{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "Cd2O8Rb12",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -72.48725744977996,
  "input_cartesian_polarization_e_A2": [
    -3.60102543202657e-18,
    0.0014380271099771118,
    -8.552435401063103e-18
  ],
  "input_reduced_polarization": [
    -4.822599141691674e-16,
    0.10724883156366198,
    -5.577565561558074e-16
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 2.0518502155353602e-14,
      "parent_symmetrization_rmsd_A": 0.6230913050009029,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -70.37596748376625,
      "reduced_polarization": [
        4.4346643669897346e-15,
        1.9832118964287206e-14,
        2.8336795933488538e-15
      ],
      "cartesian_polarization_e_A2": [
        5.34328626605119e-17,
        2.659154818111701e-16,
        4.345060833790883e-17
      ],
      "ranking_score": 0.623091305000944
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "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": 3.1230958877080105e-15,
      "parent_symmetrization_rmsd_A": 0.8296357286376931,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -65.50493819255786,
      "reduced_polarization": [
        6.456877852094607e-17,
        -9.048539868152855e-16,
        2.9884440866784646e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.5313090536892652e-17,
        -1.2132575662037574e-17,
        4.5823710575742516e-17
      ],
      "ranking_score": 0.8296357286376993
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 6.82426271604691e-06,
      "parent_symmetrization_rmsd_A": 0.020793621115658682,
      "parent_cell_rmsd_A": 0.014462704536222464,
      "energy_eV": -72.45993172430614,
      "reduced_polarization": [
        8.88818377599006e-17,
        6.82426271604691e-06,
        -4.320249566332586e-15
      ],
      "cartesian_polarization_e_A2": [
        3.966696136058882e-17,
        9.148591730244036e-08,
        -6.598852215704337e-17
      ],
      "ranking_score": 0.5244229457751464
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 5.111545191393545e-15,
      "parent_symmetrization_rmsd_A": 0.62309458363916,
      "parent_cell_rmsd_A": 0.014462704536222464,
      "energy_eV": -70.3838584265103,
      "reduced_polarization": [
        -1.5303381377152704e-15,
        -4.449934447034921e-15,
        -1.996006724689232e-15
      ],
      "cartesian_polarization_e_A2": [
        -9.389254151841502e-18,
        -5.965572425361541e-17,
        -3.0488701684069594e-17
      ],
      "ranking_score": 0.6267102597732259
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 0.00024267944671202413,
      "parent_symmetrization_rmsd_A": 0.07298558769865608,
      "parent_cell_rmsd_A": 0.049222470685026956,
      "energy_eV": -72.3694929122195,
      "reduced_polarization": [
        -2.9898475230696247e-18,
        0.499757320553288,
        3.2602680624745797e-16
      ],
      "cartesian_polarization_e_A2": [
        1.880986599442778e-16,
        0.006704967116630588,
        -6.764358487322616e-16
      ],
      "ranking_score": 0.5857765642633369
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.468385137804577e-05,
      "parent_symmetrization_rmsd_A": 0.1650123655647543,
      "parent_cell_rmsd_A": 0.06035404146477885,
      "energy_eV": -71.96217298978524,
      "reduced_polarization": [
        -6.248019399147138e-10,
        -3.91131227670794e-05,
        -0.5000216057909134
      ],
      "cartesian_polarization_e_A2": [
        0.004412033977563502,
        6.442662775378531e-05,
        -0.007641867581128826
      ],
      "ranking_score": 0.6801902436337051
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 8.164942139995943e-05,
      "parent_symmetrization_rmsd_A": 0.17887015447387328,
      "parent_cell_rmsd_A": 0.07653323823572195,
      "energy_eV": -71.69807221395561,
      "reduced_polarization": [
        1.2067874185757728e-09,
        0.499922513451456,
        -0.4999742616471345
      ],
      "cartesian_polarization_e_A2": [
        0.0045112627676090295,
        0.006773243312828043,
        -0.007813740905023275
      ],
      "ranking_score": 0.6981667628756036
    }
  ],
  "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": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.577565561558074e-16
            ],
            "branch_aligned_reduced_polarization": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.577565561558074e-16
            ],
            "target_residual": 0.10724883156366198,
            "energy_eV": -72.48725744977996,
            "max_atomic_step_A": 0.02708196117398853,
            "max_log_strain_component": 0.0037019738589300394,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0037088346276724,
              1.0000862987902384,
              1.0000862842985099
            ],
            "cell_volume_ratio": 1.0038820652724036,
            "cell_rmsd_from_input_A": 0.014262871600059353
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.915699498597432e-15,
              0.001440819951667615,
              1.224378326655648e-14
            ],
            "branch_aligned_reduced_polarization": [
              2.915699498597432e-15,
              0.001440819951667615,
              1.224378326655648e-14
            ],
