{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "H2As2O8Pb2",
  "input_spacegroup": "Pc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -78.60954386962345,
  "input_cartesian_polarization_e_A2": [
    0.0013385827398528021,
    1.8288234922652097e-11,
    -5.80096161440038e-05
  ],
  "input_reduced_polarization": [
    0.05440766797454497,
    5.404521752510157e-10,
    -0.001992130076424358
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.1476675941773614e-15,
      "parent_symmetrization_rmsd_A": 0.1026740933071159,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -78.4363213480527,
      "reduced_polarization": [
        1.3344591504216197e-15,
        2.760778730138738e-15,
        7.10725588749868e-16
      ],
      "cartesian_polarization_e_A2": [
        3.0754034538510474e-17,
        9.342134660257062e-17,
        2.069589685684685e-17
      ],
      "ranking_score": 0.1026740933071222
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.2037549614158297e-15,
      "parent_symmetrization_rmsd_A": 1.005012989433024,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -50.95861314103861,
      "reduced_polarization": [
        -2.1939192534175278e-15,
        1.2494035129095016e-16,
        1.6626529423802515e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.421165733506836e-17,
        4.227827364495897e-18,
        4.841544239987237e-18
      ],
      "ranking_score": 1.0050129894330284
    },
    {
      "candidate_id": "bec_projection_00",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.9422875067999895e-05,
      "parent_symmetrization_rmsd_A": 0.016279203917762632,
      "parent_cell_rmsd_A": 0.001597556687768152,
      "energy_eV": -78.60011949934304,
      "reduced_polarization": [
        4.132318722012796e-05,
        1.0893238360485698e-13,
        4.270213436489301e-05
      ],
      "cartesian_polarization_e_A2": [
        8.96161389982002e-07,
        3.672730918828134e-15,
        1.2441373040184463e-06
      ],
      "ranking_score": 0.5167974388398406
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1927121179612537e-15,
      "parent_symmetrization_rmsd_A": 0.10267684528185393,
      "parent_cell_rmsd_A": 0.001597556687768152,
      "energy_eV": -78.444873439594,
      "reduced_polarization": [
        -8.822756378308822e-16,
        -3.9204413358157785e-16,
        7.003237055433721e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.3536587108678486e-17,
        -1.3269177369965117e-17,
        2.039837549418802e-17
      ],
      "ranking_score": 0.10307623445379836
    },
    {
      "candidate_id": "bec_projection_01",
      "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": 3.205668178559219e-05,
      "parent_symmetrization_rmsd_A": 0.13494830005378813,
      "parent_cell_rmsd_A": 0.013246697267253187,
      "energy_eV": -77.47878364582161,
      "reduced_polarization": [
        0.4999704440373628,
        3.645320320001395e-14,
        1.2412732160598839e-05
      ],
      "cartesian_polarization_e_A2": [
        0.012224025399035067,
        -1.4103505913081615e-13,
        -1.4237011576071927e-05
      ],
      "ranking_score": 0.6383240877341726
    },
    {
      "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": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.7454401438876436e-06,
      "parent_symmetrization_rmsd_A": 0.17379515354079625,
      "parent_cell_rmsd_A": 0.009718389704195318,
      "energy_eV": -76.85725026696358,
      "reduced_polarization": [
        -1.6884629682121984e-06,
        2.8620573678143457e-13,
        -0.4999978351595004
      ],
      "cartesian_polarization_e_A2": [
        0.0013919089519090113,
        -7.288024759170852e-14,
        -0.01454791816574134
      ],
      "ranking_score": 0.6762302418471329
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0003846659163865683,
      "parent_symmetrization_rmsd_A": 0.2606401541643822,
      "parent_cell_rmsd_A": 0.07709038468128682,
      "energy_eV": -73.88139867898805,
      "reduced_polarization": [
        0.0002011245536978209,
        0.49985246632895497,
        0.00029283202870817855
      ],
      "cartesian_polarization_e_A2": [
        0.00024093528204343462,
        0.016919372845256395,
        -8.987079347619448e-06
      ],
      "ranking_score": 0.7806820821674769
    },
    {
      "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": 0.0005266306402166303,
      "parent_symmetrization_rmsd_A": 0.26610824438703684,
      "parent_cell_rmsd_A": 0.025210955657648946,
      "energy_eV": -74.13453034048848,
      "reduced_polarization": [
        0.4996253588267056,
        1.1760932022192278e-12,
        -0.4996298867437019
      ],
      "cartesian_polarization_e_A2": [
        0.01361002978778296,
        -1.2959488687293093e-12,
        -0.014512746866671516
      ],
      "ranking_score": 0.7734642445818823
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0006555427947718246,
      "parent_symmetrization_rmsd_A": 0.31388370336980004,
      "parent_cell_rmsd_A": 0.08954581098234347,
      "energy_eV": -72.32913505472754,
      "reduced_polarization": [
        0.4996734094062667,
        0.4996762172348219,
        0.00046716127925569746
      ],
      "cartesian_polarization_e_A2": [
        0.012472921051828683,
        0.017060142495552853,
        -2.828430939885037e-05
      ],
      "ranking_score": 0.8375812417049295
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.7220039452989956e-06,
      "parent_symmetrization_rmsd_A": 0.3407620151792109,
      "parent_cell_rmsd_A": 0.0989913511668504,
      "energy_eV": -70.88545646175912,
      "reduced_polarization": [
        7.57294115306292e-07,
        0.4999987800029172,
        -0.4999990495210005
      ],
      "cartesian_polarization_e_A2": [
        0.0017041083236249276,
        0.016920481069643015,
        -0.014552168705743586
      ],
      "ranking_score": 0.8655132969788141
    },
    {
      "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": 0.0019057789098962034,
      "parent_symmetrization_rmsd_A": 0.38452490383093313,
      "parent_cell_rmsd_A": 0.10199120900110886,
      "energy_eV": -68.4100031680031,
      "reduced_polarization": [
        0.4995402782536672,
        0.4995999942204402,
        -0.498194274509879
      ],
      "cartesian_polarization_e_A2": [
        0.01382501509032276,
        0.017010241990292146,
        -0.014397094418512751
      ],
      "ranking_score": 0.9138342639010028
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "target_residual": 0.05444412655805694,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.014225428507596883,
