{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "F36Sb4Xe8",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -147.04204205151925,
  "input_cartesian_polarization_e_A2": [
    0.0009034758644728226,
    -1.1545985219224623e-12,
    0.0007656614331203095
  ],
  "input_reduced_polarization": [
    0.10242410916452876,
    -1.3704110684185403e-10,
    0.0965510649609668
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.9353468624887845e-15,
      "parent_symmetrization_rmsd_A": 0.3011718178440193,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -146.33957834659947,
      "reduced_polarization": [
        -6.799517031214874e-16,
        1.924961072905051e-15,
        -3.3643937756039708e-15
      ],
      "cartesian_polarization_e_A2": [
        1.2406070044338021e-17,
        1.6218179061405924e-17,
        -2.6680042947754052e-17
      ],
      "ranking_score": 0.3011718178440272
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0004879751503661767,
      "parent_symmetrization_rmsd_A": 0.04877912563496631,
      "parent_cell_rmsd_A": 0.01121893460963697,
      "energy_eV": -146.76267453789131,
      "reduced_polarization": [
        -0.000215114793350196,
        -7.23228543593626e-13,
        -0.0004380015674136283
      ],
      "cartesian_polarization_e_A2": [
        -3.0954883878238663e-07,
        -6.0731381919745735e-15,
        -3.4750404395600997e-06
      ],
      "ranking_score": 0.5525598095881079
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.0116515534353284e-15,
      "parent_symmetrization_rmsd_A": 0.3011752449496735,
      "parent_cell_rmsd_A": 0.01121893460963697,
      "energy_eV": -146.31446443335813,
      "reduced_polarization": [
        -3.6572795844855745e-15,
        -6.836507169837894e-16,
        1.5000919719312736e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.566188335074004e-17,
        -5.76067737337549e-18,
        1.1868858974793914e-17
      ],
      "ranking_score": 0.3039799786020908
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0006123506012183693,
      "parent_symmetrization_rmsd_A": 0.367531886460635,
      "parent_cell_rmsd_A": 0.12539941544960048,
      "energy_eV": -130.6448449773851,
      "reduced_polarization": [
        0.4995081863055196,
        3.909806939022358e-13,
        -0.0003648185147905918
      ],
      "cartesian_polarization_e_A2": [
        0.00761603315537406,
        3.67009660672207e-14,
        -3.837989575292204e-05
      ],
      "ranking_score": 0.9001064415254718
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.506129415674021e-05,
      "parent_symmetrization_rmsd_A": 0.21201278928383663,
      "parent_cell_rmsd_A": 0.05546570056271718,
      "energy_eV": -142.35823686500723,
      "reduced_polarization": [
        2.0532402704003756e-05,
        -1.971907333316056e-13,
        0.4999715796765123
      ],
      "cartesian_polarization_e_A2": [
        -0.003367952482261241,
        1.1937370913976326e-13,
        0.00395251432789849
      ],
      "ranking_score": 0.7259493370128294
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.310404137551798e-06,
      "parent_symmetrization_rmsd_A": 0.16028713000509953,
      "parent_cell_rmsd_A": 0.06553686445160749,
      "energy_eV": -144.21567780859448,
      "reduced_polarization": [
        -4.5089693262846686e-06,
        -0.5000016437479958,
        -6.784548995347804e-06
      ],
      "cartesian_polarization_e_A2": [
        -2.3818333068381717e-05,
        -0.004213345468217445,
        2.4610257417618607e-06
      ],
      "ranking_score": 0.6766879669262765
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.979295202870671e-05,
      "parent_symmetrization_rmsd_A": 0.20252931045778363,
      "parent_cell_rmsd_A": 0.04747193027399053,
      "energy_eV": -142.82463644695832,
      "reduced_polarization": [
        0.4999430832911183,
        1.1682119560838478e-14,
        0.4999440768076418
      ],
      "cartesian_polarization_e_A2": [
        0.0042155439042689076,
        1.1238473744409921e-13,
        0.0039480252253301235
      ],
      "ranking_score": 0.7145568789303387
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 4.160926907907401e-06,
      "parent_symmetrization_rmsd_A": 0.4189154055198078,
      "parent_cell_rmsd_A": 0.15908486471752156,
      "energy_eV": -127.30506939876808,
      "reduced_polarization": [
        0.500001592602214,
        -0.4999962181718745,
        6.889898040998032e-07
      ],
      "cartesian_polarization_e_A2": [
        0.0075919071838035646,
        -0.004125831570679751,
        -3.554631720648346e-05
      ],
      "ranking_score": 0.9586949435530041
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0007685608308161474,
      "parent_symmetrization_rmsd_A": 0.2651782529151336,
      "parent_cell_rmsd_A": 0.08864530638275715,
      "energy_eV": -139.80923303508476,
      "reduced_polarization": [
        7.403646190777847e-05,
        -0.4995338699317311,
        0.49939343004325254
      ],
      "cartesian_polarization_e_A2": [
        -0.003388378544344542,
        -0.0042538852160439325,
        0.003950140253168611
      ],
      "ranking_score": 0.7888767011724551
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0006824877581946761,
      "parent_symmetrization_rmsd_A": 0.265900154475039,
      "parent_cell_rmsd_A": 0.08687178888184582,
      "energy_eV": -139.98590974871922,
      "reduced_polarization": [
        0.4996172221578297,
        -0.49952557541903125,
        0.4996930928795194
      ],
      "cartesian_polarization_e_A2": [
        0.004186448758970525,
        -0.00418373606367931,
        0.003947905209443894
      ],
      "ranking_score": 0.7889830772118898
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "target_residual": 0.14075797058512934,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.04625058182739455,
