{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "Na12S8Zn2",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -72.20653159063767,
  "input_cartesian_polarization_e_A2": [
    -3.727454311639258e-17,
    0.00025846680684067424,
    6.777600735834466e-11
  ],
  "input_reduced_polarization": [
    2.112807910801615e-09,
    0.01805579070740135,
    4.225620016697637e-09
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "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": 5.3219997362899e-16,
      "parent_symmetrization_rmsd_A": 0.5385951014150887,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -70.44586810844703,
      "reduced_polarization": [
        3.9656229326456947e-16,
        1.868637917431527e-16,
        3.0175666161133015e-16
      ],
      "cartesian_polarization_e_A2": [
        4.550212940887846e-18,
        2.6749361658359986e-18,
        4.83996706684061e-18
      ],
      "ranking_score": 0.5385951014150898
    },
    {
      "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": 2.555048832049521e-06,
      "parent_symmetrization_rmsd_A": 0.004012571934261384,
      "parent_cell_rmsd_A": 0.0029138554921324684,
      "energy_eV": -72.20294891758826,
      "reduced_polarization": [
        -3.468956447616627e-13,
        2.5550488320494026e-06,
        -6.96214434188687e-13
      ],
      "cartesian_polarization_e_A2": [
        2.2425764824848498e-17,
        3.658357018754385e-08,
        -1.1160336328261945e-14
      ],
      "ranking_score": 0.5047461459049586
    },
    {
      "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": 3.405409259571716e-15,
      "parent_symmetrization_rmsd_A": 0.5385952571486144,
      "parent_cell_rmsd_A": 0.0029138554921324684,
      "energy_eV": -70.43791153913718,
      "reduced_polarization": [
        7.426757522343407e-16,
        -3.3226135811224583e-15,
        7.405364785432473e-17
      ],
      "cartesian_polarization_e_A2": [
        1.3061434774421487e-17,
        -4.757367672444258e-17,
        1.1870781125398121e-18
      ],
      "ranking_score": 0.5393237210216544
    },
    {
      "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": 7.203821175139072e-06,
      "parent_symmetrization_rmsd_A": 0.11121369298494675,
      "parent_cell_rmsd_A": 0.07899464217126609,
      "energy_eV": -71.78640724392963,
      "reduced_polarization": [
        -7.786535968762257e-14,
        0.49999279617882486,
        -1.5674113359329235e-13
      ],
      "cartesian_polarization_e_A2": [
        -1.6168798705238707e-16,
        0.00711271066674656,
        -1.167510688589929e-13
      ],
      "ranking_score": 0.6309767611701136
    },
    {
      "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": 5.545637035298358e-06,
      "parent_symmetrization_rmsd_A": 0.15829774712464847,
      "parent_cell_rmsd_A": 0.0034932547035225127,
      "energy_eV": -71.32117454912779,
      "reduced_polarization": [
        -9.803125419723365e-13,
        6.16224260717589e-07,
        0.4999944887063417
      ],
      "cartesian_polarization_e_A2": [
        -0.00462728805708957,
        2.03485350975225e-06,
        0.008014698451068907
      ],
      "ranking_score": 0.6591821520745997
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.545873218862644e-06,
      "parent_symmetrization_rmsd_A": 0.15829771555248787,
      "parent_cell_rmsd_A": 0.0034928686365407412,
      "energy_eV": -71.32116523688568,
      "reduced_polarization": [
        0.49999448847182026,
        6.162522875339983e-07,
        -4.225563002753511e-11
      ],
      "cartesian_polarization_e_A2": [
        0.009254576546336064,
        2.0337672032288235e-06,
        8.887294380293173e-12
      ],
      "ranking_score": 0.6591820244580608
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 6.773924396810407e-06,
      "parent_symmetrization_rmsd_A": 0.1950610259422693,
      "parent_cell_rmsd_A": 0.08144677185382201,
      "energy_eV": -70.75857022446088,
      "reduced_polarization": [
        7.469033340394823e-12,
        0.4999945350150801,
        0.5000040024981648
      ],
      "cartesian_polarization_e_A2": [
        -0.0047081649066859615,
        0.007113397060789485,
        0.00815478114377503
      ],
      "ranking_score": 0.7154362667545184
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.774848265309204e-06,
      "parent_symmetrization_rmsd_A": 0.1950610513589836,
      "parent_cell_rmsd_A": 0.08144675421127355,
      "energy_eV": -70.75855818212366,
      "reduced_polarization": [
        0.5000040039236813,
        0.4999945349141048,
        5.748035910096285e-10
      ],
      "cartesian_polarization_e_A2": [
        0.009416328881054514,
        0.00711339595932224,
        -7.581172684581004e-10
      ],
      "ranking_score": 0.7154362896083326
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.818781873616915e-06,
      "parent_symmetrization_rmsd_A": 0.15829771856140926,
      "parent_cell_rmsd_A": 0.0032284835528696393,
      "energy_eV": -71.32116527616071,
      "reduced_polarization": [
        0.4999944884649943,
        6.162541882277959e-07,
        0.49999448850631467
      ],
      "cartesian_polarization_e_A2": [
        0.00462728846659806,
        2.0337686265969675e-06,
        0.00801469849746767
      ],
      "ranking_score": 0.6591204770133738
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 7.869294862096339e-06,
      "parent_symmetrization_rmsd_A": 0.19506105309057886,
      "parent_cell_rmsd_A": 0.08143590014840174,
      "energy_eV": -70.758558194121,
      "reduced_polarization": [
        0.5000040039463634,
        0.4999945349131958,
        0.5000040033787441
      ],
      "cartesian_polarization_e_A2": [
        0.004708163973540919,
        0.007113395960033235,
        0.008154780387507221
      ],
      "ranking_score": 0.7154357667174035
    }
  ],
  "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": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "target_residual": 0.01805579070740197,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.005858141407352019,
            "max_log_strain_component": 0.0006954079934107718,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0006956498456085,