            "max_log_strain_component": 0.00024020734945427572,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.000064677757599,
              0.999759821498021,
              0.999717730525798
            ],
            "cell_volume_ratio": 0.9995422637900996,
            "cell_rmsd_from_input_A": 0.001597556687768152
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.132318722012796e-05,
              1.0893238360485698e-13,
              4.270213436489301e-05
            ],
            "branch_aligned_reduced_polarization": [
              4.132318722012796e-05,
              1.0893238360485698e-13,
              4.270213436489301e-05
            ],
            "target_residual": 5.9422875067999895e-05,
            "energy_eV": -78.60011949934304
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2/c",
        "spacegroup_number": 13,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1476675941773614e-15,
        "parent_symmetrization_rmsd_A": 0.1026740933071159,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -78.4363213480527,
        "reduced_polarization": [
          1.3344591504216197e-15,
          2.760778730138738e-15,
          7.10725588749868e-16
        ],
        "cartesian_polarization_e_A2": [
          3.0754034538510474e-17,
          9.342134660257062e-17,
          2.069589685684685e-17
        ],
        "ranking_score": 0.1026740933071222
      },
      "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": [
          -78.60954386962345,
          -78.61099127931247,
          -78.59844333975374,
          -78.57456182661394,
          -78.5422702304435,
          -78.50573614800395,
          -78.4710416143489,
          -78.44568296256108,
          -78.4363213480527
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013385827398527904,
            1.8288234343030602e-11,
            -5.800961614399547e-05
          ],
          [
            0.0013067088643214505,
            1.749954661585977e-11,
            0.00011520987468022921
          ],
          [
            0.00125632547213088,
            1.594246555115686e-11,
            0.0002616061433805709
          ],
          [
            0.0011717405419179618,
            1.3787159222810667e-11,
            0.0003652485178078111
          ],
          [
            0.0010397444758943103,
            1.1273330985946158e-11,
            0.0004117696818567113
          ],
          [
            0.0008523419450200112,
            8.598132477079923e-12,
            0.00039231298154003704
          ],
          [
            0.0006089026941579653,
            5.832733203201405e-12,
            0.0003073021600671801
          ],
          [
            0.0003182531280937892,
            2.9620378430871972e-12,
            0.00016878556193109534
          ],
          [
            -6.409931810687328e-18,
            8.574988565892888e-17,
            -3.4947766521034636e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407995
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7499710620966816e-16,
            2.5340724475543526e-15,
            -1.2001544126336324e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407996
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7582103268031233e-16,
            2.5340724475564246e-15,
            -1.196959198423997e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.05440766797454455,
            5.404521274954277e-10,
            -0.00199213007642407
          ],
          [
            0.053770811666970064,
            5.171448824725644e-10,
            0.003956465698408018
          ],
          [
            0.052275730616730076,
            4.711302459270428e-10,
            0.008983915099732731
          ],
          [
            0.049220939967058785,
            4.074368620266e-10,
            0.012543136915233122
          ],
          [
            0.04401225970866063,
            3.3314839775755445e-10,
            0.01414073773131208
          ],
          [
            0.036289436905951655,
            2.5409119253083645e-10,
            0.01347256785767248
          ],
          [
            0.026028373954666617,
            1.7236834182199345e-10,
            0.010553179219464304
          ],
          [
            0.013635475731859081,
            8.753386904203353e-11,
            0.00579632855274248
          ],
          [
            -2.7755575615628914e-16,
            2.55351295663786e-15,
            -1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -78.4363213480527,
          -78.44568296256108,
          -78.4710416143489,
          -78.50573614800396,
          -78.54227023044352,
          -78.57456182661392,
          -78.59844333975374,
          -78.61099127931247,
          -78.60954386962345
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.137562368426616e-18,
            8.032871992542204e-17,
            1.7047690985870553e-18
          ],
          [
            -0.0003182531280936951,
            -2.961973948341382e-12,
            -0.00016878556193109442
          ],
          [
            -0.000608902694157927,
            -5.832648629606424e-12,
            -0.00030730216006723157
          ],
          [
            -0.0008523419450199729,
            -8.598109258124801e-12,
            -0.00039231298154004664
          ],
          [
            -0.0010397444758943543,
            -1.1273396738890292e-11,
            -0.00041176968185663483
          ],
          [
            -0.0011717405419179505,
            -1.3787126048004009e-11,
            -0.0003652485178078179
          ],
          [
            -0.0012563254721308437,
            -1.5942481899892515e-11,
            -0.0002616061433806096
          ],
          [
            -0.0013067088643215102,
            -1.749958846794114e-11,
            -0.000115209874680232
          ],
          [
            -0.0013385827398527902,
            -1.8288231956353866e-11,
            5.800961614400308e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6638612546857853e-16,
            2.3738666745280536e-15,
            5.854411768944547e-17
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.0019921300764243334
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6638612546857853e-16,
            2.3738666745280536e-15,
            5.854411768944547e-17
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.001992130076424333
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.054407667974545076,
          -5.404470899772013e-10,
          0.001992130076423832
        ],
        "actual_opposite_endpoint_branch_residual": 5.057165166635757e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407995
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7499710620966816e-16,
