{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 64,
  "input_formula": "H16O32P8Rb8",
  "input_spacegroup": "Fdd2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -369.0948030155499,
  "input_cartesian_polarization_e_A2": [
    3.112178921269687e-19,
    3.851321415071238e-18,
    -0.003400735353825608
  ],
  "input_reduced_polarization": [
    2.5354256257501558e-17,
    3.1039362034453534e-16,
    -0.4119598193221179
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Fddd",
      "spacegroup_number": 70,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.035953570951564e-15,
      "parent_symmetrization_rmsd_A": 0.6933937652051188,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -297.350545028645,
      "reduced_polarization": [
        6.579429498821653e-16,
        7.449446888268846e-16,
        -2.9217851812935744e-16
      ],
      "cartesian_polarization_e_A2": [
        8.076104300694838e-18,
        9.24317139617097e-18,
        -2.4119386639840076e-18
      ],
      "ranking_score": 0.6933937652051209
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.287630278706039e-15,
      "parent_symmetrization_rmsd_A": 0.718059659158921,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -271.51778096203304,
      "reduced_polarization": [
        7.099191752100435e-17,
        -9.901242960081238e-16,
        5.193616080380798e-15
      ],
      "cartesian_polarization_e_A2": [
        8.714100979555123e-19,
        -1.228532629171209e-17,
        4.287338956457274e-17
      ],
      "ranking_score": 0.7180596591589316
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.560393834821558e-15,
      "parent_symmetrization_rmsd_A": 0.7180596591589211,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -271.51778096203293,
      "reduced_polarization": [
        2.9968730896366838e-15,
        3.86267616428755e-16,
        -3.4156611280670685e-15
      ],
      "cartesian_polarization_e_A2": [
        3.67859548494077e-17,
        4.792755538755318e-18,
        -2.819634102670336e-17
      ],
      "ranking_score": 0.7180596591589302
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Fdd2",
      "spacegroup_number": 43,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0005761707040459751,
      "parent_symmetrization_rmsd_A": 0.007425231984372601,
      "parent_cell_rmsd_A": 0.01881274307508593,
      "energy_eV": -368.9333785627805,
      "reduced_polarization": [
        3.0434943575805373e-15,
        -5.974085138372192e-15,
        -0.499423829295954
      ],
      "cartesian_polarization_e_A2": [
        4.3938891713508846e-17,
        -6.793245377251563e-17,
        -0.004123483872848869
      ],
      "ranking_score": 0.513280759161236
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Fddd",
      "spacegroup_number": 70,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999992,
      "parent_symmetrization_rmsd_A": 0.6933950658109467,
      "parent_cell_rmsd_A": 0.01881274307508593,
      "energy_eV": -297.3648865677269,
      "reduced_polarization": [
        -2.52709303907765e-16,
        -7.988919580181031e-16,
        8.090108404140422e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.0984548019093766e-18,
        -9.933739515669258e-18,
        6.6795834674327764e-18
      ],
      "ranking_score": 1.6980982515797165
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999969,
      "parent_symmetrization_rmsd_A": 0.7180614609148521,
      "parent_cell_rmsd_A": 0.01881274307508593,
      "energy_eV": -271.56933401582125,
      "reduced_polarization": [
        -2.4928058470901567e-15,
        1.6128100970647606e-15,
        3.086684485342602e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.056415465401058e-17,
        2.005432052693104e-17,
        2.5485154991154034e-17
      ],
      "ranking_score": 1.7227646466836175
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Fdd2",
      "spacegroup_number": 43,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.274890917641189e-05,
      "parent_symmetrization_rmsd_A": 0.03391945494828485,
      "parent_cell_rmsd_A": 0.08630989985836254,
      "energy_eV": -367.81397010246377,
      "reduced_polarization": [
        2.5244985008314576e-15,
        6.941055121787037e-15,
        -3.274890917641189e-05
      ],
      "cartesian_polarization_e_A2": [
        3.114598273808829e-17,
        8.528288397467077e-17,
        -2.701231113604367e-07
      ],
      "ranking_score": 0.5555624277312283
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00035043544850547236,
      "parent_symmetrization_rmsd_A": 0.06029268247714383,
      "parent_cell_rmsd_A": 0.21058331307438205,
      "energy_eV": -361.8370045144393,
      "reduced_polarization": [
        4.809181590651763e-16,
        0.49970378736706844,
        -0.4998127486190679
      ],
      "cartesian_polarization_e_A2": [
        -1.1115302122890807e-16,
        0.006335578695813623,
        -0.004295097573846175
      ],
      "ranking_score": 0.6136393816427503
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 9.792538933228224e-05,
      "parent_symmetrization_rmsd_A": 0.05911077227928698,
      "parent_cell_rmsd_A": 0.24071341024433598,
      "energy_eV": -358.3577590956613,
      "reduced_polarization": [
        0.4999447365806579,
        -1.3042103790070855e-15,
        -0.49991915857275815
      ],
      "cartesian_polarization_e_A2": [
        0.005998972048441933,
        -7.772389437909865e-17,
        -0.003937403197591553
      ],
      "ranking_score": 0.6194849756190355
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00016283466273204166,
      "parent_symmetrization_rmsd_A": 0.06764240448862155,
      "parent_cell_rmsd_A": 0.21168261952425915,
      "energy_eV": -358.26281885481177,
      "reduced_polarization": [
        4.454398586457335e-16,
        0.4998436076299737,
        -4.5349244587059396e-05
      ],
      "cartesian_polarization_e_A2": [
        -9.300021311926754e-17,
        0.006146534502269233,
        -0.00015791146880021244
      ],
      "ranking_score": 0.6208887286951504
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005313035296512593,
      "parent_symmetrization_rmsd_A": 0.06272044847245319,
      "parent_cell_rmsd_A": 0.24871815525961408,
      "energy_eV": -362.01891387817034,
      "reduced_polarization": [
        0.4997032578814895,
        2.584237606533223e-15,
        0.0004407125545316238
      ],
      "cartesian_polarization_e_A2": [
