{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "Al4Ge4Li12O20",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -238.19473386622585,
  "input_cartesian_polarization_e_A2": [
    2.6714901190170428e-17,
    1.2874651175985749e-17,
    0.0027976633701477477
  ],
  "input_reduced_polarization": [
    2.1132195575859903e-15,
    3.471284997359715e-16,
    0.24385919358359268
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.826877384899993e-15,
      "parent_symmetrization_rmsd_A": 0.4068901170640795,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -228.5070945719832,
      "reduced_polarization": [
        -3.640848153431285e-16,
        2.7813671041344715e-16,
        -5.808836568213632e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.602687795414905e-18,
        1.0315814254758581e-17,
        -6.664161006706223e-17
      ],
      "ranking_score": 0.4068901170640912
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.7271613576401473e-05,
      "parent_symmetrization_rmsd_A": 0.012575919080231285,
      "parent_cell_rmsd_A": 0.049177188906672435,
      "energy_eV": -238.13455680073076,
      "reduced_polarization": [
        8.746924146749856e-15,
        1.927799248688326e-15,
        1.7271613576401473e-05
      ],
      "cartesian_polarization_e_A2": [
        1.1095946655265703e-16,
        7.179493221396505e-17,
        1.9715204709814375e-07
      ],
      "ranking_score": 0.5249047595340522
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.035512920055688e-15,
      "parent_symmetrization_rmsd_A": 0.4068909619010445,
      "parent_cell_rmsd_A": 0.049177188906672435,
      "energy_eV": -229.0241113687363,
      "reduced_polarization": [
        -1.7738928957234286e-15,
        -2.955174439037831e-16,
        -3.612663555160778e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.2502889201392034e-17,
        -1.1005709505585936e-17,
        -4.123783873615352e-17
      ],
      "ranking_score": 0.41918525912772064
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.8740225809620323e-05,
      "parent_symmetrization_rmsd_A": 0.013343415644553987,
      "parent_cell_rmsd_A": 0.0525954675405607,
      "energy_eV": -238.0285888356265,
      "reduced_polarization": [
        -4.135060539126793e-15,
        3.554117176424579e-15,
        0.4999712597741904
      ],
      "cartesian_polarization_e_A2": [
        -3.752659309718714e-17,
        1.4579925163926411e-16,
        0.005767045011111315
      ],
      "ranking_score": 0.5265497629813134
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 4.0099534038768655e-05,
      "parent_symmetrization_rmsd_A": 0.03726825840791341,
      "parent_cell_rmsd_A": 0.05778750917357318,
      "energy_eV": -237.4238247338967,
      "reduced_polarization": [
        0.49996394209470013,
        -1.5962766883180767e-17,
        -1.7544232542692076e-05
      ],
      "cartesian_polarization_e_A2": [
        0.006343149191304959,
        4.608641252377342e-17,
        -7.362561192188557e-05
      ],
      "ranking_score": 0.5517953347693842
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0005468692010016104,
      "parent_symmetrization_rmsd_A": 0.10695451923585308,
      "parent_cell_rmsd_A": 0.2931725614271484,
      "energy_eV": -231.945881964084,
      "reduced_polarization": [
        7.486153133673659e-16,
        0.4995371160730768,
        0.00029121193862944754
      ],
      "cartesian_polarization_e_A2": [
        4.2772191182215e-16,
        0.018641985074922447,
        -0.0007038790664943845
      ],
      "ranking_score": 0.6813413979946434
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.3904644561609176e-05,
      "parent_symmetrization_rmsd_A": 0.03734778287751367,
      "parent_cell_rmsd_A": 0.0595457702652864,
      "energy_eV": -237.25921851260887,
      "reduced_polarization": [
        0.5000132568981349,
        1.3941073375216394e-15,
        0.5000041944954673
      ],
      "cartesian_polarization_e_A2": [
        0.006233011164008471,
        2.957154212707715e-18,
        0.005695775151857277
      ],
      "ranking_score": 0.5522620347329585
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00020666038196299683,
      "parent_symmetrization_rmsd_A": 0.10604227607614149,
      "parent_cell_rmsd_A": 0.2730300332858454,
      "energy_eV": -231.38519346674903,
      "reduced_polarization": [
        -5.980029304385907e-15,
        0.49986437236887754,
        0.5001559283782677
      ],
      "cartesian_polarization_e_A2": [
        8.950919541258687e-17,
        0.01827392031090546,
        0.005082012524970753
      ],
      "ranking_score": 0.6747131051615288
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0008099016830373055,
      "parent_symmetrization_rmsd_A": 0.11308589902862945,
      "parent_cell_rmsd_A": 0.2964744519698034,
      "energy_eV": -231.00928753410037,
      "reduced_polarization": [
        0.49954535756836804,
        0.4994423450363026,
        0.0003718359006471431
      ],
      "cartesian_polarization_e_A2": [
        0.006349565942506102,
        0.018643006840695992,
        -0.0007810305863773718
      ],
      "ranking_score": 0.6888243153871549
    },
    {
      "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": 0.00030628104071800274,
      "parent_symmetrization_rmsd_A": 0.11204618264666985,
      "parent_cell_rmsd_A": 0.27542155600669604,
      "energy_eV": -230.407624116641,
      "reduced_polarization": [
        0.4998480148143197,
        0.4998283629056179,
        0.5002030992049937
      ],
      "cartesian_polarization_e_A2": [
        0.006238516429692748,
        0.018275158487122058,
        0.005006889025125122
      ],
      "ranking_score": 0.6815141337297799
    }
  ],
  "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": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "target_residual": 0.24385919358359268,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.017906411841415407,
            "max_log_strain_component": 0.006375338567973898,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.002884584813843,
              1.0022132158775745,
              0.9936449407841561
            ],
            "cell_volume_ratio": 0.9987166882871937,
            "cell_rmsd_from_input_A": 0.049698497316362604
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.9770344311604502e-14,
              2.9956368019449085e-16,
              -0.0025978272409398367
            ],
            "branch_aligned_reduced_polarization": [
              1.9770344311604502e-14,
              2.9956368019449085e-16,
              -0.0025978272409398367
            ],
            "target_residual": 0.0025978272409398367,
            "energy_eV": -238.13265917157983,
            "max_atomic_step_A": 0.00018709867417549366,
            "max_log_strain_component": 6.67091604047165e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0028543585605594,