            2.5340724475543526e-15,
            -1.2001544126336324e-16
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.0019921300764243334
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407996
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7582103268031233e-16,
            2.5340724475564246e-15,
            -1.196959198423997e-16
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.001992130076424333
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.05440766797454455,
            5.404521274954277e-10,
            -0.00199213007642407
          ],
          [
            0.053770811666970064,
            5.171448824725644e-10,
            0.003956465698408018
          ],
          [
            0.052275730616730076,
            4.711302459270428e-10,
            0.008983915099732731
          ],
          [
            0.049220939967058785,
            4.074368620266e-10,
            0.012543136915233122
          ],
          [
            0.04401225970866063,
            3.3314839775755445e-10,
            0.01414073773131208
          ],
          [
            0.036289436905951655,
            2.5409119253083645e-10,
            0.01347256785767248
          ],
          [
            0.026028373954666617,
            1.7236834182199345e-10,
            0.010553179219464304
          ],
          [
            0.013635475731859081,
            8.753386904203353e-11,
            0.00579632855274248
          ],
          [
            -2.7755575615628914e-16,
            2.55351295663786e-15,
            -1.1102230246251565e-16
          ],
          [
            -0.013635475731855196,
            -8.753198166289167e-11,
            -0.00579632855274248
          ],
          [
            -0.026028373954665285,
            -1.7236589933133928e-10,
            -0.01055317921946608
          ],
          [
            -0.0362894369059501,
            -2.540905263970217e-10,
            -0.013472567857672757
          ],
          [
            -0.04401225970866207,
            -3.3315034064784754e-10,
            -0.014140737731309416
          ],
          [
            -0.04922093996705834,
            -4.074358073147266e-10,
            -0.012543136915233344
          ],
          [
            -0.0522757306167288,
            -4.711306900162526e-10,
            -0.008983915099734119
          ],
          [
            -0.05377081166697245,
            -5.171461592290427e-10,
            -0.003956465698408074
          ],
          [
            -0.054407667974544494,
            -5.404520719842765e-10,
            0.001992130076424292
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454499,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "target_residual": 0.44559678515685536,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.1149412604122176,
            "max_log_strain_component": 0.0019557268981672967,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0022238381434982,
              1.0019576405793598,
              0.9995003565078744
            ],
            "cell_volume_ratio": 1.0036840972827072,
            "cell_rmsd_from_input_A": 0.012855989636112359
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48800306605851473,
              2.8994110715072145e-11,
              -0.0007136235488296637
            ],
            "branch_aligned_reduced_polarization": [
              0.48800306605851473,
              2.8994110715072145e-11,
              -0.0007136235488296637
            ],
            "target_residual": 0.012018139729833625,
            "energy_eV": -77.53927642808645,
            "max_atomic_step_A": 0.003191172982887185,
            "max_log_strain_component": 6.009224923009601e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.002290026714587,
              1.0020178522767254,
              0.9994857720166554
            ],
            "cell_volume_ratio": 1.003796054335447,
            "cell_rmsd_from_input_A": 0.013246697267253187
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999704440373628,
              3.645320320001395e-14,
              1.2412732160598839e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999704440373628,
              3.645320320001395e-14,
              1.2412732160598839e-05
            ],
            "target_residual": 3.205668178559219e-05,
            "energy_eV": -77.47878364582161
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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": 3.205668178559219e-05,
        "parent_symmetrization_rmsd_A": 0.13494830005378813,
        "parent_cell_rmsd_A": 0.013246697267253187,
        "energy_eV": -77.47878364582161,
        "reduced_polarization": [
          0.4999704440373628,
          3.645320320001395e-14,
          1.2412732160598839e-05
        ],
        "cartesian_polarization_e_A2": [
          0.012224025399035067,
          -1.4103505913081615e-13,
          -1.4237011576071927e-05
        ],
        "ranking_score": 0.6383240877341726
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.0019921300764243477
            ],
            "target_residual": 0.5009710898247975,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013581899359320772,
            "step_scale": 0.8189155151792428,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0019531405318323,
              1.000061453128477,
              0.9992305125779181
            ],
            "cell_volume_ratio": 1.0012436759679826,
            "cell_rmsd_from_input_A": 0.007516915491736485
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.010684227176441984,
              1.5770386801435336e-10,
              -0.4000906030158677
            ],
            "branch_aligned_reduced_polarization": [
              0.010684227176441984,
              1.5770386801435336e-10,
              -0.4000906030158677
            ],
            "target_residual": 0.10047905411622249,
            "energy_eV": -77.47950015155249,
            "max_atomic_step_A": 0.029275076667944076,
            "max_log_strain_component": 0.00038775550942028904,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0025151692547873,
              1.0000969003151516,
              0.9990139181725035
            ],
            "cell_volume_ratio": 1.001623655508472,
            "cell_rmsd_from_input_A": 0.009678244399312343
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0003626695776116267,
              1.1587522710695662e-11,
              -0.4981464319168016
            ],
            "branch_aligned_reduced_polarization": [
              0.0003626695776116267,
              1.1587522710695662e-11,
              -0.4981464319168016
            ],
            "target_residual": 0.0018887148703753199,