        0.006167172968859909,
        -1.494606831315087e-17,
        0.00018867391721123143
      ],
      "ranking_score": 0.6259625943466592
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0003215918025797444,
      "parent_symmetrization_rmsd_A": 0.08831213543306973,
      "parent_cell_rmsd_A": 0.34426468390203785,
      "energy_eV": -349.05022116721665,
      "reduced_polarization": [
        0.4998172307180505,
        0.49987028208900863,
        -0.4997693705555871
      ],
      "cartesian_polarization_e_A2": [
        0.005981532350127976,
        0.0063528871886532655,
        -0.004106716721880183
      ],
      "ranking_score": 0.6750214900137387
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0001527635615174508,
      "parent_symmetrization_rmsd_A": 0.09006232660435481,
      "parent_cell_rmsd_A": 0.3428117776615349,
      "energy_eV": -350.5010082155759,
      "reduced_polarization": [
        0.4998895804690702,
        0.4999449176619279,
        9.005647644258958e-05
      ],
      "cartesian_polarization_e_A2": [
        0.0061657303051514765,
        0.006147333883428738,
        3.320220915976732e-05
      ],
      "ranking_score": 0.6760707981427734
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.08804018067788211,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.012708158423698102,
            "max_log_strain_component": 0.0017206648947587378,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0015444126801485,
              0.9995845505114421,
              0.9982808146003878
            ],
            "cell_volume_ratio": 0.9994071963725577,
            "cell_rmsd_from_input_A": 0.01881274307508593
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.0434943575805373e-15,
              -5.974085138372192e-15,
              -0.499423829295954
            ],
            "branch_aligned_reduced_polarization": [
              3.0434943575805373e-15,
              -5.974085138372192e-15,
              -0.499423829295954
            ],
            "target_residual": 0.0005761707040459751,
            "energy_eV": -368.9333785627805
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Fdd2",
        "spacegroup_number": 43,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0005761707040459751,
        "parent_symmetrization_rmsd_A": 0.007425231984372601,
        "parent_cell_rmsd_A": 0.01881274307508593,
        "energy_eV": -368.9333785627805,
        "reduced_polarization": [
          3.0434943575805373e-15,
          -5.974085138372192e-15,
          -0.499423829295954
        ],
        "cartesian_polarization_e_A2": [
          4.3938891713508846e-17,
          -6.793245377251563e-17,
          -0.004123483872848869
        ],
        "ranking_score": 0.513280759161236
      },
      "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": [
          -369.09480301554987,
          -369.0834028114988,
          -369.0695021212367,
          -369.05309736994957,
          -369.0341848558398,
          -369.01276074557495,
          -368.988821075698,
          -368.9623617543017,
          -368.9333785627805
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.614230293866537e-18,
            -1.0581408332316937e-17,
            -0.0034007353538255953
          ],
          [
            -2.617536483750769e-17,
            -8.193418303773958e-18,
            -0.003491617825697737
          ],
          [
            -2.2846779948580297e-17,
            -9.26010495191095e-19,
            -0.0035823512301905907
          ],
          [
            2.555667127921617e-17,
            -5.276316421226724e-18,
            -0.003672933079249156
          ],
          [
            3.181590026391162e-17,
            -2.2095239933768365e-17,
            -0.003763360910595274
          ],
          [
            4.72603880525802e-17,
            -4.037992312529415e-17,
            -0.0038536322915317025
          ],
          [
            4.536461761022556e-17,
            -1.6883297116777496e-17,
            -0.0039437448201299205
          ],
          [
            4.278353115405031e-17,
            -5.139317188483263e-17,
            -0.004033696126304425
          ],
          [
            4.3752050217916326e-17,
            -6.995656997476798e-17,
            -0.004123483872848832
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.865653943762899e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.8656539437628992e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -8.326672684688674e-16,
            -0.41195981932211634
          ],
          [
            -2.1649348980190553e-15,
            -7.216449660063518e-16,
            -0.4229597998137043
          ],
          [
            -1.9984014443252818e-15,
            -1.6653345369377348e-16,
            -0.4339412351483628
          ],
          [
            1.887379141862766e-15,
            -6.106226635438361e-16,
            -0.4449038251647818
          ],
          [
            2.3314683517128287e-15,
            -1.9984014443252818e-15,
            -0.4558472728506228
          ],
          [
            3.552713678800501e-15,
            -3.552713678800501e-15,
            -0.46677128480294433
          ],
          [
            3.3306690738754696e-15,
            -1.7208456881689926e-15,
            -0.47767557137167166
          ],
          [
            2.9976021664879227e-15,
            -4.551914400963142e-15,
            -0.48855984678929837
          ],
          [
            2.9976021664879227e-15,
            -6.161737786669619e-15,
            -0.4994238292959495
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -368.9333785627805,
          -368.9078419342418,
          -368.8807467292088,
          -368.85209305509187,
          -368.82188102184216,
          -368.79011074243425,
          -368.7567823333746,
          -368.72189591523244,
          -368.68545161319275
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.1198549778151814e-17,
            -7.178605961911146e-17,
            -0.004123483872848851
          ],
          [
            6.018964026257588e-17,
            -8.571496752861135e-17,
            -0.004203176517354115
          ],
          [
            4.5769380842163056e-17,
            -9.456670201555085e-17,
            -0.00428274893846074
          ],
          [
            8.66440447630637e-17,
            -1.0062290789587564e-16,
            -0.004362199990788268
          ],
          [
