{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Ca2Cs4O14P4",
  "input_spacegroup": "Cm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -153.28312948313533,
  "input_cartesian_polarization_e_A2": [
    0.0011178969296839305,
    -1.924572370294555e-18,
    -3.0541512918012274e-05
  ],
  "input_reduced_polarization": [
    0.04399808934178095,
    -1.3303838880863917e-16,
    -0.0019108602789058918
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4012571877486194e-15,
      "parent_symmetrization_rmsd_A": 0.0980869663077518,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -153.31812375124628,
      "reduced_polarization": [
        1.2095477573111482e-15,
        9.26152461378422e-16,
        1.8561443701341417e-15
      ],
      "cartesian_polarization_e_A2": [
        1.476779946537283e-17,
        1.3397993269544606e-17,
        2.966698187405231e-17
      ],
      "ranking_score": 0.0980869663077566
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.7213144407924425e-05,
      "parent_symmetrization_rmsd_A": 0.009455529260262734,
      "parent_cell_rmsd_A": 0.0037621554284440755,
      "energy_eV": -153.2369471999529,
      "reduced_polarization": [
        3.0251116811471407e-05,
        -2.123961056790772e-15,
        -2.1672287566930932e-05
      ],
      "cartesian_polarization_e_A2": [
        9.390816175726639e-07,
        -3.0718605152402394e-17,
        -3.4630260451678554e-07
      ],
      "ranking_score": 0.5104704944061896
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3128406796979e-15,
      "parent_symmetrization_rmsd_A": 0.09808723456169878,
      "parent_cell_rmsd_A": 0.0037621554284440755,
      "energy_eV": -153.31792942814013,
      "reduced_polarization": [
        1.1160133140095587e-15,
        2.0163440318551954e-15,
        1.951999944179829e-16
      ],
      "cartesian_polarization_e_A2": [
        2.6321739053523478e-17,
        2.916676763450983e-17,
        3.116535944932096e-18
      ],
      "ranking_score": 0.09902777341881443
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0007534493347808671,
      "parent_symmetrization_rmsd_A": 0.1019731152316761,
      "parent_cell_rmsd_A": 0.041594075091347736,
      "energy_eV": -146.62059568559118,
      "reduced_polarization": [
        0.4992887298924864,
        9.092299519128741e-15,
        0.00024855730574523436
      ],
      "cartesian_polarization_e_A2": [
        0.012479369344096769,
        -5.728601726780141e-16,
        1.719304215533039e-05
      ],
      "ranking_score": 0.6138785326740748
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00010109765457777549,
      "parent_symmetrization_rmsd_A": 0.06767862154010544,
      "parent_cell_rmsd_A": 0.04520394999009628,
      "energy_eV": -151.46225896777918,
      "reduced_polarization": [
        6.707336926341103e-05,
        2.008300245116379e-15,
        -0.49992435676569064
      ],
      "cartesian_polarization_e_A2": [
        0.004222452514485076,
        -1.6626142681927864e-16,
        -0.008023040804844533
      ],
      "ranking_score": 0.5791818043467851
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.968011785521596e-05,
      "parent_symmetrization_rmsd_A": 0.06353334057568111,
      "parent_cell_rmsd_A": 0.012392860956830907,
      "energy_eV": -150.93133060439084,
      "reduced_polarization": [
        -6.627364141285338e-06,
        -0.4999843352067776,
        -9.899461431479619e-06
      ],
      "cartesian_polarization_e_A2": [
        -1.1843081481080018e-05,
        -0.00723236132194009,
        -5.4029803374819735e-06
      ],
      "ranking_score": 0.5666709160505993
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00024064366123880296,
      "parent_symmetrization_rmsd_A": 0.16050568503274193,
      "parent_cell_rmsd_A": 0.062470905075163126,
      "energy_eV": -138.92834545435693,
      "reduced_polarization": [
        0.500018697635156,
        -1.8489226471296034e-15,
        -0.4997600838268603
      ],
      "cartesian_polarization_e_A2": [
        0.016685522024045097,
        -1.5660505391400112e-15,
        -0.008126271762925514
      ],
      "ranking_score": 0.6766046986240103
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.172586299291542e-05,
      "parent_symmetrization_rmsd_A": 0.12321417683271586,
      "parent_cell_rmsd_A": 0.044632124194496484,
      "energy_eV": -143.63861796916754,
      "reduced_polarization": [
        0.4999911230838342,
        -0.49999235313953644,
        4.7090058906887715e-07
      ],
      "cartesian_polarization_e_A2": [
        0.012485673653620142,
        -0.0072172098362609915,
        8.01823994173459e-06
      ],
      "ranking_score": 0.6343956596073258
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0005727866519743092,
      "parent_symmetrization_rmsd_A": 0.09281103625113214,
      "parent_cell_rmsd_A": 0.04701820447668728,
      "energy_eV": -149.0901833256131,
      "reduced_polarization": [
        0.00013199521500927003,
        -0.4995775393448501,
        -0.4996364222136256
      ],
      "cartesian_polarization_e_A2": [
        0.004210063216753088,
        -0.007231925885331764,
        -0.00802420705069299
      ],
      "ranking_score": 0.6057111606742526
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00024011122505452386,
      "parent_symmetrization_rmsd_A": 0.17508010975086385,
      "parent_cell_rmsd_A": 0.06390886539395436,
      "energy_eV": -135.43827947394348,
      "reduced_polarization": [
        0.5000101745466679,
        -0.5000396377091028,
        -0.49976340175187806
      ],
      "cartesian_polarization_e_A2": [
        0.016671194661557722,
        -0.0072237160893051594,
        -0.00813118092600349
      ],
      "ranking_score": 0.6915375485494615
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "target_residual": 0.04403956462923809,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.012786460539790082,
            "max_log_strain_component": 0.000352345651425154,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0003610347564338,
              1.0001031257418265,