            "energy_eV": -76.8697881893775,
            "max_atomic_step_A": 0.0005419578222607203,
            "max_log_strain_component": 7.272966664827519e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0025255720009616,
              1.0000968827129526,
              0.9990097426369754
            ],
            "cell_volume_ratio": 1.0016298448877665,
            "cell_rmsd_from_input_A": 0.009718389704195318
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.6884629682121984e-06,
              2.8620573678143457e-13,
              -0.4999978351595004
            ],
            "branch_aligned_reduced_polarization": [
              -1.6884629682121984e-06,
              2.8620573678143457e-13,
              -0.4999978351595004
            ],
            "target_residual": 2.7454401438876436e-06,
            "energy_eV": -76.85725026696358
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.7454401438876436e-06,
        "parent_symmetrization_rmsd_A": 0.17379515354079625,
        "parent_cell_rmsd_A": 0.009718389704195318,
        "energy_eV": -76.85725026696358,
        "reduced_polarization": [
          -1.6884629682121984e-06,
          2.8620573678143457e-13,
          -0.4999978351595004
        ],
        "cartesian_polarization_e_A2": [
          0.0013919089519090113,
          -7.288024759170852e-14,
          -0.01454791816574134
        ],
        "ranking_score": 0.6762302418471329
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454497,
              5.404521830065789e-10,
              -0.001992130076424358
            ],
            "target_residual": 0.5029554278226029,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0070908578961202924,
            "step_scale": 0.6053210092011347,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0069966088929665,
              0.9999998127693894,
              0.9927770123304228
            ],
            "cell_volume_ratio": 0.9997228976248628,
            "cell_rmsd_from_input_A": 0.03906484251027718
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.019999296485694075,
              0.2860735174185314,
              0.0021560526944283303
            ],
            "branch_aligned_reduced_polarization": [
              0.019999296485694075,
              0.2860735174185314,
              0.0021560526944283303
            ],
            "target_residual": 0.2148701011607321,
            "energy_eV": -77.25242695964938,
            "max_atomic_step_A": 0.10411541868103819,
            "max_log_strain_component": 0.006472377532008439,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0134594943378912,
              1.0000086023054564,
              0.9862634171942836
            ],
            "cell_volume_ratio": 0.9995466224050781,
            "cell_rmsd_from_input_A": 0.07470566866772398
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.004143987570510011,
              0.48828016058410434,
              0.00551790017340157
            ],
            "branch_aligned_reduced_polarization": [
              0.004143987570510011,
              0.48828016058410434,
              0.00551790017340157
            ],
            "target_residual": 0.01360053275583527,
            "energy_eV": -74.11018137497695,
            "max_atomic_step_A": 0.0069074728489556545,
            "max_log_strain_component": 0.0004331790154665225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0138897277679175,
              1.0000148918787048,
              0.9858255261423107
            ],
            "cell_volume_ratio": 0.9995332590334852,
            "cell_rmsd_from_input_A": 0.07709038468128682
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0002011245536978209,
              0.49985246632895497,
              0.00029283202870817855
            ],
            "branch_aligned_reduced_polarization": [
              0.0002011245536978209,
              0.49985246632895497,
              0.00029283202870817855
            ],
            "target_residual": 0.0003846659163865683,
            "energy_eV": -73.88139867898805
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0003846659163865683,
        "parent_symmetrization_rmsd_A": 0.2606401541643822,
        "parent_cell_rmsd_A": 0.07709038468128682,
        "energy_eV": -73.88139867898805,
        "reduced_polarization": [
          0.0002011245536978209,
          0.49985246632895497,
          0.00029283202870817855
        ],
        "cartesian_polarization_e_A2": [
          0.00024093528204343462,
          0.016919372845256395,
          -8.987079347619448e-06
        ],
        "ranking_score": 0.7806820821674769
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454499,
              5.404521752510157e-10,
              -0.0019921300764243477
            ],
            "target_residual": 0.6682547155581473,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0016826642646225898,
            "step_scale": 0.5666662091086597,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0027191323595022,
              1.0012877126342012,
              0.9992013066412988
            ],
            "cell_volume_ratio": 1.0032084500590166,
            "cell_rmsd_from_input_A": 0.012002872369024612
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2979092983458623,
              2.2999956356115087e-10,
              -0.27208086828362393
            ],
            "branch_aligned_reduced_polarization": [
              0.2979092983458623,
              2.2999956356115087e-10,
              -0.27208086828362393
            ],
            "target_residual": 0.3046108702876647,
            "energy_eV": -77.47485532373352,
            "max_atomic_step_A": 0.10280287262266907,
            "max_log_strain_component": 0.0016439145289452617,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.005387294736908,
              1.0025631831761488,
              0.9984230329395583
            ],
            "cell_volume_ratio": 1.0063747600583217,
            "cell_rmsd_from_input_A": 0.023834246667892595
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48323597174859345,
              1.553006428226469e-11,
              -0.4819392587264812
            ],
            "branch_aligned_reduced_polarization": [
              0.48323597174859345,
              1.553006428226469e-11,
              -0.4819392587264812
            ],
            "target_residual": 0.024641895595975214,
            "energy_eV": -74.42661209385705,
            "max_atomic_step_A": 0.008590013401348984,
            "max_log_strain_component": 0.0001887492137559654,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0056953235520716,
              1.0027140211496075,
              0.9983340936639029