            "max_log_strain_component": 0.0004893439386655471,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0005776294674051,
              1.0000619523148702,
              0.9992866167574747
            ],
            "cell_volume_ratio": 0.9999257780327784,
            "cell_rmsd_from_input_A": 0.01121893460963697
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.000215114793350196,
              -7.23228543593626e-13,
              -0.0004380015674136283
            ],
            "branch_aligned_reduced_polarization": [
              -0.000215114793350196,
              -7.23228543593626e-13,
              -0.0004380015674136283
            ],
            "target_residual": 0.0004879751503661767,
            "energy_eV": -146.76267453789131
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.9353468624887845e-15,
        "parent_symmetrization_rmsd_A": 0.3011718178440193,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -146.33957834659947,
        "reduced_polarization": [
          -6.799517031214874e-16,
          1.924961072905051e-15,
          -3.3643937756039708e-15
        ],
        "cartesian_polarization_e_A2": [
          1.2406070044338021e-17,
          1.6218179061405924e-17,
          -2.6680042947754052e-17
        ],
        "ranking_score": 0.3011718178440272
      },
      "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": [
          -147.04204205151925,
          -146.99173979445476,
          -146.89501901214882,
          -146.77236197524184,
          -146.64129313946896,
          -146.51885686114355,
          -146.4216338486198,
          -146.36037002311974,
          -146.3395783465995
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009034758644728118,
            -1.154599738285892e-12,
            0.0007656614331203005
          ],
          [
            0.0007642043761058192,
            -1.1238729440104185e-12,
            0.0006497434322831068
          ],
          [
            0.0006322026218499205,
            -1.0522066562549935e-12,
            0.00053930702222356
          ],
          [
            0.0005074756370712732,
            -9.59488025620378e-13,
            0.00043627085192872016
          ],
          [
            0.00039005617095594255,
            -8.519447349978304e-13,
            0.0003392056987645865
          ],
          [
            0.0002820218585573986,
            -6.896965477179413e-13,
            0.00024734503612638357
          ],
          [
            0.00018340395230020677,
            -4.806372150408071e-13,
            0.00016082499099499427
          ],
          [
            9.059090370439926e-05,
            -2.5099181213249806e-13,
            7.86036539690409e-05
          ],
          [
            -2.0166534889802946e-17,
            6.710970646099002e-19,
            -1.3874644042150311e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.1058274912200974e-15,
            7.965356163745037e-17,
            -1.7496136024046683e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.105954299835844e-15,
            7.9653561638512e-17,
            -1.7503359872605984e-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": [
          [
            0.1024241091645276,
            -1.370412672230259e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945372,
            -1.333942400982835e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.2488804435051293e-10,
            0.0680074313321598
          ],
          [
            0.05787890144940866,
            -1.1388312515236976e-10,
            0.055014414391337696
          ],
          [
            0.04470450162314321,
            -1.0111866899364941e-10,
            0.04277435174327704
          ],
          [
            0.032439856499767106,
            -8.186118449771129e-11,
            0.031190583223562496
          ],
          [
            0.02109465943538158,
            -5.704758887503658e-11,
            0.020280274650407604
          ],
          [
            0.01037272254197441,
            -2.9790614419766825e-11,
            0.009912039672163697
          ],
          [
            -2.1094237467877974e-15,
            1.1102230246251565e-16,
            -1.7763568394002505e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -146.3395783465994,
          -146.3603700231197,
          -146.4216338486197,
          -146.51885686114352,
          -146.64129313946887,
          -146.77236197524186,
          -146.89501901214882,
          -146.99173979445482,
          -147.04204205151916
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.6770828195368405e-18,
            1.4848022554494042e-17,
            -1.561276816563144e-17
          ],
          [
            -9.059090370429695e-05,
            2.509879952679431e-13,
            -7.860365396913307e-05
          ],
          [
            -0.00018340395230017029,
            4.807306233634874e-13,
            -0.0001608249909950322
          ],
          [
            -0.0002820218585574033,
            6.896579875991039e-13,
            -0.00024734503612639327
          ],
          [
            -0.0003900561709559047,
            8.519401911114554e-13,
            -0.000339205698764581
          ],
          [
            -0.0005074756370712787,
            9.595137090642883e-13,
            -0.00043627085192873995
          ],
          [
            -0.0006322026218499201,
            1.0521621261685187e-12,
            -0.0005393070222236113
          ],
          [
            -0.000764204376105782,
            1.1238075260278079e-12,
            -0.0006497434322831584
          ],
          [
            -0.0009034758644728059,
            1.1546009965928882e-12,
            -0.0007656614331202539
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.995731016307621e-16,