            1.069039153681727e-16,
            -1.2985525829338682e-16,
            -0.004441528548749538
          ],
          [
            9.360403232229357e-17,
            -1.3039816807385693e-16,
            -0.00452073350713697
          ],
          [
            1.3913502230266202e-16,
            -1.6085347013525317e-16,
            -0.004599813781697446
          ],
          [
            1.7292547804660252e-16,
            -2.059248009585734e-16,
            -0.004678768309695289
          ],
          [
            1.244249132723621e-16,
            -1.6731851925476155e-16,
            -0.0047575960504619656
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.8199926616621148e-15,
            -6.284000122086111e-15,
            -0.4994238292959518
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8199926616621148e-15,
            -6.284000122086111e-15,
            -0.4994238292959518
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          7.341747722804119e-15,
          -1.0423369040299608e-14,
          -0.5870650941134633
        ],
        "actual_opposite_endpoint_branch_residual": 0.01073726926489671
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.865653943762899e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.8656539437628992e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -8.326672684688674e-16,
            -0.41195981932211634
          ],
          [
            -2.1649348980190553e-15,
            -7.216449660063518e-16,
            -0.4229597998137043
          ],
          [
            -1.9984014443252818e-15,
            -1.6653345369377348e-16,
            -0.4339412351483628
          ],
          [
            1.887379141862766e-15,
            -6.106226635438361e-16,
            -0.4449038251647818
          ],
          [
            2.3314683517128287e-15,
            -1.9984014443252818e-15,
            -0.4558472728506228
          ],
          [
            3.552713678800501e-15,
            -3.552713678800501e-15,
            -0.46677128480294433
          ],
          [
            3.3306690738754696e-15,
            -1.7208456881689926e-15,
            -0.47767557137167166
          ],
          [
            2.9976021664879227e-15,
            -4.551914400963142e-15,
            -0.48855984678929837
          ],
          [
            2.9976021664879227e-15,
            -6.161737786669619e-15,
            -0.4994238292959495
          ],
          [
            4.440892098500626e-15,
            -7.327471962526033e-15,
            0.49091274824703435
          ],
          [
            3.3306690738754696e-15,
            -7.993605777301127e-15,
            0.4812634590913365
          ],
          [
            6.661338147750939e-15,
            -8.43769498715119e-15,
            0.47162844292590167
          ],
          [
            8.43769498715119e-15,
            -1.071365218763276e-14,
            0.46200783705450954
          ],
          [
            7.438494264988549e-15,
            -1.071365218763276e-14,
            0.45240177632449585
          ],
          [
            1.1213252548714081e-14,
            -1.3100631690576847e-14,
            0.442810393056837
          ],
          [
            1.3988810110276972e-14,
            -1.6653345369377348e-14,
            0.43323381697767305
          ],
          [
            1.0103029524088925e-14,
            -1.3489209749195652e-14,
            0.4236721751514334
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.4119598193221179,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.05946433330592592,
            "max_log_strain_component": 0.008051378287741294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0080838777973031,
              1.0019462771245495,
              0.9928049295740674
            ],
            "cell_volume_ratio": 1.0027785370879096,
            "cell_rmsd_from_input_A": 0.08815076385216235
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3551269016908356e-14,
              4.049748122247261e-15,
              0.009226847889923432
            ],
            "branch_aligned_reduced_polarization": [
              -1.3551269016908356e-14,
              4.049748122247261e-15,
              0.009226847889923432
            ],
            "target_residual": 0.009226847889923432,
            "energy_eV": -367.7488054654301,
            "max_atomic_step_A": 0.0012835918178721933,
            "max_log_strain_component": 0.0001679376297652783,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.007914596794984,
              1.0019056425414536,
              0.9929544761804789
            ],
            "cell_volume_ratio": 1.0027205029157549,
            "cell_rmsd_from_input_A": 0.08630989985836254
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.5244985008314576e-15,
              6.941055121787037e-15,
              -3.274890917641189e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.5244985008314576e-15,
              6.941055121787037e-15,
              -3.274890917641189e-05
            ],
            "target_residual": 3.274890917641189e-05,
            "energy_eV": -367.81397010246377
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Fdd2",
        "spacegroup_number": 43,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.274890917641189e-05,
        "parent_symmetrization_rmsd_A": 0.03391945494828485,
        "parent_cell_rmsd_A": 0.08630989985836254,
        "energy_eV": -367.81397010246377,
        "reduced_polarization": [
          2.5244985008314576e-15,
          6.941055121787037e-15,
          -3.274890917641189e-05
        ],
        "cartesian_polarization_e_A2": [
          3.114598273808829e-17,
          8.528288397467077e-17,
          -2.701231113604367e-07
        ],
        "ranking_score": 0.5555624277312283
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              2.5354256257501558e-17,
              3.3306690738754696e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.5076919079656419,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.07750054174630336,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8307814497439558,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0206962310339331,
              0.9985715247676268,
              0.9806417117487579
            ],
            "cell_volume_ratio": 0.9995074850355894,
            "cell_rmsd_from_input_A": 0.15574974647332546
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1662067187195258e-14,