            "target_residual": 0.001440819951667615,
            "energy_eV": -72.46047186937574,
            "max_atomic_step_A": 0.00036099991572595923,
            "max_log_strain_component": 5.167383976997369e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0037607014572356,
              1.000087503440819,
              1.0000874887467908
            ],
            "cell_volume_ratio": 1.0039363594225779,
            "cell_rmsd_from_input_A": 0.014462704536222464
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.88818377599006e-17,
              6.82426271604691e-06,
              -4.320249566332586e-15
            ],
            "branch_aligned_reduced_polarization": [
              8.88818377599006e-17,
              6.82426271604691e-06,
              -4.320249566332586e-15
            ],
            "target_residual": 6.82426271604691e-06,
            "energy_eV": -72.45993172430614
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 6.82426271604691e-06,
        "parent_symmetrization_rmsd_A": 0.020793621115658682,
        "parent_cell_rmsd_A": 0.014462704536222464,
        "energy_eV": -72.45993172430614,
        "reduced_polarization": [
          8.88818377599006e-17,
          6.82426271604691e-06,
          -4.320249566332586e-15
        ],
        "cartesian_polarization_e_A2": [
          3.966696136058882e-17,
          9.148591730244036e-08,
          -6.598852215704337e-17
        ],
        "ranking_score": 0.5244229457751464
      },
      "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": [
          -72.48725744977997,
          -72.4853432133605,
          -72.48300410997933,
          -72.48023825856622,
          -72.47704363039877,
          -72.47341805187854,
          -72.46935920600365,
          -72.46486463220617,
          -72.45993172430614
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0961945065139705e-17,
            0.0014380271099771165,
            3.4633391655079065e-17
          ],
          [
            -3.43517368129706e-17,
            0.0012566402951214967,
            -1.1776982189346623e-17
          ],
          [
            -4.613252385228019e-17,
            0.0010757184017886991,
            3.8355596092778825e-18
          ],
          [
            -1.8031499165542837e-17,
            0.0008952644772824387,
            1.9644287214073795e-17
          ],
          [
            4.6245793672356987e-17,
            0.0007152812094635525,
            1.5829274519852477e-17
          ],
          [
            1.6587485619658036e-17,
            0.0005357708419195105,
            -7.319095963705799e-17
          ],
          [
            4.8629216072333326e-17,
            0.0003567351007185327,
            -4.2108360279789175e-17
          ],
          [
            4.8024821328588166e-18,
            0.00017817513662871012,
            -5.718120209837943e-17
          ],
          [
            1.345089780179541e-17,
            9.148591729123127e-08,
            -9.940477218620961e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.3994526939153134e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.503528594878242e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927172e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472176e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.8242627152107846e-06,
            -6.507914383502357e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.399452693915313e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.5035285948782426e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927171e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472177e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.824262715211457e-06,
            -6.507914383502357e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.7763568394002505e-15,
            0.10724883156366238,
            2.220446049250313e-15
          ],
          [
            -2.3869795029440866e-15,
            0.0937229558107765,
            -1.0547118733938987e-15
          ],
          [
            -2.609024107869118e-15,
            0.08023116390825713,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            0.06677368539655482,
            6.661338147750939e-16
          ],
          [
            2.9976021664879227e-15,
            0.053350723026316826,
            3.3306690738754696e-16
          ],
          [
            -1.609823385706477e-15,
            0.03996244642806168,
            -5.384581669432009e-15
          ],
          [
            1.2212453270876722e-15,
            0.026608986645121124,
            -3.2751579226442118e-15
          ],
          [
            -1.6653345369377348e-15,
            0.01329043181943057,
            -4.052314039881821e-15
          ],
          [
            -2.4980018054066022e-15,
            6.824262715254825e-06,
            -6.494804694057166e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -72.45993172430616,
          -72.45753396363511,
          -72.45454847718284,
          -72.45096085295128,
          -72.44675635454047,
          -72.44191989657725,
          -72.4364360193913,
          -72.43028886343939,
          -72.4234621440779
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2501422662845146e-17,
            9.148591728440033e-08,