              0.9997164430480607
            ],
            "cell_volume_ratio": 1.000180509151804,
            "cell_rmsd_from_input_A": 0.0037621554284440755
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.0251116811471407e-05,
              -2.123961056790772e-15,
              -2.1672287566930932e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.0251116811471407e-05,
              -2.123961056790772e-15,
              -2.1672287566930932e-05
            ],
            "target_residual": 3.7213144407924425e-05,
            "energy_eV": -153.2369471999529
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.4012571877486194e-15,
        "parent_symmetrization_rmsd_A": 0.0980869663077518,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -153.31812375124628,
        "reduced_polarization": [
          1.2095477573111482e-15,
          9.26152461378422e-16,
          1.8561443701341417e-15
        ],
        "cartesian_polarization_e_A2": [
          1.476779946537283e-17,
          1.3397993269544606e-17,
          2.966698187405231e-17
        ],
        "ranking_score": 0.0980869663077566
      },
      "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": [
          -153.28312948313535,
          -153.29319472517236,
          -153.30096683846466,
          -153.30687216748373,
          -153.31126017284333,
          -153.31440587261656,
          -153.3165151761118,
          -153.31772799619978,
          -153.3181237512463
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0011178969296839253,
            -4.472091386276938e-19,
            -3.054151291803255e-05
          ],
          [
            0.0009771976065659014,
            -2.133693316144686e-17,
            -2.3464820092940586e-05
          ],
          [
            0.0008369796599637219,
            9.632461635081054e-18,
            -1.7578849733925066e-05
          ],
          [
            0.0006971093052848201,
            1.8113390205917135e-17,
            -1.2790981982167508e-05
          ],
          [
            0.0005574770533342895,
            9.418135116439415e-19,
            -8.9769874139386e-06
          ],
          [
            0.00041799870851012415,
            -2.722658387408295e-17,
            -5.976779042541347e-06
          ],
          [
            0.0002786171735449905,
            -1.27332749982043e-18,
            -3.6129776152510565e-06
          ],
          [
            0.00013929480803349999,
            -1.7262252156396774e-17,
            -1.6927882894833251e-06
          ],
          [
            -1.035657542652121e-18,
            3.3367853555090964e-17,
            7.049493990992645e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758138e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987263e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.882070483437783e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969339e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0594571564339267e-16,
            2.306593165053339e-15,
            4.410586368113135e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758137e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987254e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.8820704834377834e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969328e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0581813203458523e-16,
            2.306593165053339e-15,
            4.410534437671032e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.04399808934178029,
            -5.551115123125783e-17,
            -0.0019108602789071338
          ],
          [
            0.03852800488821684,
            -1.4988010832439613e-15,
            -0.0014680999198579125
          ],
          [
            0.03305226121813731,
            6.661338147750939e-16,
            -0.0010998383019068525
          ],
          [
            0.02756745175696318,
            1.2212453270876722e-15,
            -0.0008002805710227157
          ],
          [
            0.02207180049317381,
            1.1102230246251565e-16,
            -0.000561654189154992
          ],
          [
            0.01656529059637557,
            -1.887379141862766e-15,
            -0.00037394315399003064
          ],
          [
            0.011049348558988314,
            -1.1102230246251565e-16,
            -0.00022604955530830528
          ],
          [
            0.005526499868731216,
            -1.1657341758564144e-15,
            -0.00010591099110429658
          ],
          [
            1.1102230246251565e-16,
            2.3314683517128287e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -153.3181237512463,
          -153.31772799619978,
          -153.31651517611175,
          -153.3144058726166,
          -153.31126017284333,
          -153.30687216748373,
          -153.3009668384646,
          -153.29319472517233,
          -153.28312948313538
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2351791808552426e-17,
            5.7801662250558686e-18,
            -4.62082942643834e-17
          ],
          [
            -0.0001392948080333965,
            -8.522873181493688e-17,
            1.6927882895099408e-06
          ],
          [
            -0.00027861717354501396,
            8.40598954042786e-19,
            3.6129776152034863e-06
          ],
          [
            -0.0004179987085101369,
            -1.934016115512259e-20,
            5.976779042600718e-06
          ],
          [
            -0.0005574770533343408,
            -3.0148442518158214e-17,
            8.976987413887054e-06
          ],
          [
            -0.0006971093052848701,
            -6.846660266005528e-18,
            1.2790981982196496e-05
          ],
          [
            -0.000836979659963817,
            -9.635247843527776e-18,
            1.7578849733929098e-05
          ],
          [
            -0.0009771976065660263,
            -3.6185540254978855e-17,
            2.3464820092935622e-05
          ],
          [
            -0.001117896929683969,
            4.3244129234516307e-17,