              1.0021900322735948,
              0.9937112282148609
            ],
            "cell_volume_ratio": 0.9987301078516556,
            "cell_rmsd_from_input_A": 0.049177188906672435
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.746924146749856e-15,
              1.927799248688326e-15,
              1.7271613576401473e-05
            ],
            "branch_aligned_reduced_polarization": [
              8.746924146749856e-15,
              1.927799248688326e-15,
              1.7271613576401473e-05
            ],
            "target_residual": 1.7271613576401473e-05,
            "energy_eV": -238.13455680073076
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.826877384899993e-15,
        "parent_symmetrization_rmsd_A": 0.4068901170640795,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -228.5070945719832,
        "reduced_polarization": [
          -3.640848153431285e-16,
          2.7813671041344715e-16,
          -5.808836568213632e-15
        ],
        "cartesian_polarization_e_A2": [
          -4.602687795414905e-18,
          1.0315814254758581e-17,
          -6.664161006706223e-17
        ],
        "ranking_score": 0.4068901170640912
      },
      "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": [
          -238.19473386622582,
          -237.64545574504743,
          -236.5020023510354,
          -235.00858242576783,
          -233.3436778412285,
          -231.6501022563958,
          -230.09469660869368,
          -228.94152015888525,
          -228.50709457198323
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.908460760844567e-18,
            1.2021705535576693e-17,
            0.0027976633701477576
          ],
          [
            4.650967737324852e-18,
            1.2102172105426604e-17,
            0.009346950782436454
          ],
          [
            2.3383585198384117e-17,
            3.894581980735689e-18,
            0.01532034961534733
          ],
          [
            -4.8601808189346205e-18,
            4.4095680277751194e-18,
            0.020229984023193988
          ],
          [
            -4.34519477189519e-18,
            7.483390996041716e-18,
            0.02329528311566856
          ],
          [
            -1.641518024938183e-17,
            -1.392071658403459e-18,
            0.023469513554114085
          ],
          [
            2.7366680405954707e-17,
            -1.1619372686327139e-17,
            0.019662545329374545
          ],
          [
            -2.5805628950866437e-17,
            9.736454951839223e-18,
            0.011409379821712255
          ],
          [
            2.083279493414194e-17,
            6.4534189019628564e-18,
            -4.809293220373196e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            0.8147298579922109
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            1.335403016131995
          ],
          [
            -3.844531966210658e-16,
            1.1889151115957026e-16,
            1.7633528189077725
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            2.030540563065817
          ],
          [
            -1.2984843064685002e-15,
            -3.753326903395192e-17,
            2.0457274131602214
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            1.7138918495290194
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            0.9945021235577494
          ],
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            -0.1852701420077891
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            -0.664596983868005
          ],
          [
            -3.8445319662106576e-16,
            1.1889151115957026e-16,
            -0.2366471810922277
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            0.03054056306581665
          ],
          [
            -1.2984843064685002e-15,
            -3.7533269033951906e-17,
            0.04572741316022122
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            -0.2861081504709806
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            -0.005497876442250638
          ],
          [
            1.6479293477681114e-15,
            1.7399816049265572e-16,
            -4.191959279697954e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.24385919358359354
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.18527014200778913
          ],
          [
            1.887379141862766e-15,
            1.1102230246251565e-16,
            0.33540301613199497
          ],
          [
            -3.885780586188048e-16,
            1.1102230246251565e-16,
            -0.2366471810922277
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.03054056306581665
          ],
          [
            -1.27675647831893e-15,
            -5.551115123125783e-17,
            0.04572741316022122
          ],
          [
            2.1094237467877974e-15,
            -3.3306690738754696e-16,
            -0.2861081504709806
          ],
          [
            -2.0539125955565396e-15,
            2.220446049250313e-16,
            -0.005497876442250638
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-16,
            -4.218847493575595e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -228.50709457198323,
          -228.9415201588852,
          -230.09469660869368,
          -231.65010225639574,
          -233.34367784122855,
          -235.0085824257678,
          -236.50200235103543,
          -237.64545574504746,
          -238.19473386622582
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.083279493414194e-17,
            6.4534189019628564e-18,
            -4.809293220373196e-17
          ],
          [
            7.016684890912233e-18,
            -1.0637680534158225e-17,
            -0.011409379821712218
          ],
          [
            4.7644256008132264e-17,
            -1.5159901759723218e-17,
            -0.019662545329374604
          ],
          [
            -2.30375789480295e-17,
            2.0060315863582795e-17,
            -0.023469513554114082
          ],
          [
            -1.3172377484430419e-17,
            4.8601808189346205e-18,
            -0.02329528311566848
          ],
          [
            -4.2888681730002524e-17,
            -1.4097743037704397e-17,
            -0.02022998402319404
          ],
          [
            2.2321426476365292e-17,
            -1.0943453499587887e-18,
            -0.015320349615347348
          ],
          [
            -3.717555527065885e-18,
            -1.8877457286789106e-17,
            -0.009346950782436438
          ],
          [
            -3.83020872485576e-17,
            -6.765629192980511e-17,
            -0.0027976633701477715
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237902e-16,
            -2.8681492290684645e-16,
            -0.9945021235577463