            1.7623350512285898e-15,
            -1.968793683700575e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.995731016307621e-16,
            1.7623350512285898e-15,
            -1.968793683700575e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.10242410916453176,
          1.3704141052105782e-10,
          -0.09655106496096916
        ],
        "actual_opposite_endpoint_branch_residual": 1.1816400628022573e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.1058274912200974e-15,
            7.965356163745037e-17,
            -1.7496136024046683e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.105954299835844e-15,
            7.9653561638512e-17,
            -1.7503359872605984e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1024241091645276,
            -1.370412672230259e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945372,
            -1.333942400982835e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.2488804435051293e-10,
            0.0680074313321598
          ],
          [
            0.05787890144940866,
            -1.1388312515236976e-10,
            0.055014414391337696
          ],
          [
            0.04470450162314321,
            -1.0111866899364941e-10,
            0.04277435174327704
          ],
          [
            0.032439856499767106,
            -8.186118449771129e-11,
            0.031190583223562496
          ],
          [
            0.02109465943538158,
            -5.704758887503658e-11,
            0.020280274650407604
          ],
          [
            0.01037272254197441,
            -2.9790614419766825e-11,
            0.009912039672163697
          ],
          [
            -2.1094237467877974e-15,
            1.1102230246251565e-16,
            -1.7763568394002505e-15
          ],
          [
            -0.010372722541972856,
            2.9790170330556975e-11,
            -0.009912039672175355
          ],
          [
            -0.021094659435381302,
            5.705869110528283e-11,
            -0.020280274650412433
          ],
          [
            -0.03243985649976794,
            8.185663258331033e-11,
            -0.031190583223563717
          ],
          [
            -0.04470450162314038,
            1.011181138821371e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941016,
            1.1388623377683871e-10,
            -0.05501441439134014
          ],
          [
            -0.07186928738838372,
            1.2488277079114596e-10,
            -0.06800743133216625
          ],
          [
            -0.08675367608945417,
            1.3338652404826234e-10,
            -0.08193362970193557
          ],
          [
            -0.10242410916452455,
            1.3704137824532836e-10,
            -0.09655106496095978
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "target_residual": 0.40913163788530865,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0015545785916118947,
            "step_scale": 0.4292262554621773,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.002410805617261,
              0.9997199683829417,
              0.9984466291397679
            ],
            "cell_volume_ratio": 1.0005734192046172,
            "cell_rmsd_from_input_A": 0.03471635783475882
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.26678440985658036,
              -7.883849154353339e-11,
              0.05419188568861587
            ],
            "branch_aligned_reduced_polarization": [
              0.26678440985658036,
              -7.883849154353339e-11,
              0.05419188568861587
            ],
            "target_residual": 0.23942905412758805,
            "energy_eV": -145.51025735308164,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0016464171982817702,
            "step_scale": 0.6732613466819217,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0050479650271043,
              0.9993532994532748,
              0.9968041219350681
            ],
            "cell_volume_ratio": 1.001188066422107,
            "cell_rmsd_from_input_A": 0.07297395639700331
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.40163362316402296,
              -2.818259125964224e-11,
              0.01433151659718782
            ],
            "branch_aligned_reduced_polarization": [
              0.40163362316402296,
              -2.818259125964224e-11,
              0.01433151659718782
            ],
            "target_residual": 0.09940491164833311,
            "energy_eV": -140.16196141951784,
            "max_atomic_step_A": 0.09483070429586549,
            "max_log_strain_component": 0.0017772619588608098,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0079011526876396,
              0.9987832853782298,
              0.9951763179288586
            ],
            "cell_volume_ratio": 1.001818945314887,
            "cell_rmsd_from_input_A": 0.11499830163531215
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4846968797667742,
              -1.94239756823778e-12,
              -0.001181213425693094
            ],
            "branch_aligned_reduced_polarization": [
              0.4846968797667742,
              -1.94239756823778e-12,
              -0.001181213425693094
            ],
            "target_residual": 0.01534864013616847,
            "energy_eV": -132.3798182913973,
            "max_atomic_step_A": 0.016104212914765985,
            "max_log_strain_component": 0.0004396420640515738,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0086006686664524,
              0.9986151919674453,
              0.9948014996092125
            ],
            "cell_volume_ratio": 1.0019680002292997,
            "cell_rmsd_from_input_A": 0.12539941544960048
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4995081863055196,
              3.909806939022358e-13,
              -0.0003648185147905918
            ],