              0.3956930963121864,
              -0.458919761243386
            ],
            "branch_aligned_reduced_polarization": [
              -1.1662067187195258e-14,
              0.3956930963121864,
              -0.458919761243386
            ],
            "target_residual": 0.11210493375957738,
            "energy_eV": -364.80697219583607,
            "max_atomic_step_A": 0.02253429631277542,
            "max_log_strain_component": 0.0063575925697208265,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0276827147612244,
              0.9972501894148974,
              0.9748205958917354
            ],
            "cell_volume_ratio": 0.9990514988881307,
            "cell_rmsd_from_input_A": 0.20694178884320075
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.059862708097588e-15,
              0.4937238621835777,
              -0.49582236290413156
            ],
            "branch_aligned_reduced_polarization": [
              -8.059862708097588e-15,
              0.4937238621835777,
              -0.49582236290413156
            ],
            "target_residual": 0.0075394003472094425,
            "energy_eV": -362.03745700677655,
            "max_atomic_step_A": 0.0015389653213379727,
            "max_log_strain_component": 0.0004397472411002574,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0281830139684012,
              0.9971186366799946,
              0.9744305078641664
            ],
            "cell_volume_ratio": 0.9990060790360513,
            "cell_rmsd_from_input_A": 0.21058331307438205
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.809181590651763e-16,
              0.49970378736706844,
              -0.4998127486190679
            ],
            "branch_aligned_reduced_polarization": [
              4.809181590651763e-16,
              0.49970378736706844,
              -0.4998127486190679
            ],
            "target_residual": 0.00035043544850547236,
            "energy_eV": -361.8370045144393
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00035043544850547236,
        "parent_symmetrization_rmsd_A": 0.06029268247714383,
        "parent_cell_rmsd_A": 0.21058331307438205,
        "energy_eV": -361.8370045144393,
        "reduced_polarization": [
          4.809181590651763e-16,
          0.49970378736706844,
          -0.4998127486190679
        ],
        "cartesian_polarization_e_A2": [
          -1.1115302122890807e-16,
          0.006335578695813623,
          -0.004295097573846175
        ],
        "ranking_score": 0.6136393816427503
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.5076919079656422,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.06841999315962728,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7056826079008052,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0194380672644385,
              1.0010896176349642,
              0.9794549448900657
            ],
            "cell_volume_ratio": 0.9995816322872938,
            "cell_rmsd_from_input_A": 0.1530788352485865
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3416470992156956,
              9.149806591728804e-15,
              -0.45862398540402516
            ],
            "branch_aligned_reduced_polarization": [
              0.3416470992156956,
              9.149806591728804e-15,
              -0.45862398540402516
            ],
            "target_residual": 0.1636692267063362,
            "energy_eV": -364.8766034031804,
            "max_atomic_step_A": 0.03299711574763171,
            "max_log_strain_component": 0.010494343673898019,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0293982923208684,
              1.0022192572093034,
              0.9684648911771339
            ],
            "cell_volume_ratio": 0.9991485627890273,
            "cell_rmsd_from_input_A": 0.23355288981411002
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48958471953639404,
              1.6099384196012655e-15,
              -0.48804584180414157
            ],
            "branch_aligned_reduced_polarization": [
              0.48958471953639404,
              1.6099384196012655e-15,
              -0.48804584180414157
            ],
            "target_residual": 0.015854966581711274,
            "energy_eV": -359.0635972460059,
            "max_atomic_step_A": 0.002930419074414719,
            "max_log_strain_component": 0.0008505765998545079,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0300834504176741,
              1.0024922058213328,
              0.9674559764241831
            ],
            "cell_volume_ratio": 0.9990440239282932,
            "cell_rmsd_from_input_A": 0.24022141497067082
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49926933837163356,
              -1.4014510476121854e-15,
              -0.4989045332619537
            ],
            "branch_aligned_reduced_polarization": [
              0.49926933837163356,
              -1.4014510476121854e-15,
              -0.4989045332619537
            ],
            "target_residual": 0.0013167816027469584,
            "energy_eV": -358.40883253713685,
            "max_atomic_step_A": 0.00023330834732734649,
            "max_log_strain_component": 6.213566568488162e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.030130380049403,
              1.002516670238375,
              0.9673792232188285
            ],
            "cell_volume_ratio": 0.9990346560215576,
            "cell_rmsd_from_input_A": 0.24071341024433598
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999447365806579,
              -1.3042103790070855e-15,
              -0.49991915857275815
            ],
            "branch_aligned_reduced_polarization": [
              0.4999447365806579,
              -1.3042103790070855e-15,
              -0.49991915857275815
            ],
            "target_residual": 9.792538933228224e-05,
            "energy_eV": -358.3577590956613
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 9.792538933228224e-05,
        "parent_symmetrization_rmsd_A": 0.05911077227928698,
        "parent_cell_rmsd_A": 0.24071341024433598,
        "energy_eV": -358.3577590956613,
        "reduced_polarization": [
          0.4999447365806579,
          -1.3042103790070855e-15,
          -0.49991915857275815
        ],
        "cartesian_polarization_e_A2": [
          0.005998972048441933,
          -7.772389437909865e-17,
          -0.003937403197591553
        ],
        "ranking_score": 0.6194849756190355