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            -1.7138918495290247
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -2.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -2.0305405630658098
          ],
          [
            -3.392608506606425e-15,
            -3.8010570721088885e-16,
            -1.763352818907777
          ],
          [
            1.765684052031186e-15,
            -2.950592247755758e-17,
            -1.3354030161319965
          ],
          [
            -2.940685047002192e-16,
            -5.089771627378682e-16,
            -0.8147298579922094
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237903e-16,
            -2.868149229068464e-16,
            0.005497876442253773
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            0.28610815047097526
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -0.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -0.030540563065809767
          ],
          [
            -3.3926085066064253e-15,
            -3.8010570721088885e-16,
            0.23664718109222305
          ],
          [
            1.7656840520311859e-15,
            -2.95059224775576e-17,
            0.6645969838680035
          ],
          [
            -2.940685047002194e-16,
            -5.089771627378682e-16,
            0.18527014200779046
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.9075864274255436e-15,
          2.3865084356848043e-17,
          -0.24385919358360197
        ],
        "actual_opposite_endpoint_branch_residual": 9.526009761346756e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            0.8147298579922109
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            1.335403016131995
          ],
          [
            -3.844531966210658e-16,
            1.1889151115957026e-16,
            1.7633528189077725
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            2.030540563065817
          ],
          [
            -1.2984843064685002e-15,
            -3.753326903395192e-17,
            2.0457274131602214
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            1.7138918495290194
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            0.9945021235577494
          ],
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237902e-16,
            -2.8681492290684645e-16,
            -0.9945021235577463
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            -1.7138918495290247
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -2.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -2.0305405630658098
          ],
          [
            -3.392608506606425e-15,
            -3.8010570721088885e-16,
            -1.763352818907777
          ],
          [
            1.765684052031186e-15,
            -2.950592247755758e-17,
            -1.3354030161319965
          ],
          [
            -2.940685047002192e-16,
            -5.089771627378682e-16,
            -0.8147298579922094
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            -0.1852701420077891
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            -0.664596983868005
          ],
          [
            -3.8445319662106576e-16,
            1.1889151115957026e-16,
            -0.2366471810922277
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            0.03054056306581665
          ],
          [
            -1.2984843064685002e-15,
            -3.7533269033951906e-17,
            0.04572741316022122
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            -0.2861081504709806
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            -0.005497876442250638
          ],
          [
            1.6479293477681114e-15,
            1.7399816049265572e-16,
            -4.191959279697954e-15
          ],
          [
            5.550383898237901e-16,
            -2.868149229068464e-16,
            0.005497876442253773
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            0.28610815047097526
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -0.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -0.030540563065809767
          ],
          [
            -3.3926085066064253e-15,
            -3.8010570721088885e-16,
            0.23664718109222305
          ],
          [
            1.7656840520311859e-15,
            -2.95059224775576e-17,
            0.6645969838680035
          ],
          [
            -2.940685047002194e-16,
            -5.089771627378682e-16,
            0.18527014200779046
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.24385919358359354
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.18527014200778913
          ],
          [
            1.887379141862766e-15,
            1.1102230246251565e-16,
            0.33540301613199497
          ],
          [
            -3.885780586188048e-16,
            1.1102230246251565e-16,
            -0.2366471810922277
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.03054056306581665
          ],
          [
            -1.27675647831893e-15,
            -5.551115123125783e-17,
            0.04572741316022122
          ],
          [
            2.1094237467877974e-15,
            -3.3306690738754696e-16,
            -0.2861081504709806
          ],
          [
            -2.0539125955565396e-15,
            2.220446049250313e-16,
            -0.005497876442250638
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-16,
            -4.218847493575595e-15
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.005497876442253746
          ],
          [
            3.774758283725532e-15,
            -3.885780586188048e-16,
            0.28610815047097526
          ],
          [
            -1.8318679906315083e-15,
            5.551115123125783e-16,
            -0.045727413160221
          ],
          [
            -1.0547118733938987e-15,
            1.1102230246251565e-16,
            -0.030540563065809767
          ],
          [
            -3.3861802251067274e-15,
            -3.885780586188048e-16,
            0.23664718109222305
          ],
          [
            1.7763568394002505e-15,
            -5.551115123125783e-17,
            -0.3354030161319965
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.18527014200779046
          ],
          [
            -3.0531133177191805e-15,
            -1.8318679906315083e-15,
            -0.24385919358359476
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359265
            ],
            "target_residual": 0.25614080641640735,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.0188082421732122,
            "max_log_strain_component": 0.006696423202181574,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0067188943748573,
              0.9976805814697852,
              0.9969790710554872
            ],
            "cell_volume_ratio": 1.0013497195460337,
