{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "H16Cl4N4O16",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -185.62416030700294,
  "input_cartesian_polarization_e_A2": [
    2.499683025046109e-17,
    9.174368549371358e-18,
    0.001408979535085533
  ],
  "input_reduced_polarization": [
    1.1157023098840378e-15,
    5.059708196846569e-16,
    0.09976961361552192
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.99109375405709e-15,
      "parent_symmetrization_rmsd_A": 0.3053935051794925,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -179.00950124388277,
      "reduced_polarization": [
        -1.139440656902847e-15,
        5.041375920771038e-17,
        -1.632050176840317e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.552867770259856e-17,
        9.141128083612767e-19,
        -2.304835326176884e-17
      ],
      "ranking_score": 0.3053935051794965
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3610678593986168e-05,
      "parent_symmetrization_rmsd_A": 0.010536283612865766,
      "parent_cell_rmsd_A": 0.0027810485265755748,
      "energy_eV": -185.48508033378036,
      "reduced_polarization": [
        1.2984083772837687e-15,
        -2.186239798026266e-15,
        2.3610678593986168e-05
      ],
      "cartesian_polarization_e_A2": [
        2.907183816716895e-17,
        -3.962076230211312e-17,
        3.335318967702504e-07
      ],
      "ranking_score": 0.5112787671016976
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3974980854074414e-15,
      "parent_symmetrization_rmsd_A": 0.305394935625489,
      "parent_cell_rmsd_A": 0.0027810485265755748,
      "energy_eV": -178.93376124860632,
      "reduced_polarization": [
        -5.0454738019565267e-17,
        -1.2512641646983626e-15,
        -6.203170223930264e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1296485687814223e-18,
        -2.2676033770391785e-17,
        -8.762794015175703e-18
      ],
      "ranking_score": 0.30609019775713564
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.000147505542019033,
      "parent_symmetrization_rmsd_A": 0.04459238231284803,
      "parent_cell_rmsd_A": 0.01177380887078884,
      "energy_eV": -183.13022703536728,
      "reduced_polarization": [
        1.0644378739587505e-15,
        -5.949819387279213e-17,
        0.49985249445798097
      ],
      "cartesian_polarization_e_A2": [
        -9.515622166337628e-17,
        5.592134972796947e-17,
        0.007050638986608613
      ],
      "ranking_score": 0.5478308456145833
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0009486769394348349,
      "parent_symmetrization_rmsd_A": 0.11739126877773008,
      "parent_cell_rmsd_A": 0.004391556228089603,
      "energy_eV": -163.39190652563204,
      "reduced_polarization": [
        0.5009262321145301,
        -2.964310238664097e-15,
        -0.00020513899051248483
      ],
      "cartesian_polarization_e_A2": [
        0.011213916218750513,
        -5.370737704376002e-16,
        -7.68026619996426e-06
      ],
      "ranking_score": 0.6203865117136221
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.295622103310448e-05,
      "parent_symmetrization_rmsd_A": 0.07778757174758567,
      "parent_cell_rmsd_A": 0.01667818186330095,
      "energy_eV": -177.64828839404387,
      "reduced_polarization": [
        2.803114845099976e-16,
        0.5000025145162771,
        -2.2818091331507546e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.2461643655961698e-16,
        0.009060470672199417,
        -2.754847473994493e-05
      ],
      "ranking_score": 0.5820030296554771
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.6060165450857457e-05,
      "parent_symmetrization_rmsd_A": 0.1192888680660222,
      "parent_cell_rmsd_A": 0.010387049888213217,
      "energy_eV": -165.0058658366488,
      "reduced_polarization": [
        0.49998515494310586,
        -2.192806805767247e-15,
        0.500006128066589
      ],
      "cartesian_polarization_e_A2": [
        0.011226644986833994,
        -8.541023017208742e-16,
        0.007049533800670339
      ],
      "ranking_score": 0.6219177508689773
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0007299171082340789,
      "parent_symmetrization_rmsd_A": 0.09887541196354944,
      "parent_cell_rmsd_A": 0.024367814897663802,
      "energy_eV": -171.72782376586696,
      "reduced_polarization": [
        1.25918094524793e-16,
        0.49988992029878965,
        0.4992784312615736
      ],
      "cartesian_polarization_e_A2": [
        -9.56470418022978e-16,
        0.009068200521757228,
        0.007008743192207653
      ],
      "ranking_score": 0.6064271999044335
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0009363885806480528,
      "parent_symmetrization_rmsd_A": 0.13927008490114054,
      "parent_cell_rmsd_A": 0.02135799616067559,
      "energy_eV": -152.0766171763351,
      "reduced_polarization": [
        0.5008034005030672,
        0.5004750431678168,
        -7.553273694319066e-05
      ],
      "cartesian_polarization_e_A2": [
        0.01121056438275112,
        0.009068596494935159,
        -4.063714104015867e-05
      ],
      "ranking_score": 0.6464823611026056
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 4.8647566161105137e-05,
      "parent_symmetrization_rmsd_A": 0.1486683462675811,
      "parent_cell_rmsd_A": 0.02739412797072591,
      "energy_eV": -148.94894244110975,
      "reduced_polarization": [
        0.5000403570518437,
        0.5000239488248994,
        0.4999871801776213
      ],
      "cartesian_polarization_e_A2": [
        0.011237831464290774,
        0.009060301182373366,
        0.007006465967466433
      ],
      "ranking_score": 0.6556141733925848
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "target_residual": 0.09976961361552192,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.025749603946545668,
            "max_log_strain_component": 0.000748731820407687,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0007490121900466,
              0.999931011735329,
              0.9997869257670422
            ],
            "cell_volume_ratio": 1.0004667531348004,
            "cell_rmsd_from_input_A": 0.0027810485265755748
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.2984083772837687e-15,
              -2.186239798026266e-15,
              2.3610678593986168e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.2984083772837687e-15,
              -2.186239798026266e-15,
              2.3610678593986168e-05
            ],
            "target_residual": 2.3610678593986168e-05,
            "energy_eV": -185.48508033378036