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              2.5354256257501558e-17,
              3.3306690738754696e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.6478509803464927,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.0912984838987252,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8307814497442605,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.018333292711335,
              1.0067113566196753,
              0.9777013304058024
            ],
            "cell_volume_ratio": 1.0023078149851532,
            "cell_rmsd_from_input_A": 0.1695684632346216
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.9318517042574926e-14,
              0.40669113009949015,
              -0.04907263662977499
            ],
            "branch_aligned_reduced_polarization": [
              -1.9318517042574926e-14,
              0.40669113009949015,
              -0.04907263662977499
            ],
            "target_residual": 0.10542612991051226,
            "energy_eV": -362.3699429848933,
            "max_atomic_step_A": 0.019486379967284473,
            "max_log_strain_component": 0.0052578999722536456,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0234292456450245,
              1.007525817441454,
              0.9723175987431302
            ],
            "cell_volume_ratio": 1.0025871944998699,
            "cell_rmsd_from_input_A": 0.209697008652821
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -7.44481292903733e-15,
              0.49547450962512407,
              -0.00043259944910531775
            ],
            "branch_aligned_reduced_polarization": [
              -7.44481292903733e-15,
              0.49547450962512407,
              -0.00043259944910531775
            ],
            "target_residual": 0.004546119819853069,
            "energy_eV": -358.46027010177465,
            "max_atomic_step_A": 0.0009268496920769968,
            "max_log_strain_component": 0.0002806940508420194,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0237121545145484,
              1.0075276273189453,
              0.9720477486761092
            ],
            "cell_volume_ratio": 1.0025878151662257,
            "cell_rmsd_from_input_A": 0.21168261952425915
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.454398586457335e-16,
              0.4998436076299737,
              -4.5349244587059396e-05
            ],
            "branch_aligned_reduced_polarization": [
              4.454398586457335e-16,
              0.4998436076299737,
              -4.5349244587059396e-05
            ],
            "target_residual": 0.00016283466273204166,
            "energy_eV": -358.26281885481177
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00016283466273204166,
        "parent_symmetrization_rmsd_A": 0.06764240448862155,
        "parent_cell_rmsd_A": 0.21168261952425915,
        "energy_eV": -358.26281885481177,
        "reduced_polarization": [
          4.454398586457335e-16,
          0.4998436076299737,
          -4.5349244587059396e-05
        ],
        "cartesian_polarization_e_A2": [
          -9.300021311926754e-17,
          0.006146534502269233,
          -0.00015791146880021244
        ],
        "ranking_score": 0.6208887286951504
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.6478509803464929,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.07976064556546354,
            "max_log_strain_component": 0.02,
            "step_scale": 0.705682607900578,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0239243658732502,
              0.9949171711034634,
              0.9835480111477172
            ],
            "cell_volume_ratio": 1.001959964528677,
            "cell_rmsd_from_input_A": 0.16704719347228425
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.34677474304141115,
              1.9652752195982966e-14,
              -0.10735125120447851
            ],
            "branch_aligned_reduced_polarization": [
              0.34677474304141115,
              1.9652752195982966e-14,
              -0.10735125120447851
            ],
            "target_residual": 0.18708893742066268,
            "energy_eV": -365.68922449636625,
            "max_atomic_step_A": 0.034613376656908425,
            "max_log_strain_component": 0.0095413605806671,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0350405758300618,
              0.9931509951230622,
              0.9753808255941178
            ],
            "cell_volume_ratio": 1.0026442587017834,
            "cell_rmsd_from_input_A": 0.24504149956275667
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4921742483100748,
              9.011194194228604e-15,
              0.004740118257346501
            ],
            "branch_aligned_reduced_polarization": [
              0.4921742483100748,
              9.011194194228604e-15,
              0.004740118257346501
            ],
            "target_residual": 0.009149377607575122,
            "energy_eV": -362.2292475994761,
            "max_atomic_step_A": 0.0017850099243496835,
            "max_log_strain_component": 0.0005499496253787619,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0355482342297997,
              0.9932282823059825,
              0.9747976540378407
            ],
            "cell_volume_ratio": 1.0026142790159935,
            "cell_rmsd_from_input_A": 0.24871815525961408
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4997032578814895,
              2.584237606533223e-15,
              0.0004407125545316238
            ],
            "branch_aligned_reduced_polarization": [
              0.4997032578814895,
              2.584237606533223e-15,
              0.0004407125545316238
            ],
            "target_residual": 0.0005313035296512593,
            "energy_eV": -362.01891387817034
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005313035296512593,
        "parent_symmetrization_rmsd_A": 0.06272044847245319,
        "parent_cell_rmsd_A": 0.24871815525961408,
        "energy_eV": -362.01891387817034,
        "reduced_polarization": [
          0.4997032578814895,
          2.584237606533223e-15,
          0.0004407125545316238
        ],
        "cartesian_polarization_e_A2": [
          0.006167172968859909,
          -1.494606831315087e-17,
          0.00018867391721123143
        ],
        "ranking_score": 0.6259625943466592
