
            ],
            "target_residual": 0.2659672034957814,
            "energy_eV": -76.02131102820022,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012650169219595409,
            "step_scale": 0.9908407182056458,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0352866859345982,
              1.0120391729047937,
              0.9464775119022214
            ],
            "cell_volume_ratio": 0.991672457980462,
            "cell_rmsd_from_input_A": 0.2537084464249823
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.44865395560319604,
              0.4478077802366681,
              0.4529411327835772
            ],
            "branch_aligned_reduced_polarization": [
              0.44865395560319604,
              0.4478077802366681,
              0.4529411327835772
            ],
            "target_residual": 0.08703436713572062,
            "energy_eV": -69.95802037983339,
            "max_atomic_step_A": 0.048456780868890034,
            "max_log_strain_component": 0.00556600274550633,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.122590438902335,
            "cell_principal_stretches": [
              1.0413353915911756,
              1.0141336458846963,
              0.9376816508337654
            ],
            "cell_volume_ratio": 0.9902417616388646,
            "cell_rmsd_from_input_A": 0.29585180867910355
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4840847189922776,
              0.487061006056757,
              0.48789340074303134
            ],
            "branch_aligned_reduced_polarization": [
              0.4840847189922776,
              0.487061006056757,
              0.48789340074303134
            ],
            "target_residual": 0.023817713563372995,
            "energy_eV": -69.87648733625687,
            "max_atomic_step_A": 0.011173581231602737,
            "max_log_strain_component": 0.002286057490760626,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.817644523342443,
            "cell_principal_stretches": [
              1.037538155242494,
              1.0145966024248092,
              0.9363236411571519
            ],
            "cell_volume_ratio": 0.9856516866576467,
            "cell_rmsd_from_input_A": 0.28978184820936514
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49981646149880093,
              0.49969749194174157,
              0.4997828517793508
            ],
            "branch_aligned_reduced_polarization": [
              0.49981646149880093,
              0.49969749194174157,
              0.4997828517793508
            ],
            "target_residual": 0.000415151606602708,
            "energy_eV": -69.89759570732696
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.000415151606602708,
        "parent_symmetrization_rmsd_A": 0.2716328526688566,
        "parent_cell_rmsd_A": 0.28978184820936514,
        "energy_eV": -69.89759570732696,
        "reduced_polarization": [
          0.49981646149880093,
          0.49969749194174157,
          0.4997828517793508
        ],
        "cartesian_polarization_e_A2": [
          0.015272424781405822,
          0.013018512638879163,
          0.012084112934736496
        ],
        "ranking_score": 0.8449086179344033
      },
      "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
        ],
        "endpoint_rmsd_A": 0.49803412593369933,
        "minimum_distance_A_by_image": [
          1.7262280893349489,
          1.7102374825378188,
          1.6908864304277471,
          1.6743377882949668,
          1.6606753363618898,
          1.649970772792437,
          1.6422819380722267,
          1.6376513096345229,
          1.6361048543896772
        ],
        "minimum_distance_A": 1.6361048543896772,
        "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": [
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374,
          246.061914451374
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.8077370088343766e-16,
        9.495946986104377e-16,
        2.0095751463272914e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -81.45033966399318,
          -81.06876881713644,
          -80.23324599254275,
          -79.19228913628882,
          -78.05400293135267,
          -76.86477549109867,
          -75.74216075237514,
          -74.97421195644932,
          -74.7181574299961
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.599155799314648e-18,
            5.8373561845656654e-18,
            0.00034246834051477763
          ],
          [
            2.6880528177474615e-18,
            1.5862380936319744e-17,
            -0.004177519790509938
          ],
          [
            6.9178792003279315e-18,
            4.624765286322556e-18,
            -0.00859732929090779
          ],
          [
            -7.183268902333534e-18,
            1.2323307500749738e-17,
            -0.01249064954751805
          ],
          [
            -2.0566928478907328e-18,
            1.7554368236193848e-17,
            -0.014440919466950091
          ],
          [
            1.3790910149029058e-18,
            -3.257075552257654e-18,
            -0.013155191862816287
          ],
          [
            1.1477950979541631e-18,
            5.428459253762757e-18,
            -0.009390648947626503
          ],
          [
            1.360530911976824e-17,
            -7.529343484439771e-18,
            -0.004554908261516678
          ],
          [
            -5.243810037889739e-18,
            2.3462223891587603e-17,