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.99109375405709e-15,
        "parent_symmetrization_rmsd_A": 0.3053935051794925,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -179.00950124388277,
        "reduced_polarization": [
          -1.139440656902847e-15,
          5.041375920771038e-17,
          -1.632050176840317e-15
        ],
        "cartesian_polarization_e_A2": [
          -2.552867770259856e-17,
          9.141128083612767e-19,
          -2.304835326176884e-17
        ],
        "ranking_score": 0.3053935051794965
      },
      "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": [
          -185.62416030700294,
          -185.25930075392196,
          -184.48235321911767,
          -183.405044127216,
          -182.17477773984865,
          -180.960858066524,
          -179.93547643729943,
          -179.25025109183406,
          -179.0095012438827
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.4193678878918733e-17,
            1.5988664029882693e-17,
            0.0014089795350855268
          ],
          [
            1.5490057043503816e-17,
            -2.1922087167791343e-17,
            0.0011580670749596225
          ],
          [
            -5.9168029050293546e-18,
            1.662023287929594e-20,
            0.0009291193944417798
          ],
          [
            -4.886348466513006e-18,
            -1.035440508380137e-17,
            0.0007230560978656916
          ],
          [
            3.955615425272434e-18,
            -1.76008266191744e-17,
            0.0005401821571735431
          ],
          [
            9.606494604233052e-18,
            -2.21049097294636e-18,
            0.0003798602050021124
          ],
          [
            -7.24642153537303e-18,
            3.540109603290035e-18,
            0.00023898233427149075
          ],
          [
            -1.5490057043503816e-17,
            -1.0952733467456024e-17,
            0.00011414542047870944
          ],
          [
            -8.077433179337827e-18,
            -1.0753290672904472e-17,
            -2.6739222518974683e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425364e-16,
            9.166138037765524e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724327e-16,
            -1.2190963590228149e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425354e-16,
            9.166138037764916e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724323e-16,
            -1.2190963590228146e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8925833122906965e-15
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            8.881784197001252e-16,
            0.0997696136155215
          ],
          [
            6.661338147750939e-16,
            -1.2212453270876722e-15,
            0.0820025427853821
          ],
          [
            -2.7755575615628914e-16,
            0.0,
            0.06579079445644098
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            0.05119948566323773
          ],
          [
            2.220446049250313e-16,
            -9.43689570931383e-16,
            0.038250211419807334
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.02689783984596561
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.016922300542679403
          ],
          [
            -6.661338147750939e-16,
            -6.106226635438361e-16,
            0.008082618812806808
          ],
          [
            -3.3306690738754696e-16,
            -6.106226635438361e-16,
            -1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -179.0095012438827,
          -179.25025109183406,
          -179.93547643729943,
          -180.9608580665239,
          -182.17477773984865,
          -183.405044127216,
          -184.48235321911758,
          -185.25930075392193,
          -185.62416030700285
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.077433179337827e-18,
            -1.0753290672904472e-17,
            -2.6739222518974683e-17
          ],
          [
            -1.894706548239737e-18,
            1.7285042194467777e-18,
            -0.00011414542047873573
          ],
          [
            -5.950043370787946e-18,
            2.0027380619551608e-17,
            -0.00023898233427149584
          ],
          [
            2.1473340880050354e-17,
            2.3750312784513896e-17,
            -0.000379860205002159
          ],
          [
            -9.506773206957277e-18,
            7.61206665871754e-18,
            -0.0005401821571735457
          ],
          [
            1.502469052288353e-17,
            1.3030262577368017e-17,
            -0.0007230560978656889
          ],
          [
            -7.44586432992458e-18,
            4.8198675349958224e-18,
            -0.0009291193944417833
          ],
          [
            5.318474521374701e-19,
            1.5855702166848325e-17,
            -0.0011580670749595857
          ],
          [
            -7.046978740821479e-18,
            -2.7240561689166043e-17,
            -0.001408979535085488
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276146e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612165e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.7060830328136325e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.323368582633304e-16,
            2.6581800309520015e-16,
            -0.06579079445644123
          ],
          [
            2.373834701880932e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897694e-15,
            -0.09976961361551873
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276143e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612166e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.706083032813632e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.3233685826333037e-16,
            2.658180030952001e-16,
            -0.06579079445644123
          ],
          [
            2.3738347018809312e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897692e-15,
            -0.09976961361551873
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3545694267608067e-15,
          -2.0678807413199022e-15,
          -0.09976961361552528
        ],
        "actual_opposite_endpoint_branch_residual": 6.656437549590671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425364e-16,
            9.166138037765524e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724327e-16,
            -1.2190963590228149e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276146e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612165e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.7060830328136325e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.323368582633304e-16,