            3.05415129180858e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4587080846905533e-15,
            3.9956096922967575e-16,
            -2.891068111224132e-15
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011164e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910922e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859984e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.501369160233632e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4587080846905533e-15,
            3.9956096922967575e-16,
            -2.891068111224132e-15
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011131e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910895e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859983e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.5013691602336322e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.04399808934178011,
          4.644100201770762e-15,
          0.0019108602789080426
        ],
        "actual_opposite_endpoint_branch_residual": 3.0729462360634305e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758138e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987263e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.882070483437783e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969339e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0594571564339267e-16,
            2.306593165053339e-15,
            4.410586368113135e-16
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011164e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910922e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859984e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.501369160233632e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758137e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987254e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.8820704834377834e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969328e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0581813203458523e-16,
            2.306593165053339e-15,
            4.410534437671032e-16
          ],
          [
            -0.0055264998687265645,
            -5.891538991140888e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011131e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910895e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859983e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.5013691602336322e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.04399808934178029,
            -5.551115123125783e-17,
            -0.0019108602789071338
          ],
          [
            0.03852800488821684,
            -1.4988010832439613e-15,
            -0.0014680999198579125
          ],
          [
            0.03305226121813731,
            6.661338147750939e-16,
            -0.0010998383019068525
          ],
          [
            0.02756745175696318,
            1.2212453270876722e-15,
            -0.0008002805710227157
          ],
          [
            0.02207180049317381,
            1.1102230246251565e-16,
            -0.000561654189154992
          ],
          [
            0.01656529059637557,
            -1.887379141862766e-15,
            -0.00037394315399003064
          ],
          [
            0.011049348558988314,
            -1.1102230246251565e-16,
            -0.00022604955530830528
          ],
          [
            0.005526499868731216,
            -1.1657341758564144e-15,
            -0.00010591099110429658
          ],
          [
            1.1102230246251565e-16,
            2.3314683517128287e-15,
            4.440892098500626e-16
          ],
          [
            -0.005526499868726553,
            -5.88418203051333e-15,
            0.0001059109911059064
          ],
          [
            -0.011049348558990257,
            1.1102230246251565e-16,
            0.0002260495553053632
          ],
          [
            -0.01656529059637485,
            0.0,
            0.0003739431539937499
          ],
          [
            -0.02207180049317692,
            -2.1094237467877974e-15,
            0.0005616541891517723
          ],
          [
            -0.02756745175696451,
            -4.996003610813204e-16,
            0.0008002805710245475
          ],
          [
            -0.03305226121814103,
            -6.661338147750939e-16,
            0.0010998383019070745
          ],
          [
            -0.038528004888221945,
            -2.4980018054066022e-15,
            0.001468099919857635
          ],
          [
            -0.043998089341780955,
            2.9976021664879227e-15,
            0.00191086027891052
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.043998089341780955,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "target_residual": 0.45600591433768917,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003291102378763418,
            "step_scale": 0.921400459737524,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0027292176962155,
              0.9990077046689024,
              0.9965757159523787
            ],
            "cell_volume_ratio": 0.9983039916855826,
            "cell_rmsd_from_input_A": 0.03596396116829854
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.44722091377914497,
              2.6119334967607285e-14,
              -0.0008947499166374811
            ],
            "branch_aligned_reduced_polarization": [
              0.44722091377914497,
              2.6119334967607285e-14,
              -0.0008947499166374811
            ],
            "target_residual": 0.052786669905590486,
            "energy_eV": -148.1453480720041,
            "max_atomic_step_A": 0.017051185977082713,
            "max_log_strain_component": 0.000518978172609976,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0031584831029612,
              0.9988519470223453,
              0.9960382003373783
            ],
            "cell_volume_ratio": 0.998037053801265,
            "cell_rmsd_from_input_A": 0.041594075091347736
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4992887298924864,
              9.092299519128741e-15,
              0.00024855730574523436
            ],