            "branch_aligned_reduced_polarization": [
              0.4995081863055196,
              3.909806939022358e-13,
              -0.0003648185147905918
            ],
            "target_residual": 0.0006123506012183693,
            "energy_eV": -130.6448449773851
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0006123506012183693,
        "parent_symmetrization_rmsd_A": 0.367531886460635,
        "parent_cell_rmsd_A": 0.12539941544960048,
        "energy_eV": -130.6448449773851,
        "reduced_polarization": [
          0.4995081863055196,
          3.909806939022358e-13,
          -0.0003648185147905918
        ],
        "cartesian_polarization_e_A2": [
          0.00761603315537406,
          3.67009660672207e-14,
          -3.837989575292204e-05
        ],
        "ranking_score": 0.9001064415254718
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.09655106496096677
            ],
            "target_residual": 0.41624721178919305,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002269847658253976,
            "step_scale": 0.6220502881341907,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0022724257126774,
              0.9995330603387106,
              0.9974630601899463
            ],
            "cell_volume_ratio": 0.9992629074381124,
            "cell_rmsd_from_input_A": 0.03230059822836831
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.03959570288565651,
              -5.729486824291e-11,
              0.34417894526599246
            ],
            "branch_aligned_reduced_polarization": [
              0.03959570288565651,
              -5.729486824291e-11,
              0.34417894526599246
            ],
            "target_residual": 0.16077319672578436,
            "energy_eV": -145.41331984992954,
            "max_atomic_step_A": 0.07637377684757925,
            "max_log_strain_component": 0.0015361658901461202,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0038132656155354,
              0.9992221597431914,
              0.995744050542222
            ],
            "cell_volume_ratio": 0.9987636037961543,
            "cell_rmsd_from_input_A": 0.054221876635217436
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0030511324293417915,
              -5.4912528648177925e-12,
              0.4954294563823946
            ],
            "branch_aligned_reduced_polarization": [
              0.0030511324293417915,
              -5.4912528648177925e-12,
              0.4954294563823946
            ],
            "target_residual": 0.005495386980169326,
            "energy_eV": -142.52720496146776,
            "max_atomic_step_A": 0.003642933147227413,
            "max_log_strain_component": 7.246477427000418e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0038860093528845,
              0.9992153306868233,
              0.9956540311109093
            ],
            "cell_volume_ratio": 0.9987388568428689,
            "cell_rmsd_from_input_A": 0.05546570056271718
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.0532402704003756e-05,
              -1.971907333316056e-13,
              0.4999715796765123
            ],
            "branch_aligned_reduced_polarization": [
              2.0532402704003756e-05,
              -1.971907333316056e-13,
              0.4999715796765123
            ],
            "target_residual": 3.506129415674021e-05,
            "energy_eV": -142.35823686500723
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.506129415674021e-05,
        "parent_symmetrization_rmsd_A": 0.21201278928383663,
        "parent_cell_rmsd_A": 0.05546570056271718,
        "energy_eV": -142.35823686500723,
        "reduced_polarization": [
          2.0532402704003756e-05,
          -1.971907333316056e-13,
          0.4999715796765123
        ],
        "cartesian_polarization_e_A2": [
          -0.003367952482261241,
          1.1937370913976326e-13,
          0.00395251432789849
        ],
        "ranking_score": 0.7259493370128294
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.370411006895722e-10,
              0.0965510649609668
            ],
            "target_residual": 0.5194350836689826,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004362526612965288,
            "step_scale": 0.8086368121636496,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0042052365431577,
              1.0003593068884489,
              0.9953949534234922
            ],
            "cell_volume_ratio": 0.9999399809323648,
            "cell_rmsd_from_input_A": 0.05070027209967436
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.018189041207900027,
              -0.3965179076784857,
              0.015616838421032175
            ],
            "branch_aligned_reduced_polarization": [
              0.018189041207900027,
              -0.3965179076784857,
              0.015616838421032175
            ],
            "target_residual": 0.10622273906075722,
            "energy_eV": -145.31058690012117,
            "max_atomic_step_A": 0.03132692392307762,
            "max_log_strain_component": 0.0012609001220200246,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0054423294406543,
              1.0004225370436337,
              0.9940895054738755
            ],
            "cell_volume_ratio": 0.9999219936910146,
            "cell_rmsd_from_input_A": 0.06524290157545501
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00010538027905937981,
              -0.49804340518164725,
              -0.0003042861756271178
            ],
            "branch_aligned_reduced_polarization": [
              -0.00010538027905937981,
              -0.49804340518164725,
              -0.0003042861756271178
            ],
            "target_residual": 0.0019829166303950477,
            "energy_eV": -144.2372953678783,
            "max_atomic_step_A": 0.000597983173691356,