            "cell_rmsd_from_input_A": 0.05193663724786205
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.9752884167716326e-14,
              -2.452608491747907e-15,
              0.4968180786393642
            ],
            "branch_aligned_reduced_polarization": [
              -2.9752884167716326e-14,
              -2.452608491747907e-15,
              0.4968180786393642
            ],
            "target_residual": 0.0031819213606357755,
            "energy_eV": -238.03195469013065,
            "max_atomic_step_A": 0.00023827939187283202,
            "max_log_strain_component": 8.51697315663125e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0068046400042685,
              0.9976511161772436,
              0.9969407076285028
            ],
            "cell_volume_ratio": 1.0013668979379085,
            "cell_rmsd_from_input_A": 0.0525954675405607
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.135060539126793e-15,
              3.554117176424579e-15,
              0.4999712597741904
            ],
            "branch_aligned_reduced_polarization": [
              -4.135060539126793e-15,
              3.554117176424579e-15,
              0.4999712597741904
            ],
            "target_residual": 2.8740225809620323e-05,
            "energy_eV": -238.0285888356265
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.8740225809620323e-05,
        "parent_symmetrization_rmsd_A": 0.013343415644553987,
        "parent_cell_rmsd_A": 0.0525954675405607,
        "energy_eV": -238.0285888356265,
        "reduced_polarization": [
          -4.135060539126793e-15,
          3.554117176424579e-15,
          0.4999712597741904
        ],
        "cartesian_polarization_e_A2": [
          -3.752659309718714e-17,
          1.4579925163926411e-16,
          0.005767045011111315
        ],
        "ranking_score": 0.5265497629813134
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1094237467877974e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "target_residual": 0.5562978575324895,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.047954675462757924,
            "max_log_strain_component": 0.011455771647455098,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0102031825549438,
              1.0028845848138475,
              0.9857859376617307
            ],
            "cell_volume_ratio": 0.9987166882872166,
            "cell_rmsd_from_input_A": 0.05729105190137411
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49279146102573745,
              3.5898858449418984e-15,
              0.0014580052191196721
            ],
            "branch_aligned_reduced_polarization": [
              0.49279146102573745,
              3.5898858449418984e-15,
              0.0014580052191196721
            ],
            "target_residual": 0.00735450972957697,
            "energy_eV": -237.44532549389604,
            "max_atomic_step_A": 0.0006747032747166116,
            "max_log_strain_component": 0.0001699809315740299,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0103601833123514,
              1.002903711465446,
              0.985605578281771
            ],
            "cell_volume_ratio": 0.998708196920434,
            "cell_rmsd_from_input_A": 0.05778750917357318
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996394209470013,
              -1.5962766883180767e-17,
              -1.7544232542692076e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49996394209470013,
              -1.5962766883180767e-17,
              -1.7544232542692076e-05
            ],
            "target_residual": 4.0099534038768655e-05,
            "energy_eV": -237.4238247338967
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 4.0099534038768655e-05,
        "parent_symmetrization_rmsd_A": 0.03726825840791341,
        "parent_cell_rmsd_A": 0.05778750917357318,
        "energy_eV": -237.4238247338967,
        "reduced_polarization": [
          0.49996394209470013,
          -1.5962766883180767e-17,
          -1.7544232542692076e-05
        ],
        "cartesian_polarization_e_A2": [
          0.006343149191304959,
          4.608641252377342e-17,
          -7.362561192188557e-05
        ],
        "ranking_score": 0.5517953347693842
      },
      "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": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1132195575859903e-15,
              3.3306690738754696e-16,
              0.24385919358359268
            ],
            "target_residual": 0.5562978575324911,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.0750500221820984,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5496350153669777,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0193861611443753,
              1.0012158553339527,
              0.9790999319198589
            ],
            "cell_volume_ratio": 0.9992944429879903,
            "cell_rmsd_from_input_A": 0.1503507999334943
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.6852182536095052e-14,
              0.27102335457320476,
              0.12430309606929593
            ],
            "branch_aligned_reduced_polarization": [
              -2.6852182536095052e-14,
              0.27102335457320476,
              0.12430309606929593
            ],
            "target_residual": 0.2605409062763867,
            "energy_eV": -236.49794321293908,
            "max_atomic_step_A": 0.06607003630309852,
            "max_log_strain_component": 0.01743022661779801,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0363833259296666,
              1.0026687962754606,
              0.9608370571599388
            ],
            "cell_volume_ratio": 0.9984530803106908,
            "cell_rmsd_from_input_A": 0.2859814683804701
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.3558665557506682e-14,
              0.49106125652473853,
              0.0202736369554512
            ],
            "branch_aligned_reduced_polarization": [
              -2.3558665557506682e-14,
              0.49106125652473853,
              0.0202736369554512
            ],
            "target_residual": 0.02215674818916273,
            "energy_eV": -232.17999429878577,
            "max_atomic_step_A": 0.0033304896379486625,
            "max_log_strain_component": 0.0007838466684908732,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0370752808897428,
              1.0028966500433145,
              0.959851125311892
            ],
            "cell_volume_ratio": 0.9983213105600464,
            "cell_rmsd_from_input_A": 0.2931725614271484
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.486153133673659e-16,
              0.4995371160730768,
              0.00029121193862944754
            ],
            "branch_aligned_reduced_polarization": [
              7.486153133673659e-16,
              0.4995371160730768,
              0.00029121193862944754
            ],