            2.6581800309520015e-16,
            -0.06579079445644123
          ],
          [
            2.373834701880932e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897694e-15,
            -0.09976961361551873
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425354e-16,
            9.166138037764916e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724323e-16,
            -1.2190963590228146e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8925833122906965e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276143e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612166e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.706083032813632e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.3233685826333037e-16,
            2.658180030952001e-16,
            -0.06579079445644123
          ],
          [
            2.3738347018809312e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897692e-15,
            -0.09976961361551873
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            8.881784197001252e-16,
            0.0997696136155215
          ],
          [
            6.661338147750939e-16,
            -1.2212453270876722e-15,
            0.0820025427853821
          ],
          [
            -2.7755575615628914e-16,
            0.0,
            0.06579079445644098
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            0.05119948566323773
          ],
          [
            2.220446049250313e-16,
            -9.43689570931383e-16,
            0.038250211419807334
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.02689783984596561
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.016922300542679403
          ],
          [
            -6.661338147750939e-16,
            -6.106226635438361e-16,
            0.008082618812806808
          ],
          [
            -3.3306690738754696e-16,
            -6.106226635438361e-16,
            -1.887379141862766e-15
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.008082618812808695
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-15,
            -0.01692230054267979
          ],
          [
            9.992007221626409e-16,
            1.3322676295501878e-15,
            -0.026897839845968885
          ],
          [
            -4.440892098500626e-16,
            4.440892098500626e-16,
            -0.038250211419807556
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            -0.05119948566323751
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            -0.0657907944564412
          ],
          [
            0.0,
            8.881784197001252e-16,
            -0.0820025427853795
          ],
          [
            -3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.09976961361551873
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552195
            ],
            "target_residual": 0.40023038638447805,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.10329571863922607,
            "max_log_strain_component": 0.0030035720789190366,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0008552136328677,
              1.0002767974396511,
              0.9970009341309932
            ],
            "cell_volume_ratio": 0.9981297862387433,
            "cell_rmsd_from_input_A": 0.011133160849071363
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.116431247700361e-15,
              -5.499826810101793e-16,
              0.48175860706740115
            ],
            "branch_aligned_reduced_polarization": [
              -7.116431247700361e-15,
              -5.499826810101793e-16,
              0.48175860706740115
            ],
            "target_residual": 0.018241392932598854,
            "energy_eV": -183.37883183899788,
            "max_atomic_step_A": 0.005198763536808474,
            "max_log_strain_component": 0.000173141264797819,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0009045348127925,
              1.0002927557959147,
              0.9968283270713866
            ],
            "cell_volume_ratio": 0.9980220842338073,
            "cell_rmsd_from_input_A": 0.01177380887078884
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0644378739587505e-15,
              -5.949819387279213e-17,
              0.49985249445798097
            ],
            "branch_aligned_reduced_polarization": [
              1.0644378739587505e-15,
              -5.949819387279213e-17,
              0.49985249445798097
            ],
            "target_residual": 0.000147505542019033,
            "energy_eV": -183.13022703536728
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.000147505542019033,
        "parent_symmetrization_rmsd_A": 0.04459238231284803,
        "parent_cell_rmsd_A": 0.01177380887078884,
        "energy_eV": -183.13022703536728,
        "reduced_polarization": [
          1.0644378739587505e-15,
          -5.949819387279213e-17,
          0.49985249445798097
        ],
        "cartesian_polarization_e_A2": [
          -9.515622166337628e-17,
          5.592134972796947e-17,
          0.007050638986608613
        ],
        "ranking_score": 0.5478308456145833
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "target_residual": 0.5098568189217336,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003998713375869944,
            "step_scale": 0.5340648369989828,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.000441923045736,
              0.999963155201495,
              0.9998442504606576
            ],
            "cell_volume_ratio": 1.0002492493371091,
            "cell_rmsd_from_input_A": 0.0018051499583405534
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24992741067346075,
              -1.982708276131751e-15,
              0.048588874711107836
            ],
            "branch_aligned_reduced_polarization": [
              0.24992741067346075,
              -1.982708276131751e-15,
              0.048588874711107836
            ],
            "target_residual": 0.25474924666850673,
            "energy_eV": -181.8724123272753,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00040043454226613995,
            "step_scale": 0.9055430583150113,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0009019389848863,
              0.9999262598687991,
              0.9996710520575187
            ],
            "cell_volume_ratio": 1.0004989119896741,
            "cell_rmsd_from_input_A": 0.0037423458781790627
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4391290026027838,
              -7.797331875140315e-15,
              0.005753634245601263
            ],
            "branch_aligned_reduced_polarization": [