            "branch_aligned_reduced_polarization": [
              0.4992887298924864,
              9.092299519128741e-15,
              0.00024855730574523436
            ],
            "target_residual": 0.0007534493347808671,
            "energy_eV": -146.62059568559118
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0007534493347808671,
        "parent_symmetrization_rmsd_A": 0.1019731152316761,
        "parent_cell_rmsd_A": 0.041594075091347736,
        "energy_eV": -146.62059568559118,
        "reduced_polarization": [
          0.4992887298924864,
          9.092299519128741e-15,
          0.00024855730574523436
        ],
        "cartesian_polarization_e_A2": [
          0.012479369344096769,
          -5.728601726780141e-16,
          1.719304215533039e-05
        ],
        "ranking_score": 0.6138785326740748
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789059126
            ],
            "target_residual": 0.5000286221545992,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.09982284042626778,
            "max_log_strain_component": 0.0052590504204099294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0049963109362474,
              1.0003040327824546,
              0.9942552030827527
            ],
            "cell_volume_ratio": 0.9995266077189257,
            "cell_rmsd_from_input_A": 0.04346182699619614
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0030671489027284922,
              1.2255630376594024e-14,
              -0.48311611454228753
            ],
            "branch_aligned_reduced_polarization": [
              0.0030671489027284922,
              1.2255630376594024e-14,
              -0.48311611454228753
            ],
            "target_residual": 0.01716021534074276,
            "energy_eV": -151.58626427905938,
            "max_atomic_step_A": 0.003907500771137677,
            "max_log_strain_component": 0.00021050936496881325,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0051958903679623,
              1.000320228478389,
              0.994030432979078
            ],
            "cell_volume_ratio": 0.9995152769237512,
            "cell_rmsd_from_input_A": 0.04520394999009628
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.707336926341103e-05,
              2.008300245116379e-15,
              -0.49992435676569064
            ],
            "branch_aligned_reduced_polarization": [
              6.707336926341103e-05,
              2.008300245116379e-15,
              -0.49992435676569064
            ],
            "target_residual": 0.00010109765457777549,
            "energy_eV": -151.46225896777918
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00010109765457777549,
        "parent_symmetrization_rmsd_A": 0.06767862154010544,
        "parent_cell_rmsd_A": 0.04520394999009628,
        "energy_eV": -151.46225896777918,
        "reduced_polarization": [
          6.707336926341103e-05,
          2.008300245116379e-15,
          -0.49992435676569064
        ],
        "cartesian_polarization_e_A2": [
          0.004222452514485076,
          -1.6626142681927864e-16,
          -0.008023040804844533
        ],
        "ranking_score": 0.5791818043467851
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.04399808934178095,
              -1.1102230246251565e-16,
              -0.0019108602789058918
            ],
            "target_residual": 0.5019357361781812,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.0832622480913181,
            "max_log_strain_component": 0.0015865650976265768,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0019082404223154,
              0.9998900687364939,
              0.9983853131357439
            ],
            "cell_volume_ratio": 1.0001805091518174,
            "cell_rmsd_from_input_A": 0.012070193443375407
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.001721175168917585,
              -0.4890639653853399,
              0.0010503948563098306
            ],
            "branch_aligned_reduced_polarization": [
              0.001721175168917585,
              -0.4890639653853399,
              0.0010503948563098306
            ],
            "target_residual": 0.011120369886352888,
            "energy_eV": -151.0366597992251,
            "max_atomic_step_A": 0.001931619825388664,
            "max_log_strain_component": 3.927619797065542e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0019543022693789,
              0.9998947338925147,
              0.9983410769841922
            ],
            "cell_volume_ratio": 1.000186840356923,
            "cell_rmsd_from_input_A": 0.012392860956830907
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.627364141285338e-06,
              -0.4999843352067776,
              -9.899461431479619e-06
            ],
            "branch_aligned_reduced_polarization": [
              -6.627364141285338e-06,
              -0.4999843352067776,
              -9.899461431479619e-06
            ],
            "target_residual": 1.968011785521596e-05,
            "energy_eV": -150.93133060439084
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.968011785521596e-05,
        "parent_symmetrization_rmsd_A": 0.06353334057568111,
        "parent_cell_rmsd_A": 0.012392860956830907,
        "energy_eV": -150.93133060439084,
        "reduced_polarization": [
          -6.627364141285338e-06,
          -0.4999843352067776,
          -9.899461431479619e-06
        ],
        "cartesian_polarization_e_A2": [
          -1.1843081481080018e-05,
          -0.00723236132194009,
          -5.4029803374819735e-06
        ],
        "ranking_score": 0.5666709160505993
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.043998089341780955,
              -1.3303838880863917e-16,
              -0.0019108602789059126
            ],
            "target_residual": 0.6753003284702637,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0031887700261055306,
            "step_scale": 0.5892304077675526,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0031959999780184,
              0.9994836074930173,
              0.9958633383108814
            ],