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              3.3306690738754696e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.7125665396394878,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.09805093001856346,
            "max_log_strain_component": 0.02,
            "step_scale": 0.705682607900968,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.026336056584245,
              1.0001229143917507,
              0.9738124057972095
            ],
            "cell_volume_ratio": 0.9995816322872909,
            "cell_rmsd_from_input_A": 0.20193718451221757
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.33377170746956053,
              0.3328931854760338,
              -0.44235787572233926
            ],
            "branch_aligned_reduced_polarization": [
              0.33377170746956053,
              0.3328931854760338,
              -0.44235787572233926
            ],
            "target_residual": 0.24265025693201706,
            "energy_eV": -361.8797819454782,
            "max_atomic_step_A": 0.05512356396662335,
            "max_log_strain_component": 0.012096050848459255,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0425917730684855,
              1.0002967310695894,
              0.9577693417194793
            ],
            "cell_volume_ratio": 0.9988587406736853,
            "cell_rmsd_from_input_A": 0.32699451958965753
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4850777354274342,
              0.481953643565049,
              -0.4819671843732863
            ],
            "branch_aligned_reduced_polarization": [
              0.4850777354274342,
              0.481953643565049,
              -0.4819671843732863
            ],
            "target_residual": 0.029555496950279824,
            "energy_eV": -350.8378194244147,
            "max_atomic_step_A": 0.006828887515148053,
            "max_log_strain_component": 0.001460229196013952,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.044577265132282,
              1.0003048415402882,
              0.9557639455374001
            ],
            "cell_volume_ratio": 0.9986736327731311,
            "cell_rmsd_from_input_A": 0.3426796219361878
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4983304586977687,
              0.4985010573602805,
              -0.49781998247892434
            ],
            "branch_aligned_reduced_polarization": [
              0.4983304586977687,
              0.4985010573602805,
              -0.49781998247892434
            ],
            "target_residual": 0.003128365961524051,
            "energy_eV": -349.21874176184446,
            "max_atomic_step_A": 0.0007000560791556604,
            "max_log_strain_component": 0.0001472416116596948,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.044774573334489,
              1.0003090877019025,
              0.9555589038498339
            ],
            "cell_volume_ratio": 0.9986522218089537,
            "cell_rmsd_from_input_A": 0.34426468390203785
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998172307180505,
              0.49987028208900863,
              -0.4997693705555871
            ],
            "branch_aligned_reduced_polarization": [
              0.4998172307180505,
              0.49987028208900863,
              -0.4997693705555871
            ],
            "target_residual": 0.0003215918025797444,
            "energy_eV": -349.05022116721665
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0003215918025797444,
        "parent_symmetrization_rmsd_A": 0.08831213543306973,
        "parent_cell_rmsd_A": 0.34426468390203785,
        "energy_eV": -349.05022116721665,
        "reduced_polarization": [
          0.4998172307180505,
          0.49987028208900863,
          -0.4997693705555871
        ],
        "cartesian_polarization_e_A2": [
          0.005981532350127976,
          0.0063528871886532655,
          -0.004106716721880183
        ],
        "ranking_score": 0.6750214900137387
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.5354256257501558e-17,
              3.1039362034453534e-16,
              -0.4119598193221179
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              3.3306690738754696e-16,
              -0.4119598193221179
            ],
            "target_residual": 0.8183586577631544,
            "energy_eV": -369.0948030155499,
            "max_atomic_step_A": 0.10627534989149708,
            "max_log_strain_component": 0.02,
            "step_scale": 0.705682607900741,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0284031335476738,
              0.9994986563684822,
              0.9747758539806527
            ],
            "cell_volume_ratio": 1.0019599645286745,
            "cell_rmsd_from_input_A": 0.21182359750247676
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3347562158444696,
              0.3412644311545635,
              -0.09686955794935936
            ],
            "branch_aligned_reduced_polarization": [
              0.3347562158444696,
              0.3412644311545635,
              -0.09686955794935936
            ],
            "target_residual": 0.248769371659833,
            "energy_eV": -361.7020634285534,
            "max_atomic_step_A": 0.05264592617141685,
            "max_log_strain_component": 0.011648375051299209,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0445242476881804,
              0.9992490418278043,
              0.9605295429327619
            ],
            "cell_volume_ratio": 1.002542964584741,
            "cell_rmsd_from_input_A": 0.3299119130624623
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48380440058110624,
              0.48666235177628236,
              0.0059827054329018485
            ],
            "branch_aligned_reduced_polarization": [
              0.48380440058110624,
              0.48666235177628236,
              0.0059827054329018485
            ],
            "target_residual": 0.021817036117992364,
            "energy_eV": -351.673087441353,
            "max_atomic_step_A": 0.0052399498774550884,
            "max_log_strain_component": 0.0012823656288895521,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0461759712620153,
              0.9992380670236313,
              0.958986088947265
            ],
            "cell_volume_ratio": 1.0025037799031353,
            "cell_rmsd_from_input_A": 0.3419235443568488
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49864489892101965,
              0.49914937435371654,
              0.0010283136361139758
            ],
            "branch_aligned_reduced_polarization": [