            ],
            "cell_volume_ratio": 1.00674486066324,
            "cell_rmsd_from_input_A": 0.025210955657648946
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4996253588267056,
              1.1760932022192278e-12,
              -0.4996298867437019
            ],
            "branch_aligned_reduced_polarization": [
              0.4996253588267056,
              1.1760932022192278e-12,
              -0.4996298867437019
            ],
            "target_residual": 0.0005266306402166303,
            "energy_eV": -74.13453034048848
          }
        ],
        "iterations": 3
      },
      "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": 0.0005266306402166303,
        "parent_symmetrization_rmsd_A": 0.26610824438703684,
        "parent_cell_rmsd_A": 0.025210955657648946,
        "energy_eV": -74.13453034048848,
        "reduced_polarization": [
          0.4996253588267056,
          1.1760932022192278e-12,
          -0.4996298867437019
        ],
        "cartesian_polarization_e_A2": [
          0.01361002978778296,
          -1.2959488687293093e-12,
          -0.014512746866671516
        ],
        "ranking_score": 0.7734642445818823
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454499,
              5.404521830065789e-10,
              -0.001992130076424358
            ],
            "target_residual": 0.6697436034794753,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006089409958995119,
            "step_scale": 0.5198310042713489,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.007110936503409,
              1.0000021333203684,
              0.9948370566234374
            ],
            "cell_volume_ratio": 1.0019134171620654,
            "cell_rmsd_from_input_A": 0.034316668513120166
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2756717093569931,
              0.24668306182381583,
              0.0021486007384515014
            ],
            "branch_aligned_reduced_polarization": [
              0.2756717093569931,
              0.24668306182381583,
              0.0021486007384515014
            ],
            "target_residual": 0.33837445180584097,
            "energy_eV": -77.39385679449222,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006578680369449013,
            "step_scale": 0.8556421720490165,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0148115930749497,
              1.0000164762226909,
              0.9892489779924438
            ],
            "cell_volume_ratio": 1.0039178718061716,
            "cell_rmsd_from_input_A": 0.07159055569711406
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4455280819362684,
              0.44349130299078704,
              0.012125985004565448
            ],
            "branch_aligned_reduced_polarization": [
              0.4455280819362684,
              0.44349130299078704,
              0.012125985004565448
            ],
            "target_residual": 0.07941953290942895,
            "energy_eV": -73.92721420915521,
            "max_atomic_step_A": 0.039851642029329955,
            "max_log_strain_component": 0.002693548423740816,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0181314474449414,
              1.0000460097413493,
              0.9870882150115771
            ],
            "cell_volume_ratio": 1.0050317922309384,
            "cell_rmsd_from_input_A": 0.08716853012541784
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4929497441562707,
              0.4949151888904625,
              0.004493744236856146
            ],
            "branch_aligned_reduced_polarization": [
              0.4929497441562707,
              0.4949151888904625,
              0.004493744236856146
            ],
            "target_residual": 0.009785455980586355,
            "energy_eV": -72.49719835066651,
            "max_atomic_step_A": 0.004841918830183178,
            "max_log_strain_component": 0.00040141416963496764,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0186571690858854,
              1.0000553094528617,
              0.9867896773325057
            ],
            "cell_volume_ratio": 1.0052559762776947,
            "cell_rmsd_from_input_A": 0.08954581098234347
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4996734094062667,
              0.4996762172348219,
              0.00046716127925569746
            ],
            "branch_aligned_reduced_polarization": [
              0.4996734094062667,
              0.4996762172348219,
              0.00046716127925569746
            ],
            "target_residual": 0.0006555427947718246,
            "energy_eV": -72.32913505472754
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0006555427947718246,
        "parent_symmetrization_rmsd_A": 0.31388370336980004,
        "parent_cell_rmsd_A": 0.08954581098234347,
        "energy_eV": -72.32913505472754,
        "reduced_polarization": [
          0.4996734094062667,
          0.4996762172348219,
          0.00046716127925569746
        ],
        "cartesian_polarization_e_A2": [
          0.012472921051828683,
          0.017060142495552853,
          -2.828430939885037e-05
        ],
        "ranking_score": 0.8375812417049295
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454497,
              5.404521830065789e-10,
              -0.0019921300764243477
            ],
            "target_residual": 0.7077937780877939,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005696000392958378,
            "step_scale": 0.4862470480202592,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0060670375060832,
              1.0001826267961946,
              0.994521741456239
            ],
            "cell_volume_ratio": 1.0007382704153482,
            "cell_rmsd_from_input_A": 0.03172850547892292
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.029982984082291986,
              0.22942500847670086,
              -0.23283122816654936
            ],
            "branch_aligned_reduced_polarization": [
              0.029982984082291986,
              0.2294250084767009,
              -0.23283122816654933
            ],
            "target_residual": 0.3814301482779079,
            "energy_eV": -77.31076824720154,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006436212466913946,
            "step_scale": 0.788375401819277,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0129891786049627,
              1.0003787245449653,
              0.9883971333774041
            ],
            "cell_volume_ratio": 1.0016147927725938,
            "cell_rmsd_from_input_A": 0.06765360274011468
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.005957038645368231,
              0.41746990932198275,
              -0.41323473308092035