              0.9998864719940218,
              0.9998864698303734
            ],
            "cell_volume_ratio": 1.0004684466148384,
            "cell_rmsd_from_input_A": 0.0029138554921324684
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.468956447616627e-13,
              2.5550488320494026e-06,
              -6.96214434188687e-13
            ],
            "branch_aligned_reduced_polarization": [
              -3.468956447616627e-13,
              2.5550488320494026e-06,
              -6.96214434188687e-13
            ],
            "target_residual": 2.555048832049521e-06,
            "energy_eV": -72.20294891758826
          }
        ],
        "iterations": 1
      },
      "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": 2.555048832049521e-06,
        "parent_symmetrization_rmsd_A": 0.004012571934261384,
        "parent_cell_rmsd_A": 0.0029138554921324684,
        "energy_eV": -72.20294891758826,
        "reduced_polarization": [
          -3.468956447616627e-13,
          2.5550488320494026e-06,
          -6.96214434188687e-13
        ],
        "cartesian_polarization_e_A2": [
          2.2425764824848498e-17,
          3.658357018754385e-08,
          -1.1160336328261945e-14
        ],
        "ranking_score": 0.5047461459049586
      },
      "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": [
          -72.20653159063767,
          -72.20615422715814,
          -72.20575673997428,
          -72.20533912398759,
          -72.20490137387196,
          -72.20444348407291,
          -72.20396544880677,
          -72.20346726205996,
          -72.20294891758827
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.8877133837711565e-17,
            0.00025846680684068194,
            6.777600720094735e-11
          ],
          [
            -9.716568287450666e-17,
            0.00022618367235724732,
            5.929865798745938e-11
          ],
          [
            -3.2276976611732495e-17,
            0.0001938944697054022,
            5.082232954784292e-11
          ],
          [
            7.940014779705361e-18,
            0.0001615992843727041,
            4.234718499661607e-11
          ],
          [
            -5.650670697977809e-17,
            0.00012929820148840934,
            3.3873163271585023e-11
          ],
          [
            -4.782047165541659e-17,
            9.699130580701358e-05,
            2.540029277186331e-11
          ],
          [
            -4.675918950224726e-17,
            6.467868169236803e-05,
            1.692858555493504e-11
          ],
          [
            7.180097584777895e-17,
            3.236041310159437e-05,
            8.458078505422962e-12
          ],
          [
            2.917637770579779e-18,
            3.65835702425356e-08,
            -1.1185021832144398e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.487195581393697e-13,
            2.5550488358901053e-06,
            -6.977543931952837e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.4871955813938927e-13,
            2.555048835890198e-06,
            -6.97754393195332e-13
          ]
        ],
        "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": [
          [
            2.1128078175891574e-09,
            0.01805579070740193,
            4.225619965048111e-09
          ],
          [
            1.8486719932653273e-09,
            0.01580012994095925,
            3.6973547556939934e-09
          ],
          [
            1.5845360579191947e-09,
            0.01354417332523905,
            3.1690757795743707e-09
          ],
          [
            1.3203970139485932e-09,
            0.011287926862304731,
            2.6407931397187667e-09
          ],
          [
            1.0562485330822824e-09,
            0.009031396528513036,
            2.1125032834135027e-09
          ],
          [
            7.921012734612987e-10,
            0.006774588273367632,
            1.5842078759931155e-09
          ],
          [
            5.279512382827534e-10,
            0.004517508018413441,
            1.05590758359142e-09
          ],
          [
            2.6380631013012135e-10,
            0.002260161656117421,
            5.276048486990703e-10
          ],
          [
            -3.4872105203476167e-13,
            2.5550488358394574e-06,
            -6.977751709769109e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -72.20294891758829,
          -72.20291015226465,
          -72.20285207880674,
          -72.20277462118185,
          -72.2026777028587,
          -72.2025612468075,
          -72.20242517549957,
          -72.2022694109078,
          -72.20209387450632
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.587538198697821e-17,
            3.6583570195502993e-08,
            -1.1198265619279482e-14
          ],
          [
            3.1352139254647704e-17,
            -2.904562060583434e-05,
            -8.470868504789818e-12
          ],
          [
            1.0184320258672392e-17,
            -5.811839270756507e-05,
            -1.693242651696608e-11
          ],
          [
            4.5889342826974704e-17,
            -8.718156681684153e-05,
            -2.539599735485788e-11
          ],
          [
            -3.6450402375816346e-17,
            -0.00011623497895627254,
            -3.386146669796111e-11
          ],
          [
            2.7582609901390875e-17,
            -0.00014527846710356786,
            -4.2328888999388354e-11
          ],
          [
            7.428282915253329e-17,
            -0.00017431187120668168,
            -5.0798153148087484e-11
          ],
          [
            6.641777350956558e-17,
            -0.0002033350331976994,
            -5.926925491638994e-11
          ],
          [
            9.420944026039491e-17,
            -0.0002323477970062145,
            -6.774220934962126e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.484326055639679e-13,
            2.5550488326052806e-06,
            -6.985805820960472e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.484326055639679e-13,
            2.5550488326052806e-06,
            -6.985805820960472e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.1135048550552218e-09,