              0.4391290026027838,
              -7.797331875140315e-15,
              0.005753634245601263
            ],
            "target_residual": 0.06114231457153103,
            "energy_eV": -169.24041170337227,
            "max_atomic_step_A": 0.04085649301898817,
            "max_log_strain_component": 9.54195401109394e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0010369557060943,
              0.9999174682814576,
              0.9996044523725487
            ],
            "cell_volume_ratio": 1.0005584132920724,
            "cell_rmsd_from_input_A": 0.004391556228089603
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5009262321145301,
              -2.964310238664097e-15,
              -0.00020513899051248483
            ],
            "branch_aligned_reduced_polarization": [
              0.5009262321145301,
              -2.964310238664097e-15,
              -0.00020513899051248483
            ],
            "target_residual": 0.0009486769394348349,
            "energy_eV": -163.39190652563204
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0009486769394348349,
        "parent_symmetrization_rmsd_A": 0.11739126877773008,
        "parent_cell_rmsd_A": 0.004391556228089603,
        "energy_eV": -163.39190652563204,
        "reduced_polarization": [
          0.5009262321145301,
          -2.964310238664097e-15,
          -0.00020513899051248483
        ],
        "cartesian_polarization_e_A2": [
          0.011213916218750513,
          -5.370737704376002e-16,
          -7.68026619996426e-06
        ],
        "ranking_score": 0.6203865117136221
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1157023098840378e-15,
              4.996003610813204e-16,
              0.09976961361552192
            ],
            "target_residual": 0.5098568189217342,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018134137653451146,
            "step_scale": 0.6720602154494059,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.002064655705919,
              0.9998567962815735,
              0.9983955882145344
            ],
            "cell_volume_ratio": 1.0003136622098094,
            "cell_rmsd_from_input_A": 0.010044627906477796
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.214216237449383e-17,
              0.3250332139722229,
              0.034446043547420556
            ],
            "branch_aligned_reduced_polarization": [
              -3.214216237449383e-17,
              0.3250332139722229,
              0.034446043547420556
            ],
            "target_residual": 0.17832528179975135,
            "energy_eV": -182.50740828576852,
            "max_atomic_step_A": 0.06808242227611828,
            "max_log_strain_component": 0.00113106368761103,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0033676548405595,
              0.999760582913783,
              0.9974051646200502
            ],
            "cell_volume_ratio": 1.00052448093043,
            "cell_rmsd_from_input_A": 0.016332934234632127
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.4895804690760766e-15,
              0.4924263904467724,
              0.0033323728542334545
            ],
            "branch_aligned_reduced_polarization": [
              -1.4895804690760766e-15,
              0.4924263904467724,
              0.0033323728542334545
            ],
            "target_residual": 0.008274313899313499,
            "energy_eV": -177.91674349591412,
            "max_atomic_step_A": 0.0033866507234016074,
            "max_log_strain_component": 5.8955816894534385e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.00344830861981,
              0.9997488965697213,
              0.9973621840157401
            ],
            "cell_volume_ratio": 1.0005500919682322,
            "cell_rmsd_from_input_A": 0.01667818186330095
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.803114845099976e-16,
              0.5000025145162771,
              -2.2818091331507546e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.803114845099976e-16,
              0.5000025145162771,
              -2.2818091331507546e-05
            ],
            "target_residual": 2.295622103310448e-05,
            "energy_eV": -177.64828839404387
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.295622103310448e-05,
        "parent_symmetrization_rmsd_A": 0.07778757174758567,
        "parent_cell_rmsd_A": 0.01667818186330095,
        "energy_eV": -177.64828839404387,
        "reduced_polarization": [
          2.803114845099976e-16,
          0.5000025145162771,
          -2.2818091331507546e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.2461643655961698e-16,
          0.009060470672199417,
          -2.754847473994493e-05
        ],
        "ranking_score": 0.5820030296554771
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-15,
              5.059708196846569e-16,
              0.09976961361552195
            ],
            "target_residual": 0.6404563702434909,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0014647285540438102,
            "step_scale": 0.48766219538803496,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0004272418823588,
              1.0001349740771643,
              0.9985260852099712
            ],
            "cell_volume_ratio": 0.9990875300926598,
            "cell_rmsd_from_input_A": 0.005513900916910623
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2313299841884073,
              1.0822041403759671e-15,
              0.29490744195463764
            ],
            "branch_aligned_reduced_polarization": [
              0.23132998418840733,
              1.0822041403759671e-15,
              0.29490744195463764
            ],
            "target_residual": 0.3380037496268226,
            "energy_eV": -182.1655864586895,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012775490851154928,
            "step_scale": 0.8227999394290225,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0008072432335715,
              1.0002527145250126,
              0.9972351151324843
            ],
            "cell_volume_ratio": 0.9982923456679497,
            "cell_rmsd_from_input_A": 0.010371836467692871
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4230085809320457,
              -8.475181385802113e-15,
              0.4742081874280472
            ],
            "branch_aligned_reduced_polarization": [
              0.4230085809320457,
              -8.475181385802113e-15,
              0.4742081874280472
            ],
            "target_residual": 0.08119665144477389,
            "energy_eV": -171.0885517169805,