            "max_log_strain_component": 2.6039088643545357e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0054693019144547,
              1.0004207340358082,
              0.9940642140126884
            ],
            "cell_volume_ratio": 0.9999215754325959,
            "cell_rmsd_from_input_A": 0.06553686445160749
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -4.5089693262846686e-06,
              -0.5000016437479958,
              -6.784548995347804e-06
            ],
            "branch_aligned_reduced_polarization": [
              -4.5089693262846686e-06,
              -0.5000016437479958,
              -6.784548995347804e-06
            ],
            "target_residual": 8.310404137551798e-06,
            "energy_eV": -144.21567780859448
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.310404137551798e-06,
        "parent_symmetrization_rmsd_A": 0.16028713000509953,
        "parent_cell_rmsd_A": 0.06553686445160749,
        "energy_eV": -144.21567780859448,
        "reduced_polarization": [
          -4.5089693262846686e-06,
          -0.5000016437479958,
          -6.784548995347804e-06
        ],
        "cartesian_polarization_e_A2": [
          -2.3818333068381717e-05,
          -0.004213345468217445,
          2.4610257417618607e-06
        ],
        "ranking_score": 0.6766879669262765
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.09655106496096677
            ],
            "target_residual": 0.566425310308207,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0012463150565666518,
            "step_scale": 0.6799923449955915,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0017788256387918,
              0.9999763441501325,
              0.9984002828598663
            ],
            "cell_volume_ratio": 1.0001526028612784,
            "cell_rmsd_from_input_A": 0.028238229533649073
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3631814830589908,
              -5.105526117438707e-11,
              0.36192690264943594
            ],
            "branch_aligned_reduced_polarization": [
              0.3631814830589908,
              -5.105526117438707e-11,
              0.36192690264943594
            ],
            "target_residual": 0.1943797489192626,
            "energy_eV": -145.5050543420894,
            "max_atomic_step_A": 0.06714684511784037,
            "max_log_strain_component": 0.0007744883584316329,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.002894331858259,
              0.999933435230133,
              0.9974348047194834
            ],
            "cell_volume_ratio": 1.000255125866764,
            "cell_rmsd_from_input_A": 0.04592174164187034
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49223730621335576,
              -1.4176864237455052e-12,
              0.4941990267829255
            ],
            "branch_aligned_reduced_polarization": [
              0.49223730621335576,
              -1.4176864237455052e-12,
              0.4941990267829255
            ],
            "target_residual": 0.009690753587333694,
            "energy_eV": -143.0365350461389,
            "max_atomic_step_A": 0.004638009112803835,
            "max_log_strain_component": 6.72761785163262e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0029944149402992,
              0.9999082537618371,
              0.9973748209381094
            ],
            "cell_volume_ratio": 1.0002695956100447,
            "cell_rmsd_from_input_A": 0.04747193027399053
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999430832911183,
              1.1682119560838478e-14,
              0.4999440768076418
            ],
            "branch_aligned_reduced_polarization": [
              0.4999430832911183,
              1.1682119560838478e-14,
              0.4999440768076418
            ],
            "target_residual": 7.979295202870671e-05,
            "energy_eV": -142.82463644695832
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.979295202870671e-05,
        "parent_symmetrization_rmsd_A": 0.20252931045778363,
        "parent_cell_rmsd_A": 0.04747193027399053,
        "energy_eV": -142.82463644695832,
        "reduced_polarization": [
          0.4999430832911183,
          1.1682119560838478e-14,
          0.4999440768076418
        ],
        "cartesian_polarization_e_A2": [
          0.0042155439042689076,
          1.1238473744409921e-13,
          0.0039480252253301235
        ],
        "ranking_score": 0.7145568789303387
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.370411006895722e-10,
              0.0965510649609668
            ],
            "target_residual": 0.6460562645634467,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.002044152011637755,
            "step_scale": 0.3789034913832436,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0029283702805347,
              1.0001023892515997,
              0.9974827447263486
            ],
            "cell_volume_ratio": 1.000506174141951,
            "cell_rmsd_from_input_A": 0.03860819102190307
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24786664946337836,
              -0.1857736239145567,
              0.058617920611961215
            ],
            "branch_aligned_reduced_polarization": [
              0.24786664946337833,
              -0.1857736239145567,
              0.058617920611961215
            ],
            "target_residual": 0.4071185361752564,
            "energy_eV": -145.54628986769018,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0020880251041525953,
            "step_scale": 0.5547954104383059,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0060272276738431,
              1.0001430158133424,
              0.9949025802937135
            ],
            "cell_volume_ratio": 1.0010422290551035,
            "cell_rmsd_from_input_A": 0.07977968653988816
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.37027384868640445,