          -0.01805067944924304,
          -4.2270147084604795e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0018194919890442175
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.487195581393697e-13,
            2.5550488358901053e-06,
            -6.977543931952837e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.4871955813938927e-13,
            2.555048835890198e-06,
            -6.97754393195332e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "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": [
          [
            2.1128078175891574e-09,
            0.01805579070740193,
            4.225619965048111e-09
          ],
          [
            1.8486719932653273e-09,
            0.01580012994095925,
            3.6973547556939934e-09
          ],
          [
            1.5845360579191947e-09,
            0.01354417332523905,
            3.1690757795743707e-09
          ],
          [
            1.3203970139485932e-09,
            0.011287926862304731,
            2.6407931397187667e-09
          ],
          [
            1.0562485330822824e-09,
            0.009031396528513036,
            2.1125032834135027e-09
          ],
          [
            7.921012734612987e-10,
            0.006774588273367632,
            1.5842078759931155e-09
          ],
          [
            5.279512382827534e-10,
            0.004517508018413441,
            1.05590758359142e-09
          ],
          [
            2.6380631013012135e-10,
            0.002260161656117421,
            5.276048486990703e-10
          ],
          [
            -3.4872105203476167e-13,
            2.5550488358394574e-06,
            -6.977751709769109e-13
          ],
          [
            -2.6419949561429235e-10,
            -0.002028645239025295,
            -5.28402432919961e-10
          ],
          [
            -5.28072863215101e-10,
            -0.0040593020482776465,
            -1.0561468366532267e-09
          ],
          [
            -7.919672695422264e-10,
            -0.006089403738788357,
            -1.5839395350880636e-09
          ],
          [
            -1.0558886542888501e-09,
            -0.008118938804663689,
            -2.111773422797114e-09
          ],
          [
            -1.3198243609124916e-09,
            -0.010147895875272928,
            -2.6396518859606033e-09
          ],
          [
            -1.5837798850171225e-09,
            -0.012176263716325353,
            -3.167567874662325e-09
          ],
          [
            -1.8477569474484312e-09,
            -0.014204031230859837,
            -3.695521222368825e-09
          ],
          [
            -2.1117512183366216e-09,
            -0.016231187460198804,
            -4.2235128172585235e-09
          ]
        ]
      },
      "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": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.112807910801615e-09,
              0.018055790707401376,
              4.225620016697637e-09
            ],
            "target_residual": 0.4819442092925986,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014244954740182812,
            "step_scale": 0.7674341852075941,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0023284260928287,
              1.002328381663736,
              0.9858560245770163
            ],
            "cell_volume_ratio": 0.9904523113426796,
            "cell_rmsd_from_input_A": 0.058968044743343
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.973844309441731e-10,
              0.3842551867737987,
              9.947897181681517e-10
            ],
            "branch_aligned_reduced_polarization": [
              4.973844309441731e-10,
              0.3842551867737987,
              9.947897181681517e-10
            ],
            "target_residual": 0.11574481322620128,
            "energy_eV": -71.98761239045857,
            "max_atomic_step_A": 0.040317105537910514,
            "max_log_strain_component": 0.004819901975672912,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0031174958629874,
              1.003117436354122,
              0.981115728235274
            ],
            "cell_volume_ratio": 0.9872424533643099,
            "cell_rmsd_from_input_A": 0.07861429130281157
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.649303495405993e-13,
              0.4978951881071865,
              -7.187812531462821e-13
            ],
            "branch_aligned_reduced_polarization": [
              -3.649303495405993e-13,
              0.4978951881071865,
              -7.187812531462821e-13
            ],
            "target_residual": 0.002104811892813474,
            "energy_eV": -71.79071524837525,
            "max_atomic_step_A": 0.0007477385256271968,
            "max_log_strain_component": 9.368359179322929e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0031328390268022,
              1.0031327792245988,
              0.9810238180951913
            ],
            "cell_volume_ratio": 0.9871801670863197,
            "cell_rmsd_from_input_A": 0.07899464217126609
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.786535968762257e-14,
              0.49999279617882486,
              -1.5674113359329235e-13
            ],
            "branch_aligned_reduced_polarization": [
              -7.786535968762257e-14,
              0.49999279617882486,
              -1.5674113359329235e-13
            ],
            "target_residual": 7.203821175139072e-06,
            "energy_eV": -71.78640724392963
          }
        ],
        "iterations": 3
      },
      "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": 7.203821175139072e-06,
        "parent_symmetrization_rmsd_A": 0.11121369298494675,
        "parent_cell_rmsd_A": 0.07899464217126609,
        "energy_eV": -71.78640724392963,
        "reduced_polarization": [
          -7.786535968762257e-14,
          0.49999279617882486,
          -1.5674113359329235e-13
        ],
        "cartesian_polarization_e_A2": [
          -1.6168798705238707e-16,
          0.00711271066674656,
          -1.167510688589929e-13
        ],
        "ranking_score": 0.6309767611701136