            "cell_volume_ratio": 0.9985302175890158,
            "cell_rmsd_from_input_A": 0.032112227209105136
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3059942377219045,
              3.1552378685618295e-14,
              -0.28112741445494727
            ],
            "branch_aligned_reduced_polarization": [
              0.3059942377219045,
              3.1552378685618295e-14,
              -0.28112741445494727
            ],
            "target_residual": 0.2924781094377515,
            "energy_eV": -149.14440191270683,
            "max_atomic_step_A": 0.09323139042014973,
            "max_log_strain_component": 0.002804367072114002,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0060165788621338,
              0.9990299946305068,
              0.9922379108866884
            ],
            "cell_volume_ratio": 0.9972395216127949,
            "cell_rmsd_from_input_A": 0.06020609285755709
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48779558527415073,
              5.991603169674271e-14,
              -0.4856966736113795
            ],
            "branch_aligned_reduced_polarization": [
              0.48779558527415073,
              5.991603169674271e-14,
              -0.4856966736113795
            ],
            "target_residual": 0.018802470172292075,
            "energy_eV": -139.68174759014147,
            "max_atomic_step_A": 0.006611950454741834,
            "max_log_strain_component": 0.0002324256516756496,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0062394540762483,
              0.998989948748501,
              0.9919506078182064
            ],
            "cell_volume_ratio": 0.9971316656889698,
            "cell_rmsd_from_input_A": 0.062470905075163126
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.500018697635156,
              -1.8489226471296034e-15,
              -0.4997600838268603
            ],
            "branch_aligned_reduced_polarization": [
              0.500018697635156,
              -1.8489226471296034e-15,
              -0.4997600838268603
            ],
            "target_residual": 0.00024064366123880296,
            "energy_eV": -138.92834545435693
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00024064366123880296,
        "parent_symmetrization_rmsd_A": 0.16050568503274193,
        "parent_cell_rmsd_A": 0.062470905075163126,
        "energy_eV": -138.92834545435693,
        "reduced_polarization": [
          0.500018697635156,
          -1.8489226471296034e-15,
          -0.4997600838268603
        ],
        "cartesian_polarization_e_A2": [
          0.016685522024045097,
          -1.5660505391400112e-15,
          -0.008126271762925514
        ],
        "ranking_score": 0.6766046986240103
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.043998089341780955,
              -1.1102230246251565e-16,
              -0.0019108602789058918
            ],
            "target_residual": 0.6767136720289844,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002790247368181222,
            "step_scale": 0.7811775241064175,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0024879848708204,
              0.9995070054673788,
              0.9965749772112557
            ],
            "cell_volume_ratio": 0.9985619123001505,
            "cell_rmsd_from_input_A": 0.031771181179336486
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3863305295905805,
              -0.3752777705672824,
              -0.0014519270044491374
            ],
            "branch_aligned_reduced_polarization": [
              0.3863305295905805,
              -0.3752777705672824,
              -0.0014519270044491374
            ],
            "target_residual": 0.16875571430280986,
            "energy_eV": -148.12966141027454,
            "max_atomic_step_A": 0.0406533989781684,
            "max_log_strain_component": 0.001099479094982932,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.003472363993484,
              0.9993153066253028,
              0.9952237690587611
            ],
            "cell_volume_ratio": 0.9979957589697748,
            "cell_rmsd_from_input_A": 0.044254715635440256
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49691992628770343,
              -0.49622917012056866,
              2.5861554489023112e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49691992628770343,
              -0.49622917012056866,
              2.5861554489023112e-05
            ],
            "target_residual": 0.004868950695251814,
            "energy_eV": -143.77806406153823,
            "max_atomic_step_A": 0.0012654788376308909,
            "max_log_strain_component": 3.3364566771889384e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0035022796389377,
              0.9993104847336971,
              0.9951818251608717
            ],
            "cell_volume_ratio": 0.9979786339029908,
            "cell_rmsd_from_input_A": 0.044632124194496484
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999911230838342,
              -0.49999235313953644,
              4.7090058906887715e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4999911230838342,
              -0.49999235313953644,
              4.7090058906887715e-07
            ],
            "target_residual": 1.172586299291542e-05,
            "energy_eV": -143.63861796916754
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.172586299291542e-05,
        "parent_symmetrization_rmsd_A": 0.12321417683271586,
        "parent_cell_rmsd_A": 0.044632124194496484,
        "energy_eV": -143.63861796916754,
        "reduced_polarization": [
          0.4999911230838342,
          -0.49999235313953644,
          4.7090058906887715e-07
        ],
        "cartesian_polarization_e_A2": [
          0.012485673653620142,
          -0.0072172098362609915,
          8.01823994173459e-06
        ],
        "ranking_score": 0.6343956596073258
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.04399808934178095,
              -1.1102230246251565e-16,
              -0.0019108602789059126
            ],