            ],
            "branch_aligned_reduced_polarization": [
              -0.005957038645368231,
              0.41746990932198275,
              -0.41323473308092035
            ],
            "target_residual": 0.11989542827098663,
            "energy_eV": -73.46715624544969,
            "max_atomic_step_A": 0.0605813301337099,
            "max_log_strain_component": 0.004516967302062843,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0181810520487735,
              1.0005305440218462,
              0.984363075941211
            ],
            "cell_volume_ratio": 1.0027915752221315,
            "cell_rmsd_from_input_A": 0.093222221614516
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.00827718968515107,
              0.488360789020746,
              -0.4851077436533314
            ],
            "branch_aligned_reduced_polarization": [
              -0.00827718968515107,
              0.488360789020746,
              -0.4851077436533314
            ],
            "target_residual": 0.0206340107685939,
            "energy_eV": -71.14887279247853,
            "max_atomic_step_A": 0.012406490586131323,
            "max_log_strain_component": 0.0010782242905702816,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0194919765695116,
              1.000570210815272,
              0.9834550513622453
            ],
            "cell_volume_ratio": 1.0031962415336129,
            "cell_rmsd_from_input_A": 0.09941753655411945
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.00037632065166703357,
              0.49901417031642586,
              -0.4988096833645645
            ],
            "branch_aligned_reduced_polarization": [
              -0.00037632065166703357,
              0.49901417031642586,
              -0.4988096833645645
            ],
            "target_residual": 0.0015907014460550056,
            "energy_eV": -70.90636638850845,
            "max_atomic_step_A": 0.000966568606990564,
            "max_log_strain_component": 7.842849992141846e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.5299440118649328,
            "cell_principal_stretches": [
              1.0194231489431291,
              1.0005996329795692,
              0.9835216068653824
            ],
            "cell_volume_ratio": 1.0032259003566824,
            "cell_rmsd_from_input_A": 0.0989913511668504
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              7.57294115306292e-07,
              0.4999987800029172,
              -0.4999990495210005
            ],
            "branch_aligned_reduced_polarization": [
              7.57294115306292e-07,
              0.4999987800029172,
              -0.4999990495210005
            ],
            "target_residual": 1.7220039452989956e-06,
            "energy_eV": -70.88545646175912
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.7220039452989956e-06,
        "parent_symmetrization_rmsd_A": 0.3407620151792109,
        "parent_cell_rmsd_A": 0.0989913511668504,
        "energy_eV": -70.88545646175912,
        "reduced_polarization": [
          7.57294115306292e-07,
          0.4999987800029172,
          -0.4999990495210005
        ],
        "cartesian_polarization_e_A2": [
          0.0017041083236249276,
          0.016920481069643015,
          -0.014552168705743586
        ],
        "ranking_score": 0.8655132969788141
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.05440766797454497,
              5.404521752510157e-10,
              -0.001992130076424358
            ],
            "branch_aligned_reduced_polarization": [
              0.05440766797454499,
              5.404521830065789e-10,
              -0.0019921300764243477
            ],
            "target_residual": 0.8346043160236162,
            "energy_eV": -78.60954386962345,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004806423799253584,
            "step_scale": 0.4103070966204335,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0060416850894585,
              1.000195236136412,
              0.99610829774087
            ],
            "cell_volume_ratio": 1.0023221216910927,
            "cell_rmsd_from_input_A": 0.027962537347728363
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.23072485919839597,
              0.19367565379487306,
              -0.1947679470343445
            ],
            "branch_aligned_reduced_polarization": [
              0.23072485919839597,
              0.19367565379487306,
              -0.19476794703434452
            ],
            "target_residual": 0.5094215471388611,
            "energy_eV": -77.43668468275357,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.005298791263804919,
            "step_scale": 0.567877006211244,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.012704890723132,
              1.0004035443666082,
              0.9918116598278327
            ],
            "cell_volume_ratio": 1.0048178435974995,
            "cell_rmsd_from_input_A": 0.05893347819931309
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3573625786391036,
              0.3457018123589535,
              -0.3387728923221601
            ],
            "branch_aligned_reduced_polarization": [
              0.3573625786391036,
              0.3457018123589535,
              -0.3387728923221601
            ],
            "target_residual": 0.26485381804300895,
            "energy_eV": -73.98537967326851,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008301021447667355,
            "step_scale": 0.8931324173712234,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.0234762813504896,
              1.00076571510944,
              0.9852709456665112
            ],
            "cell_volume_ratio": 1.0091735918151823,
            "cell_rmsd_from_input_A": 0.10847582482800672
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.42768239668534663,
              0.43629372280876777,
              -0.4318414886155651
            ],
            "branch_aligned_reduced_polarization": [
              0.42768239668534663,
              0.43629372280876777,
              -0.4318414886155651
            ],
            "target_residual": 0.11804197633419995,
            "energy_eV": -69.12693213894465,
            "max_atomic_step_A": 0.07344804875150025,
            "max_log_strain_component": 0.0034565002811909233,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9862720582722355,
            "cell_principal_stretches": [
              1.027950754388991,
              1.000885610293757,
              0.9825665042809356
            ],
            "cell_volume_ratio": 1.0109244722596245,
            "cell_rmsd_from_input_A": 0.12917028832600144
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4761383076529239,