            -5.905207878082337e-17
          ],
          [
            6.586261210777806e-17,
            -0.00016038408460442792,
            -5.855333985062481e-17
          ],
          [
            4.3401971347945706e-17,
            -0.00032057931234167773,
            -1.4773566402865217e-16
          ],
          [
            7.865849072506628e-17,
            -0.0004804961392081805,
            -1.8597529657326788e-16
          ],
          [
            1.0649745628548494e-16,
            -0.0006401373711430066,
            -2.536383586670185e-16
          ],
          [
            1.6423998946679194e-16,
            -0.0007995066124782573,
            -3.022523437837034e-16
          ],
          [
            1.9479352388084364e-16,
            -0.0009586081984207126,
            -3.4485648707693625e-16
          ],
          [
            1.4714611454554433e-16,
            -0.0011174471266447393,
            -3.6553635505450687e-16
          ],
          [
            1.741201708897553e-16,
            -0.001276028988803666,
            -4.0275880769526583e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.6418114178246253e-15,
            6.824262714701241e-06,
            -3.866140794947139e-15
          ],
          [
            1.882987806674998e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6418114178246253e-15,
            6.824262714701241e-06,
            -3.866140794947139e-15
          ],
          [
            1.8829878066749977e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.711856127217613e-15,
          -0.10723518542630381,
          -1.522423987457572e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.012068260448976728
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.3994526939153134e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.503528594878242e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927172e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472176e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.8242627152107846e-06,
            -6.507914383502357e-15
          ],
          [
            1.882987806674998e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.399452693915313e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.5035285948782426e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927171e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472177e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.824262715211457e-06,
            -6.507914383502357e-15
          ],
          [
            1.8829878066749977e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "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": [
          [
            1.7763568394002505e-15,
            0.10724883156366238,
            2.220446049250313e-15
          ],
          [
            -2.3869795029440866e-15,
            0.0937229558107765,
            -1.0547118733938987e-15
          ],
          [
            -2.609024107869118e-15,
            0.08023116390825713,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            0.06677368539655482,
            6.661338147750939e-16
          ],
          [
            2.9976021664879227e-15,
            0.053350723026316826,
            3.3306690738754696e-16
          ],
          [
            -1.609823385706477e-15,
            0.03996244642806168,
            -5.384581669432009e-15
          ],
          [
            1.2212453270876722e-15,
            0.026608986645121124,
            -3.2751579226442118e-15
          ],
          [
            -1.6653345369377348e-15,
            0.01329043181943057,
            -4.052314039881821e-15
          ],
          [
            -2.4980018054066022e-15,
            6.824262715254825e-06,
            -6.494804694057166e-15
          ],
          [
            1.887379141862766e-15,
            -0.01196336246284918,
            -3.552713678800501e-15
          ],
          [
            -2.275957200481571e-15,
            -0.02391211468571547,
            -9.2148511043888e-15
          ],
          [
            -1.4988010832439613e-15,
            -0.03583957864000764,
            -1.1601830607332886e-14
          ],
          [
            -2.1094237467877974e-15,
            -0.047745964992227774,
            -1.5987211554602254e-14
          ],
          [
            -4.440892098500626e-16,
            -0.05963154393899417,
            -1.9206858326015208e-14
          ],
          [
            -1.1102230246251565e-16,
            -0.07149664016475438,
            -2.2037927038809357e-14
          ],
          [
            -3.552713678800501e-15,
            -0.0833416277338761,
            -2.3592239273284576e-14
          ],
          [
            -3.2751579226442118e-15,
            -0.0951669249773271,
            -2.6256774532384952e-14
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.577565561558074e-16
            ],
            "branch_aligned_reduced_polarization": [
              -4.822599141691674e-16,
              0.107248831563662,
              -5.577565561558074e-16
            ],
            "target_residual": 0.392751168436338,
            "energy_eV": -72.48725744977996,
            "max_atomic_step_A": 0.09917564359027833,