            "max_atomic_step_A": 0.047269973279917714,
            "max_log_strain_component": 9.644544717843826e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0008264910911688,
              1.0002527857657086,
              0.9972153849194924
            ],
            "cell_volume_ratio": 0.9982918647491652,
            "cell_rmsd_from_input_A": 0.010522016363389336
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49976010384615566,
              -1.6876055693871117e-15,
              0.5048196656877243
            ],
            "branch_aligned_reduced_polarization": [
              0.49976010384615566,
              -1.6876055693871117e-15,
              0.5048196656877243
            ],
            "target_residual": 0.0048256323426112985,
            "energy_eV": -164.99771848757808,
            "max_atomic_step_A": 0.001325222647792701,
            "max_log_strain_component": 3.814900154882798e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0008164348132895,
              1.0002492697071985,
              0.9972526210577753
            ],
            "cell_volume_ratio": 0.998315600637446,
            "cell_rmsd_from_input_A": 0.010387049888213217
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49998515494310586,
              -2.192806805767247e-15,
              0.500006128066589
            ],
            "branch_aligned_reduced_polarization": [
              0.49998515494310586,
              -2.192806805767247e-15,
              0.500006128066589
            ],
            "target_residual": 1.6060165450857457e-05,
            "energy_eV": -165.0058658366488
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.6060165450857457e-05,
        "parent_symmetrization_rmsd_A": 0.1192888680660222,
        "parent_cell_rmsd_A": 0.010387049888213217,
        "energy_eV": -165.0058658366488,
        "reduced_polarization": [
          0.49998515494310586,
          -2.192806805767247e-15,
          0.500006128066589
        ],
        "cartesian_polarization_e_A2": [
          0.011226644986833994,
          -8.541023017208742e-16,
          0.007049533800670339
        ],
        "ranking_score": 0.6219177508689773
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1157023098840378e-15,
              4.996003610813204e-16,
              0.09976961361552195
            ],
            "target_residual": 0.6404563702434913,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017440131520864172,
            "step_scale": 0.5806463458403217,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0010423787331177,
              1.0004964876614704,
              0.9973782928891668
            ],
            "cell_volume_ratio": 0.9989136409981575,
            "cell_rmsd_from_input_A": 0.010685689194621175
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.031634616694184e-15,
              0.27583188831282324,
              0.31483911801085745
            ],
            "branch_aligned_reduced_polarization": [
              -4.031634616694184e-15,
              0.27583188831282324,
              0.31483911801085745
            ],
            "target_residual": 0.2907505709648594,
            "energy_eV": -182.5072252963862,
            "max_atomic_step_A": 0.10621766073765707,
            "max_log_strain_component": 0.0020395487517633855,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0020452558358128,
              1.0010774214407039,
              0.9945368783709304
            ],
            "cell_volume_ratio": 0.9976446876456183,
            "cell_rmsd_from_input_A": 0.022048513155369175
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.603467431864591e-15,
              0.4787588387013997,
              0.4678466713296601
            ],
            "branch_aligned_reduced_polarization": [
              -5.603467431864591e-15,
              0.4787588387013997,
              0.4678466713296601
            ],
            "target_residual": 0.03853600236007954,
            "energy_eV": -173.42444529023038,
            "max_atomic_step_A": 0.015428796042622058,
            "max_log_strain_component": 0.0005314129014973522,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0021789696762051,
              1.00122884153728,
              0.9939245528066566
            ],
            "cell_volume_ratio": 0.9973143213838473,
            "cell_rmsd_from_input_A": 0.024367814897663802
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.25918094524793e-16,
              0.49988992029878965,
              0.4992784312615736
            ],
            "branch_aligned_reduced_polarization": [
              1.25918094524793e-16,
              0.49988992029878965,
              0.4992784312615736
            ],
            "target_residual": 0.0007299171082340789,
            "energy_eV": -171.72782376586696
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0007299171082340789,
        "parent_symmetrization_rmsd_A": 0.09887541196354944,
        "parent_cell_rmsd_A": 0.024367814897663802,
        "energy_eV": -171.72782376586696,
        "reduced_polarization": [
          1.25918094524793e-16,
          0.49988992029878965,
          0.4992784312615736
        ],
        "cartesian_polarization_e_A2": [
          -9.56470418022978e-16,
          0.009068200521757228,
          0.007008743192207653
        ],
        "ranking_score": 0.6064271999044335
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-15,
              4.996003610813204e-16,
              0.09976961361552192
            ],
            "target_residual": 0.7141106187426349,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001122117544589398,
            "step_scale": 0.4158623769075129,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0012830273833715,
              0.9999120627083593,
              0.9990002959712005
            ],
            "cell_volume_ratio": 1.0001940786133907,
            "cell_rmsd_from_input_A": 0.006265321517457701
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19257509088227964,
              0.19639511758560754,
              0.059463564628387686
            ],
            "branch_aligned_reduced_polarization": [
              0.19257509088227964,
              0.19639511758560757,
              0.059463564628387686
            ],
            "target_residual": 0.43614437390640515,
            "energy_eV": -182.08943565666507,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012990058433229679,
            "step_scale": 0.5594898927973883,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0027412201463273,
              0.9998262842717422,
              0.9978222011290772