            "target_residual": 0.0005468692010016104,
            "energy_eV": -231.945881964084
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0005468692010016104,
        "parent_symmetrization_rmsd_A": 0.10695451923585308,
        "parent_cell_rmsd_A": 0.2931725614271484,
        "energy_eV": -231.945881964084,
        "reduced_polarization": [
          7.486153133673659e-16,
          0.4995371160730768,
          0.00029121193862944754
        ],
        "cartesian_polarization_e_A2": [
          4.2772191182215e-16,
          0.018641985074922447,
          -0.0007038790664943845
        ],
        "ranking_score": 0.6813413979946434
      },
      "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": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1094237467877974e-15,
              3.471284997359715e-16,
              0.24385919358359265
            ],
            "target_residual": 0.56179009666569,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.048303497256248225,
            "max_log_strain_component": 0.011455771647449002,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0146040715558524,
              0.9969790710554906,
              0.9899269282217305
            ],
            "cell_volume_ratio": 1.001349719546056,
            "cell_rmsd_from_input_A": 0.05939775740266556
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5045787665274519,
              2.1981163925097126e-15,
              0.4985626367185255
            ],
            "branch_aligned_reduced_polarization": [
              0.5045787665274519,
              2.1981163925097126e-15,
              0.4985626367185255
            ],
            "target_residual": 0.0047990745061777555,
            "energy_eV": -237.24663518059822,
            "max_atomic_step_A": 0.00042900287869520503,
            "max_log_strain_component": 0.00010520736949256173,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0145285454039206,
              0.9969607731481307,
              0.9900268936923231
            ],
            "cell_volume_ratio": 1.0013579128716896,
            "cell_rmsd_from_input_A": 0.0595457702652864
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000132568981349,
              1.3941073375216394e-15,
              0.5000041944954673
            ],
            "branch_aligned_reduced_polarization": [
              0.5000132568981349,
              1.3941073375216394e-15,
              0.5000041944954673
            ],
            "target_residual": 1.3904644561609176e-05,
            "energy_eV": -237.25921851260887
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.3904644561609176e-05,
        "parent_symmetrization_rmsd_A": 0.03734778287751367,
        "parent_cell_rmsd_A": 0.0595457702652864,
        "energy_eV": -237.25921851260887,
        "reduced_polarization": [
          0.5000132568981349,
          1.3941073375216394e-15,
          0.5000041944954673
        ],
        "cartesian_polarization_e_A2": [
          0.006233011164008471,
          2.957154212707715e-18,
          0.005695775151857277
        ],
        "ranking_score": 0.5522620347329585
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1132195575859903e-15,
              3.3306690738754696e-16,
              0.24385919358359265
            ],
            "target_residual": 0.5617900966656916,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.0751292597086942,
            "max_log_strain_component": 0.02,
            "step_scale": 0.549635015367056,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.021412528714248,
              0.9987244997768213,
              0.9810137197105274
            ],
            "cell_volume_ratio": 1.0007416277966237,
            "cell_rmsd_from_input_A": 0.1487668693357269
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.252008070994504e-14,
              0.2748640445230175,
              0.3957579640586832
            ],
            "branch_aligned_reduced_polarization": [
              -5.252008070994504e-14,
              0.2748640445230175,
              0.3957579640586832
            ],
            "target_residual": 0.248097965541285,
            "energy_eV": -236.2879002614629,
            "max_atomic_step_A": 0.062043698851509115,
            "max_log_strain_component": 0.016691689275184787,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0392568826909887,
              0.9980065749946528,
              0.9652661023972172
            ],
            "cell_volume_ratio": 1.001159717431481,
            "cell_rmsd_from_input_A": 0.2714051002637892
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.298000624024402e-14,
              0.4969608390423455,
              0.5096450857900727
            ],
            "branch_aligned_reduced_polarization": [
              -3.298000624024402e-14,
              0.4969608390423455,
              0.5096450857900727
            ],
            "target_residual": 0.010112575301296611,
            "energy_eV": -231.45037995272253,
            "max_atomic_step_A": 0.0012461450948510657,
            "max_log_strain_component": 0.00030076161564361527,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0394100274852105,
              0.9981106673491008,
              0.9649647701997383
            ],
            "cell_volume_ratio": 1.0010990688925367,
            "cell_rmsd_from_input_A": 0.2730300332858454
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.980029304385907e-15,
              0.49986437236887754,
              0.5001559283782677
            ],
            "branch_aligned_reduced_polarization": [
              -5.980029304385907e-15,
              0.49986437236887754,
              0.5001559283782677
            ],
            "target_residual": 0.00020666038196299683,
            "energy_eV": -231.38519346674903
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00020666038196299683,
        "parent_symmetrization_rmsd_A": 0.10604227607614149,
        "parent_cell_rmsd_A": 0.2730300332858454,
        "energy_eV": -231.38519346674903,
        "reduced_polarization": [
          -5.980029304385907e-15,
          0.49986437236887754,
          0.5001559283782677
        ],
        "cartesian_polarization_e_A2": [
          8.950919541258687e-17,
          0.01827392031090546,
          0.005082012524970753
        ],
        "ranking_score": 0.6747131051615288
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1094237467877974e-15,
              3.3306690738754696e-16,
              0.24385919358359268
            ],
            "target_residual": 0.7479754717203216,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.0800138532251021,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5496350153669154,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.020346971602645,
              1.001248967662265,
              0.9781456124195979