              -0.34812721679270203,
              0.02268907979778007
            ],
            "branch_aligned_reduced_polarization": [
              0.37027384868640445,
              -0.34812721679270203,
              0.02268907979778007
            ],
            "target_residual": 0.20101992676309194,
            "energy_eV": -140.6813686553378,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002209083138164123,
            "step_scale": 0.8750961344342195,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.009772707304662,
              0.9999510594630351,
              0.9920633049395126
            ],
            "cell_volume_ratio": 1.0017094226499668,
            "cell_rmsd_from_input_A": 0.1307909132700618
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4612895395761664,
              -0.4672770377189498,
              -0.0006322908470038467
            ],
            "branch_aligned_reduced_polarization": [
              0.4612895395761664,
              -0.4672770377189498,
              -0.0006322908470038467
            ],
            "target_residual": 0.050692127578031536,
            "energy_eV": -132.0498247078735,
            "max_atomic_step_A": 0.045388155486769,
            "max_log_strain_component": 0.0011830357733104311,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0118932667864307,
              0.9996760279089021,
              0.9906503356881894
            ],
            "cell_volume_ratio": 1.002107644300351,
            "cell_rmsd_from_input_A": 0.16071629844913515
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4973425933959777,
              -0.49779305022017845,
              -0.0012321542461744513
            ],
            "branch_aligned_reduced_polarization": [
              0.4973425933959777,
              -0.49779305022017845,
              -0.0012321542461744513
            ],
            "target_residual": 0.0036675115918182863,
            "energy_eV": -127.61430337844052,
            "max_atomic_step_A": 0.0023769742431591916,
            "max_log_strain_component": 0.00023993661576608057,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.491055173592158,
            "cell_principal_stretches": [
              1.0119133643822533,
              0.9995040497676199,
              0.9906961860078982
            ],
            "cell_volume_ratio": 1.0020015211954043,
            "cell_rmsd_from_input_A": 0.15908486471752156
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.500001592602214,
              -0.4999962181718745,
              6.889898040998032e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.500001592602214,
              -0.4999962181718745,
              6.889898040998032e-07
            ],
            "target_residual": 4.160926907907401e-06,
            "energy_eV": -127.30506939876808
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 4.160926907907401e-06,
        "parent_symmetrization_rmsd_A": 0.4189154055198078,
        "parent_cell_rmsd_A": 0.15908486471752156,
        "energy_eV": -127.30506939876808,
        "reduced_polarization": [
          0.500001592602214,
          -0.4999962181718745,
          6.889898040998032e-07
        ],
        "cartesian_polarization_e_A2": [
          0.0075919071838035646,
          -0.004125831570679751,
          -3.554631720648346e-05
        ],
        "ranking_score": 0.9586949435530041
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.370411006895722e-10,
              0.09655106496096677
            ],
            "target_residual": 0.6505856908857097,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0026641260728497403,
            "step_scale": 0.4938217246129791,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0034115063539852,
              0.9990636920807467,
              0.9969503407248862
            ],
            "cell_volume_ratio": 0.9994148061686223,
            "cell_rmsd_from_input_A": 0.03981089668506195
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.05133064300291337,
              -0.24333678875712764,
              0.29167147280512423
            ],
            "branch_aligned_reduced_polarization": [
              0.05133064300291337,
              -0.2433367887571276,
              0.29167147280512423
            ],
            "target_residual": 0.3345319329447967,
            "energy_eV": -145.49264680451458,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0028012461184997207,
            "step_scale": 0.9337357694599313,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0070145290908947,
              0.9980564020505402,
              0.9937770306736357
            ],
            "cell_volume_ratio": 0.9988028569821452,
            "cell_rmsd_from_input_A": 0.0812307115342286
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.006599505146065223,
              -0.4673189723641133,
              0.47513295363480174
            ],
            "branch_aligned_reduced_polarization": [
              0.006599505146065223,
              -0.4673189723641133,
              0.47513295363480174
            ],
            "target_residual": 0.04159294447907544,
            "energy_eV": -140.7705907053283,
            "max_atomic_step_A": 0.017792924154459242,
            "max_log_strain_component": 0.0005095179346741277,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0076567007950192,
              0.9978889820637391,
              0.9932058633404867
            ],
            "cell_volume_ratio": 0.9986978144558922,
            "cell_rmsd_from_input_A": 0.08864530638275715
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.403646190777847e-05,
              -0.4995338699317311,
              0.49939343004325254
            ],
            "branch_aligned_reduced_polarization": [
              7.403646190777847e-05,
              -0.4995338699317311,