            "target_residual": 0.7071270203957891,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004898121142973118,
            "step_scale": 0.9313698769579591,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.004695290231484,
              1.0006453251414598,
              0.9942461904817486
            ],
            "cell_volume_ratio": 0.9995590895259799,
            "cell_rmsd_from_input_A": 0.04184571438125084
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.003766001946123448,
              -0.4562563508271327,
              -0.4489980878460024
            ],
            "branch_aligned_reduced_polarization": [
              0.003766001946123448,
              -0.4562563508271327,
              -0.4489980878460024
            ],
            "target_residual": 0.0672969884688846,
            "energy_eV": -149.85809145893745,
            "max_atomic_step_A": 0.014197181069139073,
            "max_log_strain_component": 0.0006104691954361306,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0052809191358762,
              1.0007107159239537,
              0.9935404087657266
            ],
            "cell_volume_ratio": 0.9994970693012154,
            "cell_rmsd_from_input_A": 0.04701820447668728
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00013199521500927003,
              -0.4995775393448501,
              -0.4996364222136256
            ],
            "branch_aligned_reduced_polarization": [
              0.00013199521500927003,
              -0.4995775393448501,
              -0.4996364222136256
            ],
            "target_residual": 0.0005727866519743092,
            "energy_eV": -149.0901833256131
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0005727866519743092,
        "parent_symmetrization_rmsd_A": 0.09281103625113214,
        "parent_cell_rmsd_A": 0.04701820447668728,
        "energy_eV": -149.0901833256131,
        "reduced_polarization": [
          0.00013199521500927003,
          -0.4995775393448501,
          -0.4996364222136256
        ],
        "cartesian_polarization_e_A2": [
          0.004210063216753088,
          -0.007231925885331764,
          -0.00802420705069299
        ],
        "ranking_score": 0.6057111606742526
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.04399808934178095,
              -1.3303838880863917e-16,
              -0.0019108602789058918
            ],
            "branch_aligned_reduced_polarization": [
              0.043998089341780955,
              -1.1102230246251565e-16,
              -0.0019108602789059126
            ],
            "target_residual": 0.8402562309391379,
            "energy_eV": -153.28312948313533,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0029607080168285354,
            "step_scale": 0.5470884315125601,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0029677725364134,
              0.9997688236751453,
              0.9959105434583998
            ],
            "cell_volume_ratio": 0.9986352652056211,
            "cell_rmsd_from_input_A": 0.03046200199385589
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2864137954700115,
              -0.26490245737885976,
              -0.2620833930994126
            ],
            "branch_aligned_reduced_polarization": [
              0.2864137954700115,
              -0.26490245737885976,
              -0.2620833930994126
            ],
            "target_residual": 0.3968554310465129,
            "energy_eV": -148.94518627239285,
            "max_atomic_step_A": 0.1078699039901192,
            "max_log_strain_component": 0.003069199687028076,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0060061423351938,
              0.9995173181408997,
              0.9917434242604604
            ],
            "cell_volume_ratio": 0.9972184047471153,
            "cell_rmsd_from_input_A": 0.061600348944039346
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48412990003076356,
              -0.4918406069912817,
              -0.488184542651396
            ],
            "branch_aligned_reduced_polarization": [
              0.48412990003076356,
              -0.4918406069912817,
              -0.488184542651396
            ],
            "target_residual": 0.0214018877592833,
            "energy_eV": -136.36607254356926,
            "max_atomic_step_A": 0.0078021578304418426,
            "max_log_strain_component": 0.0002546525481816344,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0440844833694993,
            "cell_principal_stretches": [
              1.0062147067535248,
              0.9994704492098204,
              0.9914637541994589
            ],
            "cell_volume_ratio": 0.9970971173640237,
            "cell_rmsd_from_input_A": 0.06390886539395436
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000101745466679,
              -0.5000396377091028,
              -0.49976340175187806
            ],
            "branch_aligned_reduced_polarization": [
              0.5000101745466679,
              -0.5000396377091028,
              -0.49976340175187806
            ],
            "target_residual": 0.00024011122505452386,
            "energy_eV": -135.43827947394348
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00024011122505452386,
        "parent_symmetrization_rmsd_A": 0.17508010975086385,
        "parent_cell_rmsd_A": 0.06390886539395436,
        "energy_eV": -135.43827947394348,
        "reduced_polarization": [
          0.5000101745466679,
          -0.5000396377091028,
          -0.49976340175187806
        ],
        "cartesian_polarization_e_A2": [
          0.016671194661557722,
          -0.0072237160893051594,
          -0.00813118092600349
        ],
        "ranking_score": 0.6915375485494615
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.0980869663077518,
        "minimum_distance_A_by_image": [
          1.5317517952745083,
          1.5311292503174645,
          1.5303279536100405,
          1.5297043815084292,
          1.5292587514201428,
          1.528991218930745,
          1.5289018775326204,
          1.5289907584617495,
          1.5292578306431261
        ],
        "minimum_distance_A": 1.5289018775326204,