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620020559262e-09
            ],
            "target_residual": 0.5003259011408958,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005044438107997979,
            "step_scale": 0.7253926712591188,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0005410641936863,
              0.9999176463351273,
              0.999881174418793
            ],
            "cell_volume_ratio": 1.0003397858877363,
            "cell_rmsd_from_input_A": 0.002423517205505172
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.9062000844063344e-10,
              0.00436025690086159,
              0.3565687133777508
            ],
            "branch_aligned_reduced_polarization": [
              -1.9062000844063344e-10,
              0.00436025690086159,
              0.3565687133777508
            ],
            "target_residual": 0.1434975463983803,
            "energy_eV": -71.78321618340445,
            "max_atomic_step_A": 0.05097649366086186,
            "max_log_strain_component": 0.00019231398160800107,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0007514172336605,
              0.9998862516392091,
              0.9998318799285856
            ],
            "cell_volume_ratio": 1.00046935613841,
            "cell_rmsd_from_input_A": 0.003381661906585825
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.38281146663401e-10,
              0.0006107521106944025,
              0.49620576433805613
            ],
            "branch_aligned_reduced_polarization": [
              -3.38281146663401e-10,
              0.0006107521106944025,
              0.49620576433805613
            ],
            "target_residual": 0.0038430772044137237,
            "energy_eV": -71.33627657419152,
            "max_atomic_step_A": 0.0014457141846858808,
            "max_log_strain_component": 2.8581104442775795e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.000779018848744,
              0.9998815859408599,
              0.9998282148192762
            ],
            "cell_volume_ratio": 1.0004886138958302,
            "cell_rmsd_from_input_A": 0.0034932547035225127
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -9.803125419723365e-13,
              6.16224260717589e-07,
              0.4999944887063417
            ],
            "branch_aligned_reduced_polarization": [
              -9.803125419723365e-13,
              6.16224260717589e-07,
              0.4999944887063417
            ],
            "target_residual": 5.545637035298358e-06,
            "energy_eV": -71.32117454912779
          }
        ],
        "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": 5.545637035298358e-06,
        "parent_symmetrization_rmsd_A": 0.15829774712464847,
        "parent_cell_rmsd_A": 0.0034932547035225127,
        "energy_eV": -71.32117454912779,
        "reduced_polarization": [
          -9.803125419723365e-13,
          6.16224260717589e-07,
          0.4999944887063417
        ],
        "cartesian_polarization_e_A2": [
          -0.00462728805708957,
          2.03485350975225e-06,
          0.008014698451068907
        ],
        "ranking_score": 0.6591821520745997
      },
      "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": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.11280792861146e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "target_residual": 0.5003259032523317,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005044425389840044,
            "step_scale": 0.7253907688638658,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0005410259903904,
              0.9999176455269123,
              0.9998812125157751
            ],
            "cell_volume_ratio": 1.0003397849980247,
            "cell_rmsd_from_input_A": 0.0024232624247399466
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3565680350806273,
              0.0043602543500426034,
              1.2203154495714168e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.3565680350806273,
              0.0043602543500426034,
              1.2203154495714168e-07
            ],
            "target_residual": 0.1434982243048468,
            "energy_eV": -71.78321342313204,
            "max_atomic_step_A": 0.050976792291408515,
            "max_log_strain_component": 0.00019230924039721978,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0007513568090631,
              0.9998862512170333,
              0.9998319366236189
            ],
            "cell_volume_ratio": 1.0004693520395986,
            "cell_rmsd_from_input_A": 0.0033812705783306902
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4962057981246239,
              0.0006107567258816567,
              3.673705565650905e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.4962057981246239,
              0.0006107567258816567,
              3.673705565650905e-08
            ],
            "target_residual": 0.0038430445808846432,
            "energy_eV": -71.33626735573829,
            "max_atomic_step_A": 0.0014457084326683005,
            "max_log_strain_component": 2.8581155843340172e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0007789592812248,
              0.9998815854532814,
              0.9998282707557574
            ],
            "cell_volume_ratio": 1.0004886098311454,
            "cell_rmsd_from_input_A": 0.0034928686365407412
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999448847182026,
              6.162522875339983e-07,
              -4.225563002753511e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.49999448847182026,
              6.162522875339983e-07,
              -4.225563002753511e-11
            ],
            "target_residual": 5.545873218862644e-06,
            "energy_eV": -71.32116523688568
          }
        ],
        "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": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.545873218862644e-06,
        "parent_symmetrization_rmsd_A": 0.15829771555248787,
        "parent_cell_rmsd_A": 0.0034928686365407412,
        "energy_eV": -71.32116523688568,
        "reduced_polarization": [
          0.49999448847182026,
          6.162522875339983e-07,
          -4.225563002753511e-11
        ],