            ],
            "cell_volume_ratio": 1.0003836388829224,
            "cell_rmsd_from_input_A": 0.013493510272443684
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3336212594432933,
              0.3442250281077694,
              0.029283998878685238
            ],
            "branch_aligned_reduced_polarization": [
              0.3336212594432933,
              0.3442250281077694,
              0.029283998878685238
            ],
            "target_residual": 0.22979399419390403,
            "energy_eV": -170.42277943158714,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013261588999593974,
            "step_scale": 0.7088345859700876,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.004223903141292,
              0.9997439525727809,
              0.9966125542527836
            ],
            "cell_volume_ratio": 1.0005658912149487,
            "cell_rmsd_from_input_A": 0.02087831681161253
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48679652885757985,
              0.4788126247095396,
              0.0057648004353133215
            ],
            "branch_aligned_reduced_polarization": [
              0.48679652885757985,
              0.4788126247095396,
              0.0057648004353133215
            ],
            "target_residual": 0.025621659703589105,
            "energy_eV": -154.17367453107738,
            "max_atomic_step_A": 0.011368553557789863,
            "max_log_strain_component": 8.411622533598212e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0043326053586534,
              0.9997303845675181,
              0.9965479183235713
            ],
            "cell_volume_ratio": 1.0005957183719048,
            "cell_rmsd_from_input_A": 0.02135799616067559
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5008034005030672,
              0.5004750431678168,
              -7.553273694319066e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5008034005030672,
              0.5004750431678168,
              -7.553273694319066e-05
            ],
            "target_residual": 0.0009363885806480528,
            "energy_eV": -152.0766171763351
          }
        ],
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0009363885806480528,
        "parent_symmetrization_rmsd_A": 0.13927008490114054,
        "parent_cell_rmsd_A": 0.02135799616067559,
        "energy_eV": -152.0766171763351,
        "reduced_polarization": [
          0.5008034005030672,
          0.5004750431678168,
          -7.553273694319066e-05
        ],
        "cartesian_polarization_e_A2": [
          0.01121056438275112,
          0.009068596494935159,
          -4.063714104015867e-05
        ],
        "ranking_score": 0.6464823611026056
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1157023098840378e-15,
              5.059708196846569e-16,
              0.09976961361552192
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-15,
              4.996003610813204e-16,
              0.09976961361552195
            ],
            "target_residual": 0.8125172996222708,
            "energy_eV": -185.62416030700294,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0011753635969694262,
            "step_scale": 0.3913219213872826,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0007104761295509,
              1.0003310011437134,
              0.9982278609999357
            ],
            "cell_volume_ratio": 0.9992677273823667,
            "cell_rmsd_from_input_A": 0.007244372106320346
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1833408366061692,
              0.18340378537711033,
              0.2522481610233089
            ],
            "branch_aligned_reduced_polarization": [
              0.18334083660616918,
              0.18340378537711033,
              0.2522481610233089
            ],
            "target_residual": 0.5117491207526945,
            "energy_eV": -182.24875433618644,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0012992484377934517,
            "step_scale": 0.5328778807132417,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0016356021797748,
              1.0006592600481905,
              0.9962564621966721
            ],
            "cell_volume_ratio": 0.9985438077716966,
            "cell_rmsd_from_input_A": 0.015529149264862804
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3251833216942084,
              0.32503205292191034,
              0.38253065418741977
            ],
            "branch_aligned_reduced_polarization": [
              0.3251833216942084,
              0.32503205292191034,
              0.38253065418741977
            ],
            "target_residual": 0.27381325885396307,
            "energy_eV": -170.80677848752362,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0016297207129323764,
            "step_scale": 0.707714139310605,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.002924032989474,
              1.0009086017311448,
              0.9941832204700443
            ],
            "cell_volume_ratio": 0.9979962029269986,
            "cell_rmsd_from_input_A": 0.02482556008308192
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.47394983085455616,
              0.45629919436738936,
              0.4641696962091052
            ],
            "branch_aligned_reduced_polarization": [
              0.47394983085455616,
              0.45629919436738936,
              0.4641696962091052
            ],
            "target_residual": 0.06222686232804333,
            "energy_eV": -154.01924101270475,
            "max_atomic_step_A": 0.02496741932377683,
            "max_log_strain_component": 0.0005163442795855824,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5042101971961335,
            "cell_principal_stretches": [
              1.0030850535110853,
              1.0010553006006293,
              0.9935581724937247
            ],
            "cell_volume_ratio": 0.9976750898448675,
            "cell_rmsd_from_input_A": 0.02719232666734607
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5043190735229903,
              0.5024742040997665,
              0.497987992965685
            ],
            "branch_aligned_reduced_polarization": [
              0.5043190735229903,
              0.5024742040997665,
              0.497987992965685
            ],
            "target_residual": 0.00536882243424295,
            "energy_eV": -148.55146304238275,
            "max_atomic_step_A": 0.002421936132161677,
            "max_log_strain_component": 6.856717399993089e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.218648821152257,
            "cell_principal_stretches": [