              0.46891510125990743,
              -0.46810020331928714
            ],
            "branch_aligned_reduced_polarization": [
              0.4761383076529239,
              0.46891510125990743,
              -0.46810020331928714
            ],
            "target_residual": 0.05052967761245995,
            "energy_eV": -69.17026153614745,
            "max_atomic_step_A": 0.03368953158064883,
            "max_log_strain_component": 0.004792472893747421,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.1156172299622003,
            "cell_principal_stretches": [
              1.0222678476627844,
              1.0035045644907346,
              0.9870183588849404
            ],
            "cell_volume_ratio": 1.012533228865722,
            "cell_rmsd_from_input_A": 0.10199120900110886
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4995402782536672,
              0.4995999942204402,
              -0.498194274509879
            ],
            "branch_aligned_reduced_polarization": [
              0.4995402782536672,
              0.4995999942204402,
              -0.498194274509879
            ],
            "target_residual": 0.0019057789098962034,
            "energy_eV": -68.4100031680031
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0019057789098962034,
        "parent_symmetrization_rmsd_A": 0.38452490383093313,
        "parent_cell_rmsd_A": 0.10199120900110886,
        "energy_eV": -68.4100031680031,
        "reduced_polarization": [
          0.4995402782536672,
          0.4995999942204402,
          -0.498194274509879
        ],
        "cartesian_polarization_e_A2": [
          0.01382501509032276,
          0.017010241990292146,
          -0.014397094418512751
        ],
        "ranking_score": 0.9138342639010028
      },
      "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
        ],
        "endpoint_rmsd_A": 0.1026740933071159,
        "minimum_distance_A_by_image": [
          1.0607170243040265,
          1.0853927700839787,
          1.11007088651934,
          1.134751218941921,
          1.159433625839616,
          1.1841179774879271,
          1.2088041547486832,
          1.2334920480126077,
          1.2581815562660548
        ],
        "minimum_distance_A": 1.0607170243040265,
        "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": [
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883,
          203.51418587004883
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.7499710620966816e-16,
        2.5340724475543526e-15,
        -1.2001544126336324e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -78.60954386962345,
          -78.61099127931247,
          -78.59844333975374,
          -78.57456182661394,
          -78.5422702304435,
          -78.50573614800395,
          -78.4710416143489,
          -78.44568296256108,
          -78.4363213480527
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013385827398527904,
            1.8288234343030602e-11,
            -5.800961614399547e-05
          ],
          [
            0.0013067088643214505,
            1.749954661585977e-11,
            0.00011520987468022921
          ],
          [
            0.00125632547213088,
            1.594246555115686e-11,
            0.0002616061433805709
          ],
          [
            0.0011717405419179618,
            1.3787159222810667e-11,
            0.0003652485178078111
          ],
          [
            0.0010397444758943103,
            1.1273330985946158e-11,
            0.0004117696818567113
          ],
          [
            0.0008523419450200112,
            8.598132477079923e-12,
            0.00039231298154003704
          ],
          [
            0.0006089026941579653,
            5.832733203201405e-12,
            0.0003073021600671801
          ],
          [
            0.0003182531280937892,
            2.9620378430871972e-12,
            0.00016878556193109534
          ],
          [
            -6.409931810687328e-18,
            8.574988565892888e-17,
            -3.4947766521034636e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407995
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7499710620966816e-16,
            2.5340724475543526e-15,
            -1.2001544126336324e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407996
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7582103268031233e-16,
            2.5340724475564246e-15,
            -1.196959198423997e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.05440766797454455,
            5.404521274954277e-10,
            -0.00199213007642407
          ],
          [
            0.053770811666970064,
            5.171448824725644e-10,
            0.003956465698408018
          ],
          [
            0.052275730616730076,
            4.711302459270428e-10,
            0.008983915099732731
          ],
          [
            0.049220939967058785,
            4.074368620266e-10,
            0.012543136915233122
          ],
          [
            0.04401225970866063,
            3.3314839775755445e-10,
            0.01414073773131208
          ],
          [
            0.036289436905951655,
            2.5409119253083645e-10,
            0.01347256785767248
          ],
          [
            0.026028373954666617,
            1.7236834182199345e-10,
            0.010553179219464304
          ],
          [
            0.013635475731859081,
            8.753386904203353e-11,
            0.00579632855274248
          ],
          [
            -2.7755575615628914e-16,
            2.55351295663786e-15,
            -1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -78.4363213480527,
          -78.44568296256108,
          -78.4710416143489,
          -78.50573614800396,
          -78.54227023044352,
          -78.57456182661392,
          -78.59844333975374,
          -78.61099127931247,
          -78.60954386962345
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.137562368426616e-18,
            8.032871992542204e-17,
            1.7047690985870553e-18
          ],
          [
            -0.0003182531280936951,
            -2.961973948341382e-12,
            -0.00016878556193109442
          ],
          [
            -0.000608902694157927,
            -5.832648629606424e-12,
            -0.00030730216006723157
          ],
          [
            -0.0008523419450199729,
            -8.598109258124801e-12,
            -0.00039231298154004664
          ],
          [
            -0.0010397444758943543,
            -1.1273396738890292e-11,
            -0.00041176968185663483
          ],
          [
            -0.0011717405419179505,
            -1.3787126048004009e-11,
            -0.0003652485178078179