            "max_log_strain_component": 0.01355683355629378,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              0.9996840856567788,
              0.9996840326086099,
              0.9865346464520582
            ],
            "cell_volume_ratio": 0.9859113717029414,
            "cell_rmsd_from_input_A": 0.0513427524407947
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.561573766834999e-15,
              0.5187101576985019,
              4.621598016645242e-14
            ],
            "branch_aligned_reduced_polarization": [
              7.561573766834999e-15,
              0.5187101576985019,
              4.621598016645242e-14
            ],
            "target_residual": 0.018710157698501928,
            "energy_eV": -72.35640076301473,
            "max_atomic_step_A": 0.004743124688327607,
            "max_log_strain_component": 0.0005671577243715809,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              0.9996973001097401,
              0.9996972492801994,
              0.9870943258954104
            ],
            "cell_volume_ratio": 0.9864967794935104,
            "cell_rmsd_from_input_A": 0.049222470685026956
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.9898475230696247e-18,
              0.499757320553288,
              3.2602680624745797e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.9898475230696247e-18,
              0.499757320553288,
              3.2602680624745797e-16
            ],
            "target_residual": 0.00024267944671202413,
            "energy_eV": -72.3694929122195
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 0.00024267944671202413,
        "parent_symmetrization_rmsd_A": 0.07298558769865608,
        "parent_cell_rmsd_A": 0.049222470685026956,
        "energy_eV": -72.3694929122195,
        "reduced_polarization": [
          -2.9898475230696247e-18,
          0.499757320553288,
          3.2602680624745797e-16
        ],
        "cartesian_polarization_e_A2": [
          1.880986599442778e-16,
          0.006704967116630588,
          -6.764358487322616e-16
        ],
        "ranking_score": 0.5857765642633369
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.577565561558074e-16
            ],
            "branch_aligned_reduced_polarization": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.551115123125783e-16
            ],
            "target_residual": 0.5113729674824141,
            "energy_eV": -72.48725744977996,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004075309269566864,
            "step_scale": 0.6584880463155734,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0061198240696152,
              1.000056817859935,
              0.9963998504228799
            ],
            "cell_volume_ratio": 1.0025546019810796,
            "cell_rmsd_from_input_A": 0.03890252064634657
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3709827782762456e-07,
              0.03220630373681362,
              -0.3261557355314801
            ],
            "branch_aligned_reduced_polarization": [
              1.3709827782762456e-07,
              0.03220630373681362,
              -0.3261557355314801
            ],
            "target_residual": 0.17680235939887054,
            "energy_eV": -72.25822016181911,
            "max_atomic_step_A": 0.07198886594781197,
            "max_log_strain_component": 0.0022631404643752204,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0092524122702475,
              1.0000779450319324,
              0.9942289045785141
            ],
            "cell_volume_ratio": 1.0035061325159604,
            "cell_rmsd_from_input_A": 0.06018593523392565
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.6817206769619226e-08,
              -0.0024827599200683143,
              -0.4980705874544268
            ],
            "branch_aligned_reduced_polarization": [
              4.6817206769619226e-08,
              -0.0024827599200683143,
              -0.4980705874544268
            ],
            "target_residual": 0.003144317031392476,
            "energy_eV": -71.96622283892674,
            "max_atomic_step_A": 0.0009822226877836745,
            "max_log_strain_component": 9.054766406245228e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0092272796433124,
              1.0000758344513758,
              0.99416154209314
            ],
            "cell_volume_ratio": 1.0034110360080375,
            "cell_rmsd_from_input_A": 0.06035404146477885
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -6.248019399147138e-10,
              -3.91131227670794e-05,
              -0.5000216057909134
            ],
            "branch_aligned_reduced_polarization": [
              -6.248019399147138e-10,
              -3.91131227670794e-05,
              -0.5000216057909134
            ],
            "target_residual": 4.468385137804577e-05,
            "energy_eV": -71.96217298978524
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.468385137804577e-05,
        "parent_symmetrization_rmsd_A": 0.1650123655647543,
        "parent_cell_rmsd_A": 0.06035404146477885,
        "energy_eV": -71.96217298978524,
        "reduced_polarization": [
          -6.248019399147138e-10,
          -3.91131227670794e-05,
          -0.5000216057909134
        ],
        "cartesian_polarization_e_A2": [
          0.004412033977563502,