              1.0031575879302883,
              1.0011079214557894,
              0.993588480553659
            ],
            "cell_volume_ratio": 0.9978301174729769,
            "cell_rmsd_from_input_A": 0.02739412797072591
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000403570518437,
              0.5000239488248994,
              0.4999871801776213
            ],
            "branch_aligned_reduced_polarization": [
              0.5000403570518437,
              0.5000239488248994,
              0.4999871801776213
            ],
            "target_residual": 4.8647566161105137e-05,
            "energy_eV": -148.94894244110975
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.8647566161105137e-05,
        "parent_symmetrization_rmsd_A": 0.1486683462675811,
        "parent_cell_rmsd_A": 0.02739412797072591,
        "energy_eV": -148.94894244110975,
        "reduced_polarization": [
          0.5000403570518437,
          0.5000239488248994,
          0.4999871801776213
        ],
        "cartesian_polarization_e_A2": [
          0.011237831464290774,
          0.009060301182373366,
          0.007006465967466433
        ],
        "ranking_score": 0.6556141733925848
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.3053935051794925,
        "minimum_distance_A_by_image": [
          1.0287987073788936,
          1.0015276549534666,
          0.9743428477939667,
          0.9507333833630199,
          0.9309713138531771,
          0.9153058767303425,
          0.9039500807675528,
          0.8970676055042919,
          0.8947616827701758
        ],
        "minimum_distance_A": 0.8947616827701758,
        "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": [
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435,
          417.49679166957435
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.6052614534816654e-16,
        -5.930491310434294e-16,
        -1.8934000336176766e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -185.62416030700294,
          -185.25930075392196,
          -184.48235321911767,
          -183.405044127216,
          -182.17477773984865,
          -180.960858066524,
          -179.93547643729943,
          -179.25025109183406,
          -179.0095012438827
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.4193678878918733e-17,
            1.5988664029882693e-17,
            0.0014089795350855268
          ],
          [
            1.5490057043503816e-17,
            -2.1922087167791343e-17,
            0.0011580670749596225
          ],
          [
            -5.9168029050293546e-18,
            1.662023287929594e-20,
            0.0009291193944417798
          ],
          [
            -4.886348466513006e-18,
            -1.035440508380137e-17,
            0.0007230560978656916
          ],
          [
            3.955615425272434e-18,
            -1.76008266191744e-17,
            0.0005401821571735431
          ],
          [
            9.606494604233052e-18,
            -2.21049097294636e-18,
            0.0003798602050021124
          ],
          [
            -7.24642153537303e-18,
            3.540109603290035e-18,
            0.00023898233427149075
          ],
          [
            -1.5490057043503816e-17,
            -1.0952733467456024e-17,
            0.00011414542047870944
          ],
          [
            -8.077433179337827e-18,
            -1.0753290672904472e-17,
            -2.6739222518974683e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425364e-16,
            9.166138037765524e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724327e-16,
            -1.2190963590228149e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425354e-16,
            9.166138037764916e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724323e-16,
            -1.2190963590228146e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8925833122906965e-15
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            8.881784197001252e-16,
            0.0997696136155215
          ],
          [
            6.661338147750939e-16,
            -1.2212453270876722e-15,
            0.0820025427853821
          ],
          [
            -2.7755575615628914e-16,
            0.0,
            0.06579079445644098
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            0.05119948566323773
          ],
          [
            2.220446049250313e-16,
            -9.43689570931383e-16,
            0.038250211419807334
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.02689783984596561
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.016922300542679403
          ],
          [
            -6.661338147750939e-16,
            -6.106226635438361e-16,
            0.008082618812806808
          ],
          [
            -3.3306690738754696e-16,
            -6.106226635438361e-16,
            -1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -179.0095012438827,
          -179.25025109183406,
          -179.93547643729943,
          -180.9608580665239,
          -182.17477773984865,
          -183.405044127216,
          -184.48235321911758,
          -185.25930075392193,
          -185.62416030700285
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.077433179337827e-18,
            -1.0753290672904472e-17,
            -2.6739222518974683e-17
          ],
          [
            -1.894706548239737e-18,
            1.7285042194467777e-18,
            -0.00011414542047873573
          ],
          [
            -5.950043370787946e-18,
            2.0027380619551608e-17,
            -0.00023898233427149584
          ],
          [
            2.1473340880050354e-17,
            2.3750312784513896e-17,
            -0.000379860205002159
          ],
          [
            -9.506773206957277e-18,
            7.61206665871754e-18,
            -0.0005401821571735457
          ],
          [
            1.502469052288353e-17,
            1.3030262577368017e-17,
            -0.0007230560978656889
          ],
          [
            -7.44586432992458e-18,
            4.8198675349958224e-18,
            -0.0009291193944417833
          ],
          [
            5.318474521374701e-19,
            1.5855702166848325e-17,
            -0.0011580670749595857
          ],
          [
            -7.046978740821479e-18,
            -2.7240561689166043e-17,
            -0.001408979535085488
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276146e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612165e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.7060830328136325e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.323368582633304e-16,