          ],
          [
            -0.0012563254721308437,
            -1.5942481899892515e-11,
            -0.0002616061433806096
          ],
          [
            -0.0013067088643215102,
            -1.749958846794114e-11,
            -0.000115209874680232
          ],
          [
            -0.0013385827398527902,
            -1.8288231956353866e-11,
            5.800961614400308e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6638612546857853e-16,
            2.3738666745280536e-15,
            5.854411768944547e-17
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.0019921300764243334
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6638612546857853e-16,
            2.3738666745280536e-15,
            5.854411768944547e-17
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.001992130076424333
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.054407667974545076,
          -5.404470899772013e-10,
          0.001992130076423832
        ],
        "actual_opposite_endpoint_branch_residual": 5.057165166635757e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407995
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7499710620966816e-16,
            2.5340724475543526e-15,
            -1.2001544126336324e-16
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.0019921300764243334
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.054407667974544535,
            5.404521581220965e-10,
            -0.0019921300764240723
          ],
          [
            0.053770811666970036,
            5.171449335842436e-10,
            0.003956465698407996
          ],
          [
            0.05227573061673013,
            4.711302223767379e-10,
            0.008983915099732781
          ],
          [
            0.04922093996705876,
            4.0743681519919835e-10,
            0.012543136915233137
          ],
          [
            0.04401225970866058,
            3.33148402754427e-10,
            0.014140737731312062
          ],
          [
            0.03628943690595164,
            2.5409119141282193e-10,
            0.013472567857672438
          ],
          [
            0.02602837395466665,
            1.7236837566125743e-10,
            0.010553179219464302
          ],
          [
            0.01363547573185905,
            8.75338600057831e-11,
            0.005796328552742495
          ],
          [
            -2.7582103268031233e-16,
            2.5340724475564246e-15,
            -1.196959198423997e-16
          ],
          [
            -0.013635475731855204,
            -8.753197179434505e-11,
            -0.005796328552742463
          ],
          [
            -0.02602837395466529,
            -1.7236587635043987e-10,
            -0.01055317921946607
          ],
          [
            -0.036289436905950115,
            -2.540905052484733e-10,
            -0.013472567857672767
          ],
          [
            -0.04401225970866208,
            -3.3315034587916464e-10,
            -0.014140737731309437
          ],
          [
            -0.049220939967058314,
            -4.074358348204741e-10,
            -0.01254313691523337
          ],
          [
            -0.05227573061672879,
            -4.711307055130157e-10,
            -0.00898391509973411
          ],
          [
            -0.05377081166697247,
            -5.17146170392963e-10,
            -0.003956465698408092
          ],
          [
            -0.05440766797454449,
            -5.404520875912531e-10,
            0.001992130076424333
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.05440766797454455,
            5.404521274954277e-10,
            -0.00199213007642407
          ],
          [
            0.053770811666970064,
            5.171448824725644e-10,
            0.003956465698408018
          ],
          [
            0.052275730616730076,
            4.711302459270428e-10,
            0.008983915099732731
          ],
          [
            0.049220939967058785,
            4.074368620266e-10,
            0.012543136915233122
          ],
          [
            0.04401225970866063,
            3.3314839775755445e-10,
            0.01414073773131208
          ],
          [
            0.036289436905951655,
            2.5409119253083645e-10,
            0.01347256785767248
          ],
          [
            0.026028373954666617,
            1.7236834182199345e-10,
            0.010553179219464304
          ],
          [
            0.013635475731859081,
            8.753386904203353e-11,
            0.00579632855274248
          ],
          [
            -2.7755575615628914e-16,
            2.55351295663786e-15,
            -1.1102230246251565e-16
          ],
          [
            -0.013635475731855196,
            -8.753198166289167e-11,
            -0.00579632855274248
          ],
          [
            -0.026028373954665285,
            -1.7236589933133928e-10,
            -0.01055317921946608
          ],
          [
            -0.0362894369059501,
            -2.540905263970217e-10,
            -0.013472567857672757
          ],
          [
            -0.04401225970866207,
            -3.3315034064784754e-10,
            -0.014140737731309416
          ],
          [
            -0.04922093996705834,
            -4.074358073147266e-10,
            -0.012543136915233344
          ],
          [
            -0.0522757306167288,
            -4.711306900162526e-10,
            -0.008983915099734119
          ],
          [
            -0.05377081166697245,
            -5.171461592290427e-10,
            -0.003956465698408074
          ],
          [
            -0.054407667974544494,
            -5.404520719842765e-10,
            0.001992130076424292
          ]
        ]
      },
      "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": "P2/c",
        "spacegroup_number": 13,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1476675941773614e-15,
        "parent_symmetrization_rmsd_A": 0.1026740933071159,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -78.4363213480527,
        "reduced_polarization": [
          1.3344591504216197e-15,
          2.760778730138738e-15,
          7.10725588749868e-16
        ],
        "cartesian_polarization_e_A2": [
          3.0754034538510474e-17,
          9.342134660257062e-17,
          2.069589685684685e-17
        ],
        "ranking_score": 0.1026740933071222
      }
    }
  ],
  "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": 84,
      "full_response": 27,
      "energy_polarization": 57
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 109,
      "full_response": 52,
      "energy_polarization": 57
    },
    "elapsed_seconds": 285.8769685999723
  }
}