            ],
            "cell_volume_ratio": 0.999294442988003,
            "cell_rmsd_from_input_A": 0.1511763717924653
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.27165738600933637,
              0.2707791473060597,
              0.12556726089797196
            ],
            "branch_aligned_reduced_polarization": [
              0.27165738600933637,
              0.2707791473060597,
              0.12556726089797196
            ],
            "target_residual": 0.34705861995237297,
            "energy_eV": -236.27298753480667,
            "max_atomic_step_A": 0.07029446253352979,
            "max_log_strain_component": 0.01750665477347782,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0382347728409222,
              1.0027894584262154,
              0.9589817811024894
            ],
            "cell_volume_ratio": 0.9984255510108809,
            "cell_rmsd_from_input_A": 0.28836367880084884
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4928547301100978,
              0.49020242624673055,
              0.023295554354991758
            ],
            "branch_aligned_reduced_polarization": [
              0.4928547301100978,
              0.49020242624673055,
              0.023295554354991758
            ],
            "target_residual": 0.02626271474841611,
            "energy_eV": -231.29926383306264,
            "max_atomic_step_A": 0.003809226394638901,
            "max_log_strain_component": 0.0008717359164758315,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0390145006838563,
              1.0030621311951147,
              0.9578537937495255
            ],
            "cell_volume_ratio": 0.9982714876398845,
            "cell_rmsd_from_input_A": 0.2964744519698034
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49954535756836804,
              0.4994423450363026,
              0.0003718359006471431
            ],
            "branch_aligned_reduced_polarization": [
              0.49954535756836804,
              0.4994423450363026,
              0.0003718359006471431
            ],
            "target_residual": 0.0008099016830373055,
            "energy_eV": -231.00928753410037
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0008099016830373055,
        "parent_symmetrization_rmsd_A": 0.11308589902862945,
        "parent_cell_rmsd_A": 0.2964744519698034,
        "energy_eV": -231.00928753410037,
        "reduced_polarization": [
          0.49954535756836804,
          0.4994423450363026,
          0.0003718359006471431
        ],
        "cartesian_polarization_e_A2": [
          0.006349565942506102,
          0.018643006840695992,
          -0.0007810305863773718
        ],
        "ranking_score": 0.6888243153871549
      },
      "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": [
              2.1132195575859903e-15,
              3.471284997359715e-16,
              0.24385919358359268
            ],
            "branch_aligned_reduced_polarization": [
              2.1094237467877974e-15,
              3.3306690738754696e-16,
              0.24385919358359265
            ],
            "target_residual": 0.752069220691583,
            "energy_eV": -238.19473386622585,
            "max_atomic_step_A": 0.08008905973893907,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.5496350153669937,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0224089569843928,
              0.9986898204400245,
              0.9800916671103266
            ],
            "cell_volume_ratio": 1.0007416277966361,
            "cell_rmsd_from_input_A": 0.1496113783590267
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.27528087522396494,
              0.27462505048824687,
              0.3966601868537534
            ],
            "branch_aligned_reduced_polarization": [
              0.27528087522396494,
              0.27462505048824687,
              0.3966601868537534
            ],
            "target_residual": 0.3346216817372025,
            "energy_eV": -236.0459542228934,
            "max_atomic_step_A": 0.06603072224033026,
            "max_log_strain_component": 0.016760070114272697,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0411405238201634,
              0.9979865238842152,
              0.9635206654715891
            ],
            "cell_volume_ratio": 1.0011405708340804,
            "cell_rmsd_from_input_A": 0.27341410256297344
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4981939537056154,
              0.49630924265048076,
              0.5113921426055441
            ],
            "branch_aligned_reduced_polarization": [
              0.4981939537056154,
              0.49630924265048076,
              0.5113921426055441
            ],
            "target_residual": 0.012110508089074705,
            "energy_eV": -230.4965233640785,
            "max_atomic_step_A": 0.0015148392358839712,
            "max_log_strain_component": 0.0003616922932049277,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.253034742924228,
            "cell_principal_stretches": [
              1.0413322294302243,
              0.9981154261507158,
              0.9631487023482568
            ],
            "cell_volume_ratio": 1.001067637474669,
            "cell_rmsd_from_input_A": 0.27542155600669604
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4998480148143197,
              0.4998283629056179,
              0.5002030992049937
            ],
            "branch_aligned_reduced_polarization": [
              0.4998480148143197,
              0.4998283629056179,
              0.5002030992049937
            ],
            "target_residual": 0.00030628104071800274,
            "energy_eV": -230.407624116641
          }
        ],
        "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": 0.00030628104071800274,
        "parent_symmetrization_rmsd_A": 0.11204618264666985,
        "parent_cell_rmsd_A": 0.27542155600669604,
        "energy_eV": -230.407624116641,
        "reduced_polarization": [
          0.4998480148143197,
          0.4998283629056179,
          0.5002030992049937
        ],
        "cartesian_polarization_e_A2": [
          0.006238516429692748,
          0.018275158487122058,
          0.005006889025125122
        ],
        "ranking_score": 0.6815141337297799
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.4068901170640795,
        "minimum_distance_A_by_image": [
          1.740091877540532,
          1.7235388417977273,
          1.7090631985100235,
          1.6967181186720786,
          1.684897605259086,
          1.6691435980279878,
          1.6577990792017316,
          1.6509549505364116,
          1.648667260526982
        ],
        "minimum_distance_A": 1.648667260526982,
        "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": [
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796,
          431.16625431218796