            2.6581800309520015e-16,
            -0.06579079445644123
          ],
          [
            2.373834701880932e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897694e-15,
            -0.09976961361551873
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276143e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612166e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.706083032813632e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.3233685826333037e-16,
            2.658180030952001e-16,
            -0.06579079445644123
          ],
          [
            2.3738347018809312e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897692e-15,
            -0.09976961361551873
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3545694267608067e-15,
          -2.0678807413199022e-15,
          -0.09976961361552528
        ],
        "actual_opposite_endpoint_branch_residual": 6.656437549590671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425364e-16,
            9.166138037765524e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724327e-16,
            -1.2190963590228149e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8934000336176766e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276146e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612165e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.7060830328136325e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.323368582633304e-16,
            2.6581800309520015e-16,
            -0.06579079445644123
          ],
          [
            2.373834701880932e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897694e-15,
            -0.09976961361551873
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.335171360644736e-16,
            8.817824792330432e-16,
            0.09976961361552149
          ],
          [
            6.913793569228214e-16,
            -1.2090136071812726e-15,
            0.0820025427853821
          ],
          [
            -2.6408911058425354e-16,
            9.166138037764916e-19,
            0.06579079445644097
          ],
          [
            -2.180960632353106e-16,
            -5.710503997527921e-16,
            0.05119948566323769
          ],
          [
            1.7655395595239432e-16,
            -9.70694018199369e-16,
            0.03825021141980737
          ],
          [
            4.2877389302724323e-16,
            -1.2190963590228146e-16,
            0.02689783984596557
          ],
          [
            -3.2343497813127697e-16,
            1.9523874020440567e-16,
            0.016922300542679437
          ],
          [
            -6.913793569228214e-16,
            -6.04048496688748e-16,
            0.008082618812806811
          ],
          [
            -3.6052614534816654e-16,
            -5.930491310434294e-16,
            -1.8925833122906965e-15
          ],
          [
            -8.45678612545082e-17,
            9.532783559276143e-17,
            -0.008082618812808674
          ],
          [
            -2.655727572729292e-16,
            1.1045196335507457e-15,
            -0.016922300542679795
          ],
          [
            9.584357608844261e-16,
            1.3098411255966934e-15,
            -0.026897839845968878
          ],
          [
            -4.243229529612166e-16,
            4.1980912212966094e-16,
            -0.038250211419807556
          ],
          [
            6.706083032813632e-16,
            7.186252221608171e-16,
            -0.051199485663237496
          ],
          [
            -3.3233685826333037e-16,
            2.658180030952001e-16,
            -0.06579079445644123
          ],
          [
            2.3738347018809312e-17,
            8.744495688028308e-16,
            -0.08200254278537948
          ],
          [
            -3.1453309799922346e-16,
            -1.5023300243897692e-15,
            -0.09976961361551873
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            8.881784197001252e-16,
            0.0997696136155215
          ],
          [
            6.661338147750939e-16,
            -1.2212453270876722e-15,
            0.0820025427853821
          ],
          [
            -2.7755575615628914e-16,
            0.0,
            0.06579079445644098
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            0.05119948566323773
          ],
          [
            2.220446049250313e-16,
            -9.43689570931383e-16,
            0.038250211419807334
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.02689783984596561
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            0.016922300542679403
          ],
          [
            -6.661338147750939e-16,
            -6.106226635438361e-16,
            0.008082618812806808
          ],
          [
            -3.3306690738754696e-16,
            -6.106226635438361e-16,
            -1.887379141862766e-15
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.008082618812808695
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-15,
            -0.01692230054267979
          ],
          [
            9.992007221626409e-16,
            1.3322676295501878e-15,
            -0.026897839845968885
          ],
          [
            -4.440892098500626e-16,
            4.440892098500626e-16,
            -0.038250211419807556
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            -0.05119948566323751
          ],
          [
            -3.3306690738754696e-16,
            2.220446049250313e-16,
            -0.0657907944564412
          ],
          [
            0.0,
            8.881784197001252e-16,
            -0.0820025427853795
          ],
          [
            -3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.09976961361551873
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.99109375405709e-15,
        "parent_symmetrization_rmsd_A": 0.3053935051794925,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -179.00950124388277,
        "reduced_polarization": [
          -1.139440656902847e-15,
          5.041375920771038e-17,
          -1.632050176840317e-15
        ],
        "cartesian_polarization_e_A2": [
          -2.552867770259856e-17,
          9.141128083612767e-19,
          -2.304835326176884e-17
        ],
        "ranking_score": 0.3053935051794965
      }
    }
  ],
  "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": 70,
      "full_response": 26,
      "energy_polarization": 44
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 95,
      "full_response": 51,
      "energy_polarization": 44
    },
    "elapsed_seconds": 1658.1738328149659
  }
}