        "cartesian_polarization_e_A2": [
          0.009254576546336064,
          2.0337672032288235e-06,
          8.887294380293173e-12
        ],
        "ranking_score": 0.6591820244580608
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.112807910801615e-09,
              0.018055790707401376,
              4.225620020559262e-09
            ],
            "target_residual": 0.6944567780971311,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009977607359429019,
            "step_scale": 0.5375346629577958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.001631410361139,
              1.0016303027688036,
              0.9900709390662858
            ],
            "cell_volume_ratio": 0.9933028997323892,
            "cell_rmsd_from_input_A": 0.04145506372484194
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.636568074155086e-09,
              0.27407071511293724,
              0.2651394539474503
            ],
            "branch_aligned_reduced_polarization": [
              1.636568074155086e-09,
              0.27407071511293724,
              0.2651394539474503
            ],
            "target_residual": 0.32588881211493187,
            "energy_eV": -71.87196306294268,
            "max_atomic_step_A": 0.10533574500975737,
            "max_log_strain_component": 0.009352768277201528,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.003163068970676,
              1.0031609225733988,
              0.9808532170345955
            ],
            "cell_volume_ratio": 0.9870659312675375,
            "cell_rmsd_from_input_A": 0.07970968897708253
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.172706088732221e-10,
              0.4913705674507622,
              0.4916824734852319
            ],
            "branch_aligned_reduced_polarization": [
              3.172706088732221e-10,
              0.4913705674507622,
              0.4916824734852319
            ],
            "target_residual": 0.01198533910432722,
            "energy_eV": -70.81805569498678,
            "max_atomic_step_A": 0.004183484220640911,
            "max_log_strain_component": 0.0004280759546000788,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0032332222615783,
              1.0032310349513234,
              0.9804333886549553
            ],
            "cell_volume_ratio": 0.9867814045078487,
            "cell_rmsd_from_input_A": 0.08144677185382201
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.469033340394823e-12,
              0.4999945350150801,
              0.5000040024981648
            ],
            "branch_aligned_reduced_polarization": [
              7.469033340394823e-12,
              0.4999945350150801,
              0.5000040024981648
            ],
            "target_residual": 6.773924396810407e-06,
            "energy_eV": -70.75857022446088
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 6.773924396810407e-06,
        "parent_symmetrization_rmsd_A": 0.1950610259422693,
        "parent_cell_rmsd_A": 0.08144677185382201,
        "energy_eV": -70.75857022446088,
        "reduced_polarization": [
          7.469033340394823e-12,
          0.4999945350150801,
          0.5000040024981648
        ],
        "cartesian_polarization_e_A2": [
          -0.0047081649066859615,
          0.007113397060789485,
          0.00815478114377503
        ],
        "ranking_score": 0.7154362667545184
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.11280792861146e-09,
              0.018055790707401376,
              4.225620016697637e-09
            ],
            "target_residual": 0.6944567796183289,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00997760232897415,
            "step_scale": 0.5375343939875631,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0016313886863286,
              1.0016303216230347,
              0.9900709451843941
            ],
            "cell_volume_ratio": 0.9933029030733633,
            "cell_rmsd_from_input_A": 0.04145503523503613
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.26513939135787473,
              0.27407058918012506,
              4.479676169353658e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.26513939135787473,
              0.27407058918012506,
              4.479676169353658e-08
            ],
            "target_residual": 0.3258889445273763,
            "energy_eV": -71.87196029579849,
            "max_atomic_step_A": 0.1053359221815379,
            "max_log_strain_component": 0.009352773786330884,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.003163028590358,
              1.0031609608310257,
              0.9808532187475307
            ],
            "cell_volume_ratio": 0.9870659309027721,
            "cell_rmsd_from_input_A": 0.07970967604299223
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4916826753468826,
              0.4913705791154874,
              1.1752771845397995e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4916826753468826,
              0.4913705791154874,
              1.1752771845397995e-07
            ],
            "target_residual": 0.011985190620145728,
            "energy_eV": -70.8180434744381,
            "max_atomic_step_A": 0.0041834361536195,
            "max_log_strain_component": 0.00042807486397883094,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0032331808107842,
              1.0032310738772963,
              0.980433391479181
            ],
            "cell_volume_ratio": 0.9867814048670256,
            "cell_rmsd_from_input_A": 0.08144675421127355
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000040039236813,
              0.4999945349141048,
              5.748035910096285e-10
            ],
            "branch_aligned_reduced_polarization": [
              0.5000040039236813,
              0.4999945349141048,
              5.748035910096285e-10
            ],
            "target_residual": 6.774848265309204e-06,
            "energy_eV": -70.75855818212366
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.774848265309204e-06,
        "parent_symmetrization_rmsd_A": 0.1950610513589836,
        "parent_cell_rmsd_A": 0.08144675421127355,
        "energy_eV": -70.75855818212366,
        "reduced_polarization": [