          6.442662775378531e-05,
          -0.007641867581128826
        ],
        "ranking_score": 0.6801902436337051
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.822599141691674e-16,
              0.10724883156366198,
              -5.577565561558074e-16
            ],
            "branch_aligned_reduced_polarization": [
              -4.822599141691674e-16,
              0.107248831563662,
              -5.551115123125783e-16
            ],
            "target_residual": 0.6358093112782387,
            "energy_eV": -72.48725744977996,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008181382184561452,
            "step_scale": 0.6034876913264468,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0016942872662373,
              0.9998093325469369,
              0.9899855387988828
            ],
            "cell_volume_ratio": 0.9914737808594647,
            "cell_rmsd_from_input_A": 0.04621110758471219
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.4427040042662146e-07,
              0.34707174365880894,
              -0.29804417046000603
            ],
            "branch_aligned_reduced_polarization": [
              1.4427040042662146e-07,
              0.34707174365880894,
              -0.29804417046000603
            ],
            "target_residual": 0.2533243152024001,
            "energy_eV": -72.2390927257106,
            "max_atomic_step_A": 0.08527721835779878,
            "max_log_strain_component": 0.0050516316979715365,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.003003970713654,
              0.9996916222134229,
              0.9835951078655224
            ],
            "cell_volume_ratio": 0.9862455687203527,
            "cell_rmsd_from_input_A": 0.07638178748218222
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.9021887087301764e-07,
              0.5024644629542866,
              -0.4965768214835353
            ],
            "branch_aligned_reduced_polarization": [
              1.9021887087301764e-07,
              0.5024644629542866,
              -0.4965768214835353
            ],
            "target_residual": 0.004218024282151482,
            "energy_eV": -71.70500957799018,
            "max_atomic_step_A": 0.0014924668711182938,
            "max_log_strain_component": 6.970575616195821e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.546848788763512,
            "cell_principal_stretches": [
              1.0030575554384806,
              0.9996932463641697,
              0.9836127220277556
            ],
            "cell_volume_ratio": 0.986317523130266,
            "cell_rmsd_from_input_A": 0.07653323823572195
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.2067874185757728e-09,
              0.499922513451456,
              -0.4999742616471345
            ],
            "branch_aligned_reduced_polarization": [
              1.2067874185757728e-09,
              0.499922513451456,
              -0.4999742616471345
            ],
            "target_residual": 8.164942139995943e-05,
            "energy_eV": -71.69807221395561
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 8.164942139995943e-05,
        "parent_symmetrization_rmsd_A": 0.17887015447387328,
        "parent_cell_rmsd_A": 0.07653323823572195,
        "energy_eV": -71.69807221395561,
        "reduced_polarization": [
          1.2067874185757728e-09,
          0.499922513451456,
          -0.4999742616471345
        ],
        "cartesian_polarization_e_A2": [
          0.0045112627676090295,
          0.006773243312828043,
          -0.007813740905023275
        ],
        "ranking_score": 0.6981667628756036
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21
        ],
        "endpoint_rmsd_A": 0.020793621115658682,
        "minimum_distance_A_by_image": [
          2.2553488299999995,
          2.2508207488087355,
          2.2462879206574247,
          2.2417503420877547,
          2.237208009639226,
          2.2326609198491267,
          2.228109069252554,
          2.223552454382384,
          2.218991071769298
        ],
        "minimum_distance_A": 2.218991071769298,
        "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": [
          524.1226915747145,
          524.3801404458136,
          524.6377157757029,
          524.8954176264982,
          525.1532460603464,
          525.4112011394259,
          525.6692829259438,
          525.9274914821391,
          526.1858268702822
        ],
        "cell_deformation_log_strain_norm": 0.0037556864671277643
      },
      "parent_reduced_polarization": [
        -2.4913010182211864e-15,
        6.8242627152107846e-06,
        -6.507914383502357e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -72.48725744977997,
          -72.4853432133605,
          -72.48300410997933,
          -72.48023825856622,
          -72.47704363039877,
          -72.47341805187854,
          -72.46935920600365,
          -72.46486463220617,
          -72.45993172430614
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0961945065139705e-17,
            0.0014380271099771165,
            3.4633391655079065e-17
          ],
          [
            -3.43517368129706e-17,
            0.0012566402951214967,
            -1.1776982189346623e-17
          ],
          [
            -4.613252385228019e-17,