            4.630979503254176e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714134e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.871797242453267e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911727e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.1970790803186213e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.047377217896477e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343766e-16,
            9.495946986104377e-16,
            2.0095751463272914e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714131e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.8717972424532672e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911732e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.197079080318621e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.0473772178964773e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343764e-16,
            9.495946986104377e-16,
            1.942890293094024e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            0.014861129595128642
          ],
          [
            1.1102230246251565e-16,
            6.661338147750939e-16,
            -0.181280006495386
          ],
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.3730739739974976
          ],
          [
            -2.220446049250313e-16,
            4.440892098500626e-16,
            0.4579786225670365
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            0.37334827695729367
          ],
          [
            0.0,
            -1.1102230246251565e-16,
            0.42914135996270575
          ],
          [
            0.0,
            2.220446049250313e-16,
            -0.40749942252549387
          ],
          [
            4.440892098500626e-16,
            -2.7755575615628914e-16,
            -0.19765646619063365
          ],
          [
            -1.6653345369377348e-16,
            9.992007221626409e-16,
            2.220446049250313e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -74.71815742999613,
          -74.97421195644932,
          -75.74216075237513,
          -76.86477549109865,
          -78.05400293135267,
          -79.19228913628882,
          -80.23324599254275,
          -81.06876881713643,
          -81.45033966399319
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.4434108617693464e-18,
            9.587928032619933e-19,
            2.2771803813786217e-18
          ],
          [
            1.429174151656162e-18,
            6.683349834502718e-18,
            0.004554908261516611
          ],
          [
            -9.540266174152854e-19,
            7.331944966121126e-18,
            0.009390648947626501
          ],
          [
            3.4545380262311542e-18,
            2.81997883312351e-20,
            0.013155191862816286
          ],
          [
            -2.105488041422025e-18,
            9.89812570426352e-18,
            0.014440919466950093
          ],
          [
            -4.386988653565702e-18,
            1.1082516814175394e-17,
            0.012490649547518067
          ],
          [
            9.77349938062897e-18,
            2.6789798914673346e-19,
            0.00859732929090779
          ],
          [
            -7.541554909944026e-18,
            2.4280017753193422e-17,
            0.0041775197905099745
          ],
          [
            2.5487103667055196e-18,
            9.3200300434732e-18,
            -0.00034246834051474386
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.22128417959117e-16,
            3.880555258744577e-17,
            9.881635396803036e-17
          ],
          [
            4.926896640706729e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.288885774376234e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819836993e-18,
            0.5708586400372941
          ],
          [
            -7.25840300589629e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845144e-17,
            0.3730739739974976
          ],
          [
            -2.59985541359328e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.7721279794561264e-16,
            -0.0148611295951272
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.22128417959117e-16,
            3.880555258744577e-17,
            9.881635396803036e-17
          ],
          [
            4.9268966407067283e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.2888857743762345e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819837049e-18,
            0.5708586400372941
          ],
          [
            -7.258403005896289e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845147e-17,
            0.3730739739974976
          ],
          [
            -2.5998554135932806e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.772127979456127e-16,
            -0.014861129595127198
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.0299733821113758e-16,
          1.66293206235025e-15,
          -0.014861129595128263
        ],
        "actual_opposite_endpoint_branch_residual": 1.6947433901315731e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714134e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.871797242453267e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911727e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.1970790803186213e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.047377217896477e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343766e-16,
            9.495946986104377e-16,
            2.0095751463272914e-16
          ],
          [
            4.926896640706729e-17,
            2.7049752833013673e-16,
            0.1976564661906308
          ],
          [