              0.49864489892101965,
              0.49914937435371654,
              0.0010283136361139758
            ],
            "target_residual": 0.0019019179421275805,
            "energy_eV": -350.57806241195124,
            "max_atomic_step_A": 0.00043150172963218625,
            "max_log_strain_component": 0.0001045052305649632,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4213128515889073,
            "cell_principal_stretches": [
              1.0462993975569574,
              0.9992352028576953,
              0.9588690143886818
            ],
            "cell_volume_ratio": 1.0024967785955987,
            "cell_rmsd_from_input_A": 0.3428117776615349
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998895804690702,
              0.4999449176619279,
              9.005647644258958e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4998895804690702,
              0.4999449176619279,
              9.005647644258958e-05
            ],
            "target_residual": 0.0001527635615174508,
            "energy_eV": -350.5010082155759
          }
        ],
        "iterations": 4
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0001527635615174508,
        "parent_symmetrization_rmsd_A": 0.09006232660435481,
        "parent_cell_rmsd_A": 0.3428117776615349,
        "energy_eV": -350.5010082155759,
        "reduced_polarization": [
          0.4998895804690702,
          0.4999449176619279,
          9.005647644258958e-05
        ],
        "cartesian_polarization_e_A2": [
          0.0061657303051514765,
          0.006147333883428738,
          3.320220915976732e-05
        ],
        "ranking_score": 0.6760707981427734
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63
        ],
        "endpoint_rmsd_A": 0.007425231984372601,
        "minimum_distance_A_by_image": [
          1.0538731853127392,
          1.0534327709196412,
          1.0529927357164952,
          1.0525530800308314,
          1.0521138041905165,
          1.0516749085237422,
          1.0512363933590345,
          1.050798259025244,
          1.0503605058515584
        ],
        "minimum_distance_A": 1.0503605058515584,
        "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": [
          891.8374013119196,
          891.7712986103503,
          891.7052008082904,
          891.63910790538,
          891.5730199012535,
          891.5069367955477,
          891.4408585879022,
          891.3747852779513,
          891.308716865333
        ],
        "cell_deformation_log_strain_norm": 0.0023483802238601767
      },
      "parent_reduced_polarization": [
        3.0282556055861044e-15,
        -6.136868766181519e-15,
        -0.4994238292959495
      ],
      "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": [
          -369.09480301554987,
          -369.0834028114988,
          -369.0695021212367,
          -369.05309736994957,
          -369.0341848558398,
          -369.01276074557495,
          -368.988821075698,
          -368.9623617543017,
          -368.9333785627805
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.614230293866537e-18,
            -1.0581408332316937e-17,
            -0.0034007353538255953
          ],
          [
            -2.617536483750769e-17,
            -8.193418303773958e-18,
            -0.003491617825697737
          ],
          [
            -2.2846779948580297e-17,
            -9.26010495191095e-19,
            -0.0035823512301905907
          ],
          [
            2.555667127921617e-17,
            -5.276316421226724e-18,
            -0.003672933079249156
          ],
          [
            3.181590026391162e-17,
            -2.2095239933768365e-17,
            -0.003763360910595274
          ],
          [
            4.72603880525802e-17,
            -4.037992312529415e-17,
            -0.0038536322915317025
          ],
          [
            4.536461761022556e-17,
            -1.6883297116777496e-17,
            -0.0039437448201299205
          ],
          [
            4.278353115405031e-17,
            -5.139317188483263e-17,
            -0.004033696126304425
          ],
          [
            4.3752050217916326e-17,
            -6.995656997476798e-17,
            -0.004123483872848832
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.865653943762899e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.8656539437628992e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -8.326672684688674e-16,
            -0.41195981932211634
          ],
          [
            -2.1649348980190553e-15,
            -7.216449660063518e-16,
            -0.4229597998137043
          ],
          [
            -1.9984014443252818e-15,
            -1.6653345369377348e-16,
            -0.4339412351483628
          ],
          [
            1.887379141862766e-15,
            -6.106226635438361e-16,
            -0.4449038251647818
          ],
          [
            2.3314683517128287e-15,
            -1.9984014443252818e-15,
            -0.4558472728506228
          ],
          [
            3.552713678800501e-15,
            -3.552713678800501e-15,
            -0.46677128480294433
          ],
          [
            3.3306690738754696e-15,
            -1.7208456881689926e-15,
            -0.47767557137167166
          ],
          [
            2.9976021664879227e-15,
            -4.551914400963142e-15,
            -0.48855984678929837
          ],
          [
            2.9976021664879227e-15,
            -6.161737786669619e-15,
            -0.4994238292959495
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -368.9333785627805,
          -368.9078419342418,
          -368.8807467292088,
          -368.85209305509187,
          -368.82188102184216,
          -368.79011074243425,
          -368.7567823333746,
          -368.72189591523244,
          -368.68545161319275
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.1198549778151814e-17,
            -7.178605961911146e-17,
            -0.004123483872848851
          ],
          [
            6.018964026257588e-17,
            -8.571496752861135e-17,
            -0.004203176517354115
          ],
          [
            4.5769380842163056e-17,
            -9.456670201555085e-17,
            -0.00428274893846074
          ],
          [
            8.66440447630637e-17,
            -1.0062290789587564e-16,
            -0.004362199990788268
          ],
          [
            1.069039153681727e-16,
            -1.2985525829338682e-16,