            0.0010757184017886991,
            3.8355596092778825e-18
          ],
          [
            -1.8031499165542837e-17,
            0.0008952644772824387,
            1.9644287214073795e-17
          ],
          [
            4.6245793672356987e-17,
            0.0007152812094635525,
            1.5829274519852477e-17
          ],
          [
            1.6587485619658036e-17,
            0.0005357708419195105,
            -7.319095963705799e-17
          ],
          [
            4.8629216072333326e-17,
            0.0003567351007185327,
            -4.2108360279789175e-17
          ],
          [
            4.8024821328588166e-18,
            0.00017817513662871012,
            -5.718120209837943e-17
          ],
          [
            1.345089780179541e-17,
            9.148591729123127e-08,
            -9.940477218620961e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.3994526939153134e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.503528594878242e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927172e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472176e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.8242627152107846e-06,
            -6.507914383502357e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.399452693915313e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.5035285948782426e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927171e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472177e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.824262715211457e-06,
            -6.507914383502357e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.7763568394002505e-15,
            0.10724883156366238,
            2.220446049250313e-15
          ],
          [
            -2.3869795029440866e-15,
            0.0937229558107765,
            -1.0547118733938987e-15
          ],
          [
            -2.609024107869118e-15,
            0.08023116390825713,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            0.06677368539655482,
            6.661338147750939e-16
          ],
          [
            2.9976021664879227e-15,
            0.053350723026316826,
            3.3306690738754696e-16
          ],
          [
            -1.609823385706477e-15,
            0.03996244642806168,
            -5.384581669432009e-15
          ],
          [
            1.2212453270876722e-15,
            0.026608986645121124,
            -3.2751579226442118e-15
          ],
          [
            -1.6653345369377348e-15,
            0.01329043181943057,
            -4.052314039881821e-15
          ],
          [
            -2.4980018054066022e-15,
            6.824262715254825e-06,
            -6.494804694057166e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -72.45993172430616,
          -72.45753396363511,
          -72.45454847718284,
          -72.45096085295128,
          -72.44675635454047,
          -72.44191989657725,
          -72.4364360193913,
          -72.43028886343939,
          -72.4234621440779
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2501422662845146e-17,
            9.148591728440033e-08,
            -5.905207878082337e-17
          ],
          [
            6.586261210777806e-17,
            -0.00016038408460442792,
            -5.855333985062481e-17
          ],
          [
            4.3401971347945706e-17,
            -0.00032057931234167773,
            -1.4773566402865217e-16
          ],
          [
            7.865849072506628e-17,
            -0.0004804961392081805,
            -1.8597529657326788e-16
          ],
          [
            1.0649745628548494e-16,
            -0.0006401373711430066,
            -2.536383586670185e-16
          ],
          [
            1.6423998946679194e-16,
            -0.0007995066124782573,
            -3.022523437837034e-16
          ],
          [
            1.9479352388084364e-16,
            -0.0009586081984207126,
            -3.4485648707693625e-16
          ],
          [
            1.4714611454554433e-16,
            -0.0011174471266447393,
            -3.6553635505450687e-16
          ],
          [
            1.741201708897553e-16,
            -0.001276028988803666,
            -4.0275880769526583e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.6418114178246253e-15,
            6.824262714701241e-06,
            -3.866140794947139e-15
          ],
          [
            1.882987806674998e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6418114178246253e-15,
            6.824262714701241e-06,
            -3.866140794947139e-15
          ],
          [
            1.8829878066749977e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.711856127217613e-15,
          -0.10723518542630381,
          -1.522423987457572e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.012068260448976728
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.3994526939153134e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.503528594878242e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927172e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472176e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.8242627152107846e-06,
            -6.507914383502357e-15
          ],
          [
            1.882987806674998e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.7484451437448575e-15,