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.6479293477681112e-15,
        1.7399816049265572e-16,
        -4.192035321123394e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -238.19473386622582,
          -237.64545574504743,
          -236.5020023510354,
          -235.00858242576783,
          -233.3436778412285,
          -231.6501022563958,
          -230.09469660869368,
          -228.94152015888525,
          -228.50709457198323
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.908460760844567e-18,
            1.2021705535576693e-17,
            0.0027976633701477576
          ],
          [
            4.650967737324852e-18,
            1.2102172105426604e-17,
            0.009346950782436454
          ],
          [
            2.3383585198384117e-17,
            3.894581980735689e-18,
            0.01532034961534733
          ],
          [
            -4.8601808189346205e-18,
            4.4095680277751194e-18,
            0.020229984023193988
          ],
          [
            -4.34519477189519e-18,
            7.483390996041716e-18,
            0.02329528311566856
          ],
          [
            -1.641518024938183e-17,
            -1.392071658403459e-18,
            0.023469513554114085
          ],
          [
            2.7366680405954707e-17,
            -1.1619372686327139e-17,
            0.019662545329374545
          ],
          [
            -2.5805628950866437e-17,
            9.736454951839223e-18,
            0.011409379821712255
          ],
          [
            2.083279493414194e-17,
            6.4534189019628564e-18,
            -4.809293220373196e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            0.8147298579922109
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            1.335403016131995
          ],
          [
            -3.844531966210658e-16,
            1.1889151115957026e-16,
            1.7633528189077725
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            2.030540563065817
          ],
          [
            -1.2984843064685002e-15,
            -3.753326903395192e-17,
            2.0457274131602214
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            1.7138918495290194
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            0.9945021235577494
          ],
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            -0.1852701420077891
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            -0.664596983868005
          ],
          [
            -3.8445319662106576e-16,
            1.1889151115957026e-16,
            -0.2366471810922277
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            0.03054056306581665
          ],
          [
            -1.2984843064685002e-15,
            -3.7533269033951906e-17,
            0.04572741316022122
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            -0.2861081504709806
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            -0.005497876442250638
          ],
          [
            1.6479293477681114e-15,
            1.7399816049265572e-16,
            -4.191959279697954e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.24385919358359354
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.18527014200778913
          ],
          [
            1.887379141862766e-15,
            1.1102230246251565e-16,
            0.33540301613199497
          ],
          [
            -3.885780586188048e-16,
            1.1102230246251565e-16,
            -0.2366471810922277
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.03054056306581665
          ],
          [
            -1.27675647831893e-15,
            -5.551115123125783e-17,
            0.04572741316022122
          ],
          [
            2.1094237467877974e-15,
            -3.3306690738754696e-16,
            -0.2861081504709806
          ],
          [
            -2.0539125955565396e-15,
            2.220446049250313e-16,
            -0.005497876442250638
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-16,
            -4.218847493575595e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -228.50709457198323,
          -228.9415201588852,
          -230.09469660869368,
          -231.65010225639574,
          -233.34367784122855,
          -235.0085824257678,
          -236.50200235103543,
          -237.64545574504746,
          -238.19473386622582
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.083279493414194e-17,
            6.4534189019628564e-18,
            -4.809293220373196e-17
          ],
          [
            7.016684890912233e-18,
            -1.0637680534158225e-17,
            -0.011409379821712218
          ],
          [
            4.7644256008132264e-17,
            -1.5159901759723218e-17,
            -0.019662545329374604
          ],
          [
            -2.30375789480295e-17,
            2.0060315863582795e-17,
            -0.023469513554114082
          ],
          [
            -1.3172377484430419e-17,
            4.8601808189346205e-18,
            -0.02329528311566848
          ],
          [
            -4.2888681730002524e-17,
            -1.4097743037704397e-17,
            -0.02022998402319404
          ],
          [
            2.2321426476365292e-17,
            -1.0943453499587887e-18,
            -0.015320349615347348
          ],
          [
            -3.717555527065885e-18,
            -1.8877457286789106e-17,
            -0.009346950782436438
          ],
          [
            -3.83020872485576e-17,
            -6.765629192980511e-17,
            -0.0027976633701477715
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237902e-16,
            -2.8681492290684645e-16,
            -0.9945021235577463
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            -1.7138918495290247
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -2.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -2.0305405630658098
          ],
          [
            -3.392608506606425e-15,
            -3.8010570721088885e-16,
            -1.763352818907777
          ],
          [
            1.765684052031186e-15,
            -2.950592247755758e-17,
            -1.3354030161319965
          ],
          [
            -2.940685047002192e-16,
            -5.089771627378682e-16,
            -0.8147298579922094
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237903e-16,
            -2.868149229068464e-16,
            0.005497876442253773
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            0.28610815047097526
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -0.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -0.030540563065809767
          ],
          [
            -3.3926085066064253e-15,
            -3.8010570721088885e-16,
            0.23664718109222305
          ],
          [
            1.7656840520311859e-15,