            -0.004441528548749538
          ],
          [
            9.360403232229357e-17,
            -1.3039816807385693e-16,
            -0.00452073350713697
          ],
          [
            1.3913502230266202e-16,
            -1.6085347013525317e-16,
            -0.004599813781697446
          ],
          [
            1.7292547804660252e-16,
            -2.059248009585734e-16,
            -0.004678768309695289
          ],
          [
            1.244249132723621e-16,
            -1.6731851925476155e-16,
            -0.0047575960504619656
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.8199926616621148e-15,
            -6.284000122086111e-15,
            -0.4994238292959518
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8199926616621148e-15,
            -6.284000122086111e-15,
            -0.4994238292959518
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          7.341747722804119e-15,
          -1.0423369040299608e-14,
          -0.5870650941134633
        ],
        "actual_opposite_endpoint_branch_residual": 0.01073726926489671
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.865653943762899e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.1297575256301309e-16,
            -8.527986336738748e-16,
            -0.41195981932211634
          ],
          [
            -2.189937847796424e-15,
            -7.147415266255767e-16,
            -0.4229597998137043
          ],
          [
            -1.9791546355334133e-15,
            -1.8656539437628992e-16,
            -0.4339412351483628
          ],
          [
            1.9024390700942787e-15,
            -5.970827888015851e-16,
            -0.4449038251647818
          ],
          [
            2.346843811140129e-15,
            -2.014040328916966e-15,
            -0.4558472728506228
          ],
          [
            3.5372656099116992e-15,
            -3.5510436191399207e-15,
            -0.46677128480294433
          ],
          [
            3.311222976215551e-15,
            -1.7281126752273232e-15,
            -0.47767557137167166
          ],
          [
            3.0263076207769827e-15,
            -4.575217777774621e-15,
            -0.48855984678929837
          ],
          [
            3.0282556055861044e-15,
            -6.136868766181519e-15,
            -0.4994238292959495
          ],
          [
            4.426308669790921e-15,
            -7.35471279220009e-15,
            -0.5090872517529657
          ],
          [
            3.310902623138692e-15,
            -8.010681333010434e-15,
            -0.5187365409086635
          ],
          [
            6.706373200099055e-15,
            -8.439515980199716e-15,
            -0.5283715570740983
          ],
          [
            8.42311756945977e-15,
            -1.073196915802988e-14,
            -0.5379921629454905
          ],
          [
            7.406795751505548e-15,
            -1.0712829714119944e-14,
            -0.5475982236755041
          ],
          [
            1.118754702739073e-14,
            -1.3100689699432835e-14,
            -0.557189606943163
          ],
          [
            1.401322538950414e-14,
            -1.6665017440031782e-14,
            -0.566766183022327
          ],
          [
            1.0136631651749121e-14,
            -1.3484878394968144e-14,
            -0.5763278248485666
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -8.326672684688674e-16,
            -0.41195981932211634
          ],
          [
            -2.1649348980190553e-15,
            -7.216449660063518e-16,
            -0.4229597998137043
          ],
          [
            -1.9984014443252818e-15,
            -1.6653345369377348e-16,
            -0.4339412351483628
          ],
          [
            1.887379141862766e-15,
            -6.106226635438361e-16,
            -0.4449038251647818
          ],
          [
            2.3314683517128287e-15,
            -1.9984014443252818e-15,
            -0.4558472728506228
          ],
          [
            3.552713678800501e-15,
            -3.552713678800501e-15,
            -0.46677128480294433
          ],
          [
            3.3306690738754696e-15,
            -1.7208456881689926e-15,
            -0.47767557137167166
          ],
          [
            2.9976021664879227e-15,
            -4.551914400963142e-15,
            -0.48855984678929837
          ],
          [
            2.9976021664879227e-15,
            -6.161737786669619e-15,
            -0.4994238292959495
          ],
          [
            4.440892098500626e-15,
            -7.327471962526033e-15,
            0.49091274824703435
          ],
          [
            3.3306690738754696e-15,
            -7.993605777301127e-15,
            0.4812634590913365
          ],
          [
            6.661338147750939e-15,
            -8.43769498715119e-15,
            0.47162844292590167
          ],
          [
            8.43769498715119e-15,
            -1.071365218763276e-14,
            0.46200783705450954
          ],
          [
            7.438494264988549e-15,
            -1.071365218763276e-14,
            0.45240177632449585
          ],
          [
            1.1213252548714081e-14,
            -1.3100631690576847e-14,
            0.442810393056837
          ],
          [
            1.3988810110276972e-14,
            -1.6653345369377348e-14,
            0.43323381697767305
          ],
          [
            1.0103029524088925e-14,
            -1.3489209749195652e-14,
            0.4236721751514334
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Fdd2",
        "spacegroup_number": 43,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0005761707040459751,
        "parent_symmetrization_rmsd_A": 0.007425231984372601,
        "parent_cell_rmsd_A": 0.01881274307508593,
        "energy_eV": -368.9333785627805,
        "reduced_polarization": [
          3.0434943575805373e-15,
          -5.974085138372192e-15,
          -0.499423829295954
        ],
        "cartesian_polarization_e_A2": [
          4.3938891713508846e-17,
          -6.793245377251563e-17,
          -0.004123483872848869
        ],
        "ranking_score": 0.513280759161236
      }
    }
  ],
  "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": 60,
      "full_response": 25,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 85,
      "full_response": 50,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1454.3004329269752
  }
}