          0.5000040039236813,
          0.4999945349141048,
          5.748035910096285e-10
        ],
        "cartesian_polarization_e_A2": [
          0.009416328881054514,
          0.00711339595932224,
          -7.581172684581004e-10
        ],
        "ranking_score": 0.7154362896083326
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.11280792861146e-09,
              0.01805579070740135,
              4.225620020559262e-09
            ],
            "target_residual": 0.7073372641389972,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0005044424720641911,
            "step_scale": 0.7253907461943486,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0005410259877334,
              0.9999176452583637,
              0.9998812127747041
            ],
            "cell_volume_ratio": 1.000339784985754,
            "cell_rmsd_from_input_A": 0.0022424967725526213
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3565680227399675,
              0.0043602554724974365,
              0.356567901655296
            ],
            "branch_aligned_reduced_polarization": [
              0.3565680227399675,
              0.0043602554724974365,
              0.356567901655296
            ],
            "target_residual": 0.20289039100970938,
            "energy_eV": -71.78321347925697,
            "max_atomic_step_A": 0.05097679965928331,
            "max_log_strain_component": 0.00019230931611727812,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.000751356910868,
              0.9998862508302904,
              0.9998319369617283
            ],
            "cell_volume_ratio": 1.0004693520927308,
            "cell_rmsd_from_input_A": 0.003112519922906305
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4962057966715397,
              0.0006107570040415499,
              0.49620575960639124
            ],
            "branch_aligned_reduced_polarization": [
              0.4962057966715397,
              0.0006107570040415499,
              0.49620575960639124
            ],
            "target_residual": 0.0054004873095099,
            "energy_eV": -71.33626740107263,
            "max_atomic_step_A": 0.0014457091796430687,
            "max_log_strain_component": 2.858117065222982e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.000778959395967,
              0.9998815850477549,
              0.9998282711101254
            ],
            "cell_volume_ratio": 1.0004886098946841,
            "cell_rmsd_from_input_A": 0.0032284835528696393
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999944884649943,
              6.162541882277959e-07,
              0.49999448850631467
            ],
            "branch_aligned_reduced_polarization": [
              0.4999944884649943,
              6.162541882277959e-07,
              0.49999448850631467
            ],
            "target_residual": 7.818781873616915e-06,
            "energy_eV": -71.32116527616071
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.818781873616915e-06,
        "parent_symmetrization_rmsd_A": 0.15829771856140926,
        "parent_cell_rmsd_A": 0.0032284835528696393,
        "energy_eV": -71.32116527616071,
        "reduced_polarization": [
          0.4999944884649943,
          6.162541882277959e-07,
          0.49999448850631467
        ],
        "cartesian_polarization_e_A2": [
          0.00462728846659806,
          2.0337686265969675e-06,
          0.00801469849746767
        ],
        "ranking_score": 0.6591204770133738
      },
      "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": [
              2.112807910801615e-09,
              0.01805579070740135,
              4.225620016697637e-09
            ],
            "branch_aligned_reduced_polarization": [
              2.11280792861146e-09,
              0.018055790707401376,
              4.225620020559262e-09
            ],
            "target_residual": 0.8557278857979563,
            "energy_eV": -72.20653159063767,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009977602540499125,
            "step_scale": 0.5375344033410523,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0016313828777872,
              1.0016303275269192,
              0.9900709449731692
            ],
            "cell_volume_ratio": 0.9933029029560058,
            "cell_rmsd_from_input_A": 0.04144951476734433
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2651393963399736,
              0.2740705935925673,
              0.26513935511805586
            ],
            "branch_aligned_reduced_polarization": [
              0.2651393963399736,
              0.2740705935925673,
              0.26513935511805586
            ],
            "target_residual": 0.40170028920269596,
            "energy_eV": -71.87196029108142,
            "max_atomic_step_A": 0.10533591942980176,
            "max_log_strain_component": 0.00935277365630068,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.003163017265775,
              1.0031609722329795,
              0.9808532186641848
            ],
            "cell_volume_ratio": 0.987065930895051,
            "cell_rmsd_from_input_A": 0.07969902207037666
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49168267552744915,
              0.4913705792710753,
              0.4916825583290857
            ],
            "branch_aligned_reduced_polarization": [
              0.49168267552744915,
              0.4913705792710753,
              0.4916825583290857
            ],
            "target_residual": 0.014588510014650237,
            "energy_eV": -70.81804348531774,
            "max_atomic_step_A": 0.004183436091604014,
            "max_log_strain_component": 0.0004280748585159443,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2549027554601861,
            "cell_principal_stretches": [
              1.0032331692328458,
              1.0032310855318545,
              0.980433391401164
            ],
            "cell_volume_ratio": 0.9867814048638905,
            "cell_rmsd_from_input_A": 0.08143590014840174
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000040039463634,
              0.4999945349131958,
              0.5000040033787441
            ],
            "branch_aligned_reduced_polarization": [