        "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": [
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002,
          415.5597996159002
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.0594571564339267e-16,
        2.306593165053339e-15,
        4.410586368113135e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -153.28312948313535,
          -153.29319472517236,
          -153.30096683846466,
          -153.30687216748373,
          -153.31126017284333,
          -153.31440587261656,
          -153.3165151761118,
          -153.31772799619978,
          -153.3181237512463
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0011178969296839253,
            -4.472091386276938e-19,
            -3.054151291803255e-05
          ],
          [
            0.0009771976065659014,
            -2.133693316144686e-17,
            -2.3464820092940586e-05
          ],
          [
            0.0008369796599637219,
            9.632461635081054e-18,
            -1.7578849733925066e-05
          ],
          [
            0.0006971093052848201,
            1.8113390205917135e-17,
            -1.2790981982167508e-05
          ],
          [
            0.0005574770533342895,
            9.418135116439415e-19,
            -8.9769874139386e-06
          ],
          [
            0.00041799870851012415,
            -2.722658387408295e-17,
            -5.976779042541347e-06
          ],
          [
            0.0002786171735449905,
            -1.27332749982043e-18,
            -3.6129776152510565e-06
          ],
          [
            0.00013929480803349999,
            -1.7262252156396774e-17,
            -1.6927882894833251e-06
          ],
          [
            -1.035657542652121e-18,
            3.3367853555090964e-17,
            7.049493990992645e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758138e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987263e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.882070483437783e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969339e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0594571564339267e-16,
            2.306593165053339e-15,
            4.410586368113135e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758137e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987254e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.8820704834377834e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969328e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0581813203458523e-16,
            2.306593165053339e-15,
            4.410534437671032e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.04399808934178029,
            -5.551115123125783e-17,
            -0.0019108602789071338
          ],
          [
            0.03852800488821684,
            -1.4988010832439613e-15,
            -0.0014680999198579125
          ],
          [
            0.03305226121813731,
            6.661338147750939e-16,
            -0.0010998383019068525
          ],
          [
            0.02756745175696318,
            1.2212453270876722e-15,
            -0.0008002805710227157
          ],
          [
            0.02207180049317381,
            1.1102230246251565e-16,
            -0.000561654189154992
          ],
          [
            0.01656529059637557,
            -1.887379141862766e-15,
            -0.00037394315399003064
          ],
          [
            0.011049348558988314,
            -1.1102230246251565e-16,
            -0.00022604955530830528
          ],
          [
            0.005526499868731216,
            -1.1657341758564144e-15,
            -0.00010591099110429658
          ],
          [
            1.1102230246251565e-16,
            2.3314683517128287e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -153.3181237512463,
          -153.31772799619978,
          -153.31651517611175,
          -153.3144058726166,
          -153.31126017284333,
          -153.30687216748373,
          -153.3009668384646,
          -153.29319472517233,
          -153.28312948313538
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2351791808552426e-17,
            5.7801662250558686e-18,
            -4.62082942643834e-17
          ],
          [
            -0.0001392948080333965,
            -8.522873181493688e-17,
            1.6927882895099408e-06
          ],
          [
            -0.00027861717354501396,
            8.40598954042786e-19,
            3.6129776152034863e-06
          ],
          [
            -0.0004179987085101369,
            -1.934016115512259e-20,
            5.976779042600718e-06
          ],
          [
            -0.0005574770533343408,
            -3.0148442518158214e-17,
            8.976987413887054e-06
          ],
          [
            -0.0006971093052848701,
            -6.846660266005528e-18,
            1.2790981982196496e-05
          ],
          [
            -0.000836979659963817,
            -9.635247843527776e-18,
            1.7578849733929098e-05
          ],
          [
            -0.0009771976065660263,
            -3.6185540254978855e-17,
            2.3464820092935622e-05
          ],
          [
            -0.001117896929683969,
            4.3244129234516307e-17,
            3.05415129180858e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4587080846905533e-15,
            3.9956096922967575e-16,
            -2.891068111224132e-15
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011164e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910922e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859984e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.501369160233632e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4587080846905533e-15,
            3.9956096922967575e-16,
            -2.891068111224132e-15
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011131e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910895e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859983e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.5013691602336322e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.04399808934178011,