            -2.95059224775576e-17,
            0.6645969838680035
          ],
          [
            -2.940685047002194e-16,
            -5.089771627378682e-16,
            0.18527014200779046
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.9075864274255436e-15,
          2.3865084356848043e-17,
          -0.24385919358360197
        ],
        "actual_opposite_endpoint_branch_residual": 9.526009761346756e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            0.8147298579922109
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            1.335403016131995
          ],
          [
            -3.844531966210658e-16,
            1.1889151115957026e-16,
            1.7633528189077725
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            2.030540563065817
          ],
          [
            -1.2984843064685002e-15,
            -3.753326903395192e-17,
            2.0457274131602214
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            1.7138918495290194
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            0.9945021235577494
          ],
          [
            1.6479293477681112e-15,
            1.7399816049265572e-16,
            -4.192035321123394e-15
          ],
          [
            5.550383898237902e-16,
            -2.8681492290684645e-16,
            -0.9945021235577463
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            -1.7138918495290247
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -2.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -2.0305405630658098
          ],
          [
            -3.392608506606425e-15,
            -3.8010570721088885e-16,
            -1.763352818907777
          ],
          [
            1.765684052031186e-15,
            -2.950592247755758e-17,
            -1.3354030161319965
          ],
          [
            -2.940685047002192e-16,
            -5.089771627378682e-16,
            -0.8147298579922094
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.88272268110679e-16,
            3.241312366284634e-16,
            0.24385919358359356
          ],
          [
            3.679038868327417e-16,
            3.263007897518132e-16,
            -0.1852701420077891
          ],
          [
            1.8497036248026773e-15,
            1.0500637117013138e-16,
            -0.664596983868005
          ],
          [
            -3.8445319662106576e-16,
            1.1889151115957026e-16,
            -0.2366471810922277
          ],
          [
            -3.437164340651912e-16,
            2.0176844047153343e-16,
            0.03054056306581665
          ],
          [
            -1.2984843064685002e-15,
            -3.7533269033951906e-17,
            0.04572741316022122
          ],
          [
            2.164777022695769e-15,
            -3.132834710117143e-16,
            -0.2861081504709806
          ],
          [
            -2.0412937111982748e-15,
            2.6251592792532848e-16,
            -0.005497876442250638
          ],
          [
            1.6479293477681114e-15,
            1.7399816049265572e-16,
            -4.191959279697954e-15
          ],
          [
            5.550383898237901e-16,
            -2.868149229068464e-16,
            0.005497876442253773
          ],
          [
            3.7687870483333286e-15,
            -4.087438084391064e-16,
            0.28610815047097526
          ],
          [
            -1.822333612460449e-15,
            5.408695936511106e-16,
            -0.045727413160221
          ],
          [
            -1.041970004749478e-15,
            1.3104100865032927e-16,
            -0.030540563065809767
          ],
          [
            -3.3926085066064253e-15,
            -3.8010570721088885e-16,
            0.23664718109222305
          ],
          [
            1.7656840520311859e-15,
            -2.95059224775576e-17,
            0.6645969838680035
          ],
          [
            -2.940685047002194e-16,
            -5.089771627378682e-16,
            0.18527014200779046
          ],
          [
            -3.0297967150931675e-15,
            -1.8241602661125305e-15,
            -0.24385919358359476
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.24385919358359354
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.18527014200778913
          ],
          [
            1.887379141862766e-15,
            1.1102230246251565e-16,
            0.33540301613199497
          ],
          [
            -3.885780586188048e-16,
            1.1102230246251565e-16,
            -0.2366471810922277
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.03054056306581665
          ],
          [
            -1.27675647831893e-15,
            -5.551115123125783e-17,
            0.04572741316022122
          ],
          [
            2.1094237467877974e-15,
            -3.3306690738754696e-16,
            -0.2861081504709806
          ],
          [
            -2.0539125955565396e-15,
            2.220446049250313e-16,
            -0.005497876442250638
          ],
          [
            1.6653345369377348e-15,
            2.220446049250313e-16,
            -4.218847493575595e-15
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.005497876442253746
          ],
          [
            3.774758283725532e-15,
            -3.885780586188048e-16,
            0.28610815047097526
          ],
          [
            -1.8318679906315083e-15,
            5.551115123125783e-16,
            -0.045727413160221
          ],
          [
            -1.0547118733938987e-15,
            1.1102230246251565e-16,
            -0.030540563065809767
          ],
          [
            -3.3861802251067274e-15,
            -3.885780586188048e-16,
            0.23664718109222305
          ],
          [
            1.7763568394002505e-15,
            -5.551115123125783e-17,
            -0.3354030161319965
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.18527014200779046
          ],
          [
            -3.0531133177191805e-15,
            -1.8318679906315083e-15,
            -0.24385919358359476
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.826877384899993e-15,
        "parent_symmetrization_rmsd_A": 0.4068901170640795,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -228.5070945719832,
        "reduced_polarization": [
          -3.640848153431285e-16,
          2.7813671041344715e-16,
          -5.808836568213632e-15
        ],
        "cartesian_polarization_e_A2": [
          -4.602687795414905e-18,
          1.0315814254758581e-17,
          -6.664161006706223e-17
        ],
        "ranking_score": 0.4068901170640912
      }
    }
  ],
  "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": 53,
      "full_response": 21,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 46,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1171.921856465051
  }
}