            0.10724883156366234,
            2.2586550323585012e-15
          ],
          [
            -2.399452693915313e-15,
            0.09372295581077646,
            -1.0608195634038873e-15
          ],
          [
            -2.609832462700529e-15,
            0.08023116390825714,
            -2.5035285948782426e-16
          ],
          [
            -5.369750930989324e-16,
            0.0667736853965548,
            6.577121023927171e-16
          ],
          [
            2.9650922932655503e-15,
            0.05335072302631685,
            3.680649077842711e-16
          ],
          [
            -1.6115225067830388e-15,
            0.03996244642806171,
            -5.408658832627389e-15
          ],
          [
            1.2509255690472177e-15,
            0.026608986645121086,
            -3.2527337683551848e-15
          ],
          [
            -1.6724155679212688e-15,
            0.013290431819430605,
            -4.032338888448865e-15
          ],
          [
            -2.4913010182211864e-15,
            6.824262715211457e-06,
            -6.507914383502357e-15
          ],
          [
            1.8829878066749977e-15,
            -0.011963362462849205,
            -3.569849930070174e-15
          ],
          [
            -2.2592411089885042e-15,
            -0.023912114685715448,
            -9.214414635656844e-15
          ],
          [
            -1.4837160264198868e-15,
            -0.03583957864000763,
            -1.1598153696172588e-14
          ],
          [
            -2.1089031042393025e-15,
            -0.047745964992227795,
            -1.597685483036781e-14
          ],
          [
            -4.3898580798506567e-16,
            -0.05963154393899419,
            -1.918175479605781e-14
          ],
          [
            -1.3044396642824098e-16,
            -0.07149664016475438,
            -2.206558537058773e-14
          ],
          [
            -3.5445732564866057e-15,
            -0.08334162773387613,
            -2.3590293891409934e-14
          ],
          [
            -3.2990807956015126e-15,
            -0.09516692497732708,
            -2.626636215382658e-14
          ]
        ],
        "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": [
          [
            1.7763568394002505e-15,
            0.10724883156366238,
            2.220446049250313e-15
          ],
          [
            -2.3869795029440866e-15,
            0.0937229558107765,
            -1.0547118733938987e-15
          ],
          [
            -2.609024107869118e-15,
            0.08023116390825713,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            0.06677368539655482,
            6.661338147750939e-16
          ],
          [
            2.9976021664879227e-15,
            0.053350723026316826,
            3.3306690738754696e-16
          ],
          [
            -1.609823385706477e-15,
            0.03996244642806168,
            -5.384581669432009e-15
          ],
          [
            1.2212453270876722e-15,
            0.026608986645121124,
            -3.2751579226442118e-15
          ],
          [
            -1.6653345369377348e-15,
            0.01329043181943057,
            -4.052314039881821e-15
          ],
          [
            -2.4980018054066022e-15,
            6.824262715254825e-06,
            -6.494804694057166e-15
          ],
          [
            1.887379141862766e-15,
            -0.01196336246284918,
            -3.552713678800501e-15
          ],
          [
            -2.275957200481571e-15,
            -0.02391211468571547,
            -9.2148511043888e-15
          ],
          [
            -1.4988010832439613e-15,
            -0.03583957864000764,
            -1.1601830607332886e-14
          ],
          [
            -2.1094237467877974e-15,
            -0.047745964992227774,
            -1.5987211554602254e-14
          ],
          [
            -4.440892098500626e-16,
            -0.05963154393899417,
            -1.9206858326015208e-14
          ],
          [
            -1.1102230246251565e-16,
            -0.07149664016475438,
            -2.2037927038809357e-14
          ],
          [
            -3.552713678800501e-15,
            -0.0833416277338761,
            -2.3592239273284576e-14
          ],
          [
            -3.2751579226442118e-15,
            -0.0951669249773271,
            -2.6256774532384952e-14
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 6.82426271604691e-06,
        "parent_symmetrization_rmsd_A": 0.020793621115658682,
        "parent_cell_rmsd_A": 0.014462704536222464,
        "energy_eV": -72.45993172430614,
        "reduced_polarization": [
          8.88818377599006e-17,
          6.82426271604691e-06,
          -4.320249566332586e-15
        ],
        "cartesian_polarization_e_A2": [
          3.966696136058882e-17,
          9.148591730244036e-08,
          -6.598852215704337e-17
        ],
        "ranking_score": 0.5244229457751464
      }
    }
  ],
  "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": 44,
      "full_response": 11,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 69,
      "full_response": 36,
      "energy_polarization": 33
    },
    "elapsed_seconds": 175.71128385700285
  }
}