              0.5000040039463634,
              0.4999945349131958,
              0.5000040033787441
            ],
            "target_residual": 7.869294862096339e-06,
            "energy_eV": -70.758558194121
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 7.869294862096339e-06,
        "parent_symmetrization_rmsd_A": 0.19506105309057886,
        "parent_cell_rmsd_A": 0.08143590014840174,
        "energy_eV": -70.758558194121,
        "reduced_polarization": [
          0.5000040039463634,
          0.4999945349131958,
          0.5000040033787441
        ],
        "cartesian_polarization_e_A2": [
          0.004708163973540919,
          0.007113395960033235,
          0.008154780387507221
        ],
        "ranking_score": 0.7154357667174035
      },
      "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": 0.004012571934261384,
        "minimum_distance_A_by_image": [
          2.3828096288991483,
          2.3831513019330823,
          2.3834933741354196,
          2.383835845541568,
          2.384178716186781,
          2.3845219861061557,
          2.3848656553346435,
          2.3852097239070384,
          2.385421319846203
        ],
        "minimum_distance_A": 2.3828096288991483,
        "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": [
          484.93736229670776,
          484.9657523870232,
          484.99414413940235,
          485.02253755394383,
          485.05093263074457,
          485.07932936990187,
          485.10772777151215,
          485.13612783567487,
          485.1645295624844
        ],
        "cell_deformation_log_strain_norm": 0.000713703658167444
      },
      "parent_reduced_polarization": [
        -3.487195581393697e-13,
        2.5550488358901053e-06,
        -6.977543931952837e-13
      ],
      "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": [
          -72.20653159063767,
          -72.20615422715814,
          -72.20575673997428,
          -72.20533912398759,
          -72.20490137387196,
          -72.20444348407291,
          -72.20396544880677,
          -72.20346726205996,
          -72.20294891758827
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.8877133837711565e-17,
            0.00025846680684068194,
            6.777600720094735e-11
          ],
          [
            -9.716568287450666e-17,
            0.00022618367235724732,
            5.929865798745938e-11
          ],
          [
            -3.2276976611732495e-17,
            0.0001938944697054022,
            5.082232954784292e-11
          ],
          [
            7.940014779705361e-18,
            0.0001615992843727041,
            4.234718499661607e-11
          ],
          [
            -5.650670697977809e-17,
            0.00012929820148840934,
            3.3873163271585023e-11
          ],
          [
            -4.782047165541659e-17,
            9.699130580701358e-05,
            2.540029277186331e-11
          ],
          [
            -4.675918950224726e-17,
            6.467868169236803e-05,
            1.692858555493504e-11
          ],
          [
            7.180097584777895e-17,
            3.236041310159437e-05,
            8.458078505422962e-12
          ],
          [
            2.917637770579779e-18,
            3.65835702425356e-08,
            -1.1185021832144398e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.487195581393697e-13,
            2.5550488358901053e-06,
            -6.977543931952837e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.4871955813938927e-13,
            2.555048835890198e-06,
            -6.97754393195332e-13
          ]
        ],
        "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": [
          [
            2.1128078175891574e-09,
            0.01805579070740193,
            4.225619965048111e-09
          ],
          [
            1.8486719932653273e-09,
            0.01580012994095925,
            3.6973547556939934e-09
          ],
          [
            1.5845360579191947e-09,
            0.01354417332523905,
            3.1690757795743707e-09
          ],
          [
            1.3203970139485932e-09,
            0.011287926862304731,
            2.6407931397187667e-09
          ],
          [
            1.0562485330822824e-09,
            0.009031396528513036,
            2.1125032834135027e-09
          ],
          [
            7.921012734612987e-10,
            0.006774588273367632,
            1.5842078759931155e-09
          ],
          [
            5.279512382827534e-10,
            0.004517508018413441,
            1.05590758359142e-09
          ],
          [
            2.6380631013012135e-10,
            0.002260161656117421,
            5.276048486990703e-10
          ],
          [
            -3.4872105203476167e-13,
            2.5550488358394574e-06,
            -6.977751709769109e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -72.20294891758829,
          -72.20291015226465,
          -72.20285207880674,
          -72.20277462118185,
          -72.2026777028587,
          -72.2025612468075,
          -72.20242517549957,
          -72.2022694109078,
          -72.20209387450632
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.587538198697821e-17,
            3.6583570195502993e-08,
            -1.1198265619279482e-14
          ],
          [
            3.1352139254647704e-17,
            -2.904562060583434e-05,
            -8.470868504789818e-12
          ],
          [
            1.0184320258672392e-17,
            -5.811839270756507e-05,
            -1.693242651696608e-11
          ],
          [
            4.5889342826974704e-17,
            -8.718156681684153e-05,
            -2.539599735485788e-11
          ],
          [
            -3.6450402375816346e-17,
            -0.00011623497895627254,
            -3.386146669796111e-11
          ],
          [
            2.7582609901390875e-17,
            -0.00014527846710356786,
            -4.2328888999388354e-11
          ],
          [
            7.428282915253329e-17,
            -0.00017431187120668168,
            -5.0798153148087484e-11
          ],
          [
            6.641777350956558e-17,
            -0.0002033350331976994,