            -3.288885774376234e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819836993e-18,
            0.5708586400372941
          ],
          [
            -7.25840300589629e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845144e-17,
            0.3730739739974976
          ],
          [
            -2.59985541359328e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.7721279794561264e-16,
            -0.0148611295951272
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5855006355573777e-16,
            2.3625733487062573e-16,
            0.014861129595128666
          ],
          [
            9.266721191714131e-17,
            6.420036273658309e-16,
            -0.18128000649538598
          ],
          [
            2.3848511221262744e-16,
            1.8717972424532672e-16,
            -0.3730739739974976
          ],
          [
            -2.4763408562342094e-16,
            4.987654847268766e-16,
            -0.5420213774329635
          ],
          [
            -7.090187764378406e-17,
            7.1048401428485275e-16,
            -0.6266517230427063
          ],
          [
            4.754241378267419e-17,
            -1.3182474481911732e-16,
            -0.5708586400372943
          ],
          [
            3.956878037415375e-17,
            2.197079080318621e-16,
            -0.40749942252549387
          ],
          [
            4.690257777212421e-16,
            -3.0473772178964773e-16,
            -0.19765646619063365
          ],
          [
            -1.8077370088343764e-16,
            9.495946986104377e-16,
            1.942890293094024e-16
          ],
          [
            4.9268966407067283e-17,
            2.704975283301367e-16,
            0.1976564661906308
          ],
          [
            -3.2888857743762345e-17,
            2.9674834331576184e-16,
            0.4074994225254938
          ],
          [
            1.1909081742703338e-16,
            1.1413397819837049e-18,
            0.5708586400372941
          ],
          [
            -7.258403005896289e-17,
            4.0061026347627845e-16,
            0.6266517230427064
          ],
          [
            -1.5123587027532148e-16,
            4.485465343195939e-16,
            0.5420213774329643
          ],
          [
            3.369289964457395e-16,
            1.0842727928845147e-17,
            0.3730739739974976
          ],
          [
            -2.5998554135932806e-16,
            9.826935522879652e-16,
            0.18128000649538756
          ],
          [
            8.786355763084724e-17,
            3.772127979456127e-16,
            -0.014861129595127198
          ]
        ],
        "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": [
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            0.014861129595128642
          ],
          [
            1.1102230246251565e-16,
            6.661338147750939e-16,
            -0.181280006495386
          ],
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.3730739739974976
          ],
          [
            -2.220446049250313e-16,
            4.440892098500626e-16,
            0.4579786225670365
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            0.37334827695729367
          ],
          [
            0.0,
            -1.1102230246251565e-16,
            0.42914135996270575
          ],
          [
            0.0,
            2.220446049250313e-16,
            -0.40749942252549387
          ],
          [
            4.440892098500626e-16,
            -2.7755575615628914e-16,
            -0.19765646619063365
          ],
          [
            -1.6653345369377348e-16,
            9.992007221626409e-16,
            2.220446049250313e-16
          ],
          [
            0.0,
            2.220446049250313e-16,
            0.19765646619063082
          ],
          [
            -5.551115123125783e-17,
            3.3306690738754696e-16,
            0.40749942252549376
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.42914135996270586
          ],
          [
            -5.551115123125783e-17,
            4.440892098500626e-16,
            -0.37334827695729356
          ],
          [
            -1.6653345369377348e-16,
            4.440892098500626e-16,
            -0.4579786225670357
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.37307397399749753
          ],
          [
            -2.7755575615628914e-16,
            9.992007221626409e-16,
            0.18128000649538756
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.014861129595127198
          ]
        ]
      },
      "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": "Pmmn",
        "spacegroup_number": 59,
        "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": 2.7104755324278027e-16,
        "parent_symmetrization_rmsd_A": 0.49803412593369933,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -74.71815742999611,
        "reduced_polarization": [
          1.4607704654343645e-16,
          -1.483741716578809e-17,
          2.2783354371973604e-16
        ],
        "cartesian_polarization_e_A2": [
          4.237343591608346e-18,
          -3.665972483060563e-19,
          5.2503260355710195e-18
        ],
        "ranking_score": 0.4980341259336999
      }
    }
  ],
  "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": 101,
      "full_response": 30,
      "energy_polarization": 71
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 126,
      "full_response": 55,
      "energy_polarization": 71
    },
    "elapsed_seconds": 311.6542424840154
  }
}