          4.644100201770762e-15,
          0.0019108602789080426
        ],
        "actual_opposite_endpoint_branch_residual": 3.0729462360634305e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758138e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987263e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.882070483437783e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969339e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0594571564339267e-16,
            2.306593165053339e-15,
            4.410586368113135e-16
          ],
          [
            -0.0055264998687265645,
            -5.891538991140887e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011164e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910922e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859984e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.501369160233632e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.043998089341780316,
            -3.091387166408396e-17,
            -0.0019108602789071605
          ],
          [
            0.03852800488821687,
            -1.4749412668135013e-15,
            -0.001468099919857906
          ],
          [
            0.033052261218137334,
            6.658555406758137e-16,
            -0.0010998383019068523
          ],
          [
            0.027567451756963138,
            1.2521099679346355e-15,
            -0.0008002805710227265
          ],
          [
            0.022071800493173786,
            6.510399612987254e-17,
            -0.0005616541891550081
          ],
          [
            0.016565290596375588,
            -1.8820704834377834e-15,
            -0.0003739431539900527
          ],
          [
            0.011049348558988337,
            -8.802030082969328e-17,
            -0.0002260495553083001
          ],
          [
            0.0055264998687312526,
            -1.1932740226048237e-15,
            -0.00010591099110427618
          ],
          [
            1.0581813203458523e-16,
            2.306593165053339e-15,
            4.410534437671032e-16
          ],
          [
            -0.0055264998687265645,
            -5.891538991140888e-15,
            0.00010591099110594142
          ],
          [
            -0.011049348558990266,
            5.810741763011131e-17,
            0.0002260495553053238
          ],
          [
            -0.01656529059637486,
            -1.3369119909910895e-18,
            0.00037394315399376734
          ],
          [
            -0.02207180049317691,
            -2.084047490036332e-15,
            0.0005616541891517832
          ],
          [
            -0.02756745175696453,
            -4.732836574859983e-16,
            0.0008002805710245402
          ],
          [
            -0.03305226121814105,
            -6.660481406987375e-16,
            0.0010998383019071047
          ],
          [
            -0.038528004888221966,
            -2.5013691602336322e-15,
            0.0014680999198575955
          ],
          [
            -0.04399808934178095,
            2.9893026459234195e-15,
            0.001910860278910492
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.04399808934178029,
            -5.551115123125783e-17,
            -0.0019108602789071338
          ],
          [
            0.03852800488821684,
            -1.4988010832439613e-15,
            -0.0014680999198579125
          ],
          [
            0.03305226121813731,
            6.661338147750939e-16,
            -0.0010998383019068525
          ],
          [
            0.02756745175696318,
            1.2212453270876722e-15,
            -0.0008002805710227157
          ],
          [
            0.02207180049317381,
            1.1102230246251565e-16,
            -0.000561654189154992
          ],
          [
            0.01656529059637557,
            -1.887379141862766e-15,
            -0.00037394315399003064
          ],
          [
            0.011049348558988314,
            -1.1102230246251565e-16,
            -0.00022604955530830528
          ],
          [
            0.005526499868731216,
            -1.1657341758564144e-15,
            -0.00010591099110429658
          ],
          [
            1.1102230246251565e-16,
            2.3314683517128287e-15,
            4.440892098500626e-16
          ],
          [
            -0.005526499868726553,
            -5.88418203051333e-15,
            0.0001059109911059064
          ],
          [
            -0.011049348558990257,
            1.1102230246251565e-16,
            0.0002260495553053632
          ],
          [
            -0.01656529059637485,
            0.0,
            0.0003739431539937499
          ],
          [
            -0.02207180049317692,
            -2.1094237467877974e-15,
            0.0005616541891517723
          ],
          [
            -0.02756745175696451,
            -4.996003610813204e-16,
            0.0008002805710245475
          ],
          [
            -0.03305226121814103,
            -6.661338147750939e-16,
            0.0010998383019070745
          ],
          [
            -0.038528004888221945,
            -2.4980018054066022e-15,
            0.001468099919857635
          ],
          [
            -0.043998089341780955,
            2.9976021664879227e-15,
            0.00191086027891052
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.4012571877486194e-15,
        "parent_symmetrization_rmsd_A": 0.0980869663077518,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -153.31812375124628,
        "reduced_polarization": [
          1.2095477573111482e-15,
          9.26152461378422e-16,
          1.8561443701341417e-15
        ],
        "cartesian_polarization_e_A2": [
          1.476779946537283e-17,
          1.3397993269544606e-17,
          2.966698187405231e-17
        ],
        "ranking_score": 0.0980869663077566
      }
    }
  ],
  "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": 51,
      "full_response": 19,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 44,
      "energy_polarization": 32
    },
    "elapsed_seconds": 247.36877356795594
  }
}