            -5.926925491638994e-11
          ],
          [
            9.420944026039491e-17,
            -0.0002323477970062145,
            -6.774220934962126e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.484326055639679e-13,
            2.5550488326052806e-06,
            -6.985805820960472e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.484326055639679e-13,
            2.5550488326052806e-06,
            -6.985805820960472e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.1135048550552218e-09,
          -0.01805067944924304,
          -4.2270147084604795e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0018194919890442175
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.487195581393697e-13,
            2.5550488358901053e-06,
            -6.977543931952837e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.1128078193648e-09,
            0.018055790707401893,
            4.225620006884412e-09
          ],
          [
            1.848672042158108e-09,
            0.01580012994095924,
            3.697354731327769e-09
          ],
          [
            1.5845360555356936e-09,
            0.013544173325239007,
            3.1690757328748304e-09
          ],
          [
            1.3203969648683508e-09,
            0.011287926862304757,
            2.6407931887481993e-09
          ],
          [
            1.0562485492294628e-09,
            0.009031396528513078,
            2.1125032983568484e-09
          ],
          [
            7.921012998039892e-10,
            0.006774588273367625,
            1.5842078396647054e-09
          ],
          [
            5.279512347069331e-10,
            0.004517508018413431,
            1.055907571861342e-09
          ],
          [
            2.6380626726647834e-10,
            0.002260161656117435,
            5.276048030411801e-10
          ],
          [
            -3.4871955813938927e-13,
            2.555048835890198e-06,
            -6.97754393195332e-13
          ],
          [
            -2.6419951567468086e-10,
            -0.002028645239025296,
            -5.284024444365164e-10
          ],
          [
            -5.280728456044991e-10,
            -0.004059302048277622,
            -1.0561468415943153e-09
          ],
          [
            -7.91967261954381e-10,
            -0.00608940373878833,
            -1.5839395544617916e-09
          ],
          [
            -1.0558886384535237e-09,
            -0.008118938804663686,
            -2.111773434675529e-09
          ],
          [
            -1.3198243829069786e-09,
            -0.010147895875272933,
            -2.6396518607529073e-09
          ],
          [
            -1.5837798642511319e-09,
            -0.01217626371632536,
            -3.1675678863268912e-09
          ],
          [
            -1.8477569527477851e-09,
            -0.014204031230859846,
            -3.695521231380273e-09
          ],
          [
            -2.111751237150471e-09,
            -0.01623118746019882,
            -4.2235128175905695e-09
          ]
        ],
        "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": [
          [
            2.1128078175891574e-09,
            0.01805579070740193,
            4.225619965048111e-09
          ],
          [
            1.8486719932653273e-09,
            0.01580012994095925,
            3.6973547556939934e-09
          ],
          [
            1.5845360579191947e-09,
            0.01354417332523905,
            3.1690757795743707e-09
          ],
          [
            1.3203970139485932e-09,
            0.011287926862304731,
            2.6407931397187667e-09
          ],
          [
            1.0562485330822824e-09,
            0.009031396528513036,
            2.1125032834135027e-09
          ],
          [
            7.921012734612987e-10,
            0.006774588273367632,
            1.5842078759931155e-09
          ],
          [
            5.279512382827534e-10,
            0.004517508018413441,
            1.05590758359142e-09
          ],
          [
            2.6380631013012135e-10,
            0.002260161656117421,
            5.276048486990703e-10
          ],
          [
            -3.4872105203476167e-13,
            2.5550488358394574e-06,
            -6.977751709769109e-13
          ],
          [
            -2.6419949561429235e-10,
            -0.002028645239025295,
            -5.28402432919961e-10
          ],
          [
            -5.28072863215101e-10,
            -0.0040593020482776465,
            -1.0561468366532267e-09
          ],
          [
            -7.919672695422264e-10,
            -0.006089403738788357,
            -1.5839395350880636e-09
          ],
          [
            -1.0558886542888501e-09,
            -0.008118938804663689,
            -2.111773422797114e-09
          ],
          [
            -1.3198243609124916e-09,
            -0.010147895875272928,
            -2.6396518859606033e-09
          ],
          [
            -1.5837798850171225e-09,
            -0.012176263716325353,
            -3.167567874662325e-09
          ],
          [
            -1.8477569474484312e-09,
            -0.014204031230859837,
            -3.695521222368825e-09
          ],
          [
            -2.1117512183366216e-09,
            -0.016231187460198804,
            -4.2235128172585235e-09
          ]
        ]
      },
      "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": 2.555048832049521e-06,
        "parent_symmetrization_rmsd_A": 0.004012571934261384,
        "parent_cell_rmsd_A": 0.0029138554921324684,
        "energy_eV": -72.20294891758826,
        "reduced_polarization": [
          -3.468956447616627e-13,
          2.5550488320494026e-06,
          -6.96214434188687e-13
        ],
        "cartesian_polarization_e_A2": [
          2.2425764824848498e-17,
          3.658357018754385e-08,
          -1.1160336328261945e-14
        ],
        "ranking_score": 0.5047461459049586
      }
    }
  ],
  "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": 55,
      "full_response": 23,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 48,
      "energy_polarization": 32
    },
    "elapsed_seconds": 232.68822139198892
  }
}