              0.49939343004325254
            ],
            "target_residual": 0.0007685608308161474,
            "energy_eV": -139.80923303508476
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0007685608308161474,
        "parent_symmetrization_rmsd_A": 0.2651782529151336,
        "parent_cell_rmsd_A": 0.08864530638275715,
        "energy_eV": -139.80923303508476,
        "reduced_polarization": [
          7.403646190777847e-05,
          -0.4995338699317311,
          0.49939343004325254
        ],
        "cartesian_polarization_e_A2": [
          -0.003388378544344542,
          -0.0042538852160439325,
          0.003950140253168611
        ],
        "ranking_score": 0.7888767011724551
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.10242410916452876,
              -1.3704110684185403e-10,
              0.0965510649609668
            ],
            "branch_aligned_reduced_polarization": [
              0.10242410916452876,
              -1.370411006895722e-10,
              0.09655106496096677
            ],
            "target_residual": 0.75553797523401,
            "energy_eV": -147.04204205151925,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0028574723619034276,
            "step_scale": 0.5296603426561769,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0035755433980236,
              0.9990796124418865,
              0.9974736980141479
            ],
            "cell_volume_ratio": 1.0001188635567013,
            "cell_rmsd_from_input_A": 0.039525789157864914
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3060448735870795,
              -0.258923560392383,
              0.3026533936150057
            ],
            "branch_aligned_reduced_polarization": [
              0.3060448735870795,
              -0.258923560392383,
              0.3026533936150057
            ],
            "target_residual": 0.3669906318251337,
            "energy_eV": -145.52542347531434,
            "max_atomic_step_A": 0.11910162806448507,
            "max_log_strain_component": 0.0029498107920556847,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0073261218638363,
              0.9980929251171548,
              0.9948723276257095
            ],
            "cell_volume_ratio": 1.0002496876872915,
            "cell_rmsd_from_input_A": 0.08131543373233376
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48161769709299174,
              -0.4817776978271948,
              0.4856844048809214
            ],
            "branch_aligned_reduced_polarization": [
              0.48161769709299174,
              -0.4817776978271948,
              0.4856844048809214
            ],
            "target_residual": 0.029578668331339934,
            "energy_eV": -140.7092359797835,
            "max_atomic_step_A": 0.013579905163749123,
            "max_log_strain_component": 0.0003333255664015449,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.72783243569484,
            "cell_principal_stretches": [
              1.0077823368209058,
              0.99799431627136,
              0.9945574731536166
            ],
            "cell_volume_ratio": 1.0002871627019045,
            "cell_rmsd_from_input_A": 0.08687178888184582
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4996172221578297,
              -0.49952557541903125,
              0.4996930928795194
            ],
            "branch_aligned_reduced_polarization": [
              0.4996172221578297,
              -0.49952557541903125,
              0.4996930928795194
            ],
            "target_residual": 0.0006824877581946761,
            "energy_eV": -139.98590974871922
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0006824877581946761,
        "parent_symmetrization_rmsd_A": 0.265900154475039,
        "parent_cell_rmsd_A": 0.08687178888184582,
        "energy_eV": -139.98590974871922,
        "reduced_polarization": [
          0.4996172221578297,
          -0.49952557541903125,
          0.4996930928795194
        ],
        "cartesian_polarization_e_A2": [
          0.004186448758970525,
          -0.00418373606367931,
          0.003947905209443894
        ],
        "ranking_score": 0.7889830772118898
      },
      "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,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.3011718178440193,
        "minimum_distance_A_by_image": [
          1.9175942852468317,
          1.914814614074797,
          1.9124493656295907,
          1.9070320470677489,
          1.9020682150701822,
          1.8981984826753915,
          1.8954295510770325,
          1.8937662488213889,
          1.8932114899999997
        ],
        "minimum_distance_A": 1.8932114899999997,
        "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": [
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952,
          992.604274259952
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.1058274912200974e-15,
        7.965356163745037e-17,
        -1.7496136024046683e-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": [
          -147.04204205151925,
          -146.99173979445476,
          -146.89501901214882,
          -146.77236197524184,
          -146.64129313946896,
          -146.51885686114355,
          -146.4216338486198,
          -146.36037002311974,
          -146.3395783465995
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009034758644728118,
            -1.154599738285892e-12,
            0.0007656614331203005
          ],
          [
            0.0007642043761058192,
            -1.1238729440104185e-12,
            0.0006497434322831068
          ],
          [
            0.0006322026218499205,
            -1.0522066562549935e-12,
            0.00053930702222356
          ],
          [
            0.0005074756370712732,
            -9.59488025620378e-13,
            0.00043627085192872016
          ],
          [
            0.00039005617095594255,
            -8.519447349978304e-13,
            0.0003392056987645865
          ],
          [
            0.0002820218585573986,
            -6.896965477179413e-13,
            0.00024734503612638357
          ],
          [
            0.00018340395230020677,
            -4.806372150408071e-13,
            0.00016082499099499427
          ],
          [
            9.059090370439926e-05,
            -2.5099181213249806e-13,
            7.86036539690409e-05
          ],
          [
            -2.0166534889802946e-17,
            6.710970646099002e-19,
            -1.3874644042150311e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.1058274912200974e-15,
            7.965356163745037e-17,
            -1.7496136024046683e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.105954299835844e-15,
            7.9653561638512e-17,
            -1.7503359872605984e-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": [
          [
            0.1024241091645276,
            -1.370412672230259e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945372,
            -1.333942400982835e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.2488804435051293e-10,
            0.0680074313321598
          ],
          [
            0.05787890144940866,
            -1.1388312515236976e-10,
            0.055014414391337696
          ],
          [
            0.04470450162314321,
            -1.0111866899364941e-10,
            0.04277435174327704
          ],
          [
            0.032439856499767106,
            -8.186118449771129e-11,
            0.031190583223562496
          ],
          [
            0.02109465943538158,
            -5.704758887503658e-11,
            0.020280274650407604
          ],
          [
            0.01037272254197441,
            -2.9790614419766825e-11,
            0.009912039672163697
          ],
          [
            -2.1094237467877974e-15,
            1.1102230246251565e-16,
            -1.7763568394002505e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -146.3395783465994,
          -146.3603700231197,
          -146.4216338486197,
          -146.51885686114352,
          -146.64129313946887,
          -146.77236197524186,
          -146.89501901214882,
          -146.99173979445482,
          -147.04204205151916
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.6770828195368405e-18,
            1.4848022554494042e-17,
            -1.561276816563144e-17
          ],
          [
            -9.059090370429695e-05,
            2.509879952679431e-13,
            -7.860365396913307e-05
          ],
          [
            -0.00018340395230017029,
            4.807306233634874e-13,
            -0.0001608249909950322
          ],
          [
            -0.0002820218585574033,
            6.896579875991039e-13,
            -0.00024734503612639327
          ],
          [
            -0.0003900561709559047,
            8.519401911114554e-13,
            -0.000339205698764581
          ],
          [
            -0.0005074756370712787,
            9.595137090642883e-13,
            -0.00043627085192873995
          ],
          [
            -0.0006322026218499201,
            1.0521621261685187e-12,
            -0.0005393070222236113
          ],
          [
            -0.000764204376105782,
            1.1238075260278079e-12,
            -0.0006497434322831584
          ],
          [
            -0.0009034758644728059,
            1.1546009965928882e-12,
            -0.0007656614331202539
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.995731016307621e-16,
            1.7623350512285898e-15,
            -1.968793683700575e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.995731016307621e-16,
            1.7623350512285898e-15,
            -1.968793683700575e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.10242410916453176,
          1.3704141052105782e-10,
          -0.09655106496096916
        ],
        "actual_opposite_endpoint_branch_residual": 1.1816400628022573e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.1058274912200974e-15,
            7.965356163745037e-17,
            -1.7496136024046683e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10242410916452757,
            -1.3704125121393453e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945375,
            -1.3339423987859903e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.248880559447261e-10,
            0.06800743133215978
          ],
          [
            0.0578789014494087,
            -1.1388313646338796e-10,
            0.05501441439133768
          ],
          [
            0.044704501623143184,
            -1.0111865487043574e-10,
            0.04277435174327706
          ],
          [
            0.0324398564997671,
            -8.186116341713072e-11,
            0.031190583223562492
          ],
          [
            0.021094659435381587,
            -5.704758380333502e-11,
            0.02028027465040763
          ],
          [
            0.010372722541974445,
            -2.979061127292013e-11,
            0.009912039672163702
          ],
          [
            -2.105954299835844e-15,
            7.9653561638512e-17,
            -1.7503359872605984e-15
          ],
          [
            -0.01037272254197288,
            2.9790158243288315e-11,
            -0.009912039672175327
          ],
          [
            -0.02109465943538131,
            5.705867058344543e-11,
            -0.020280274650412416
          ],
          [
            -0.03243985649976795,
            8.185658665623496e-11,
            -0.031190583223563714
          ],
          [
            -0.04470450162314039,
            1.0111811554944548e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941018,
            1.1388618487156981e-10,
            -0.055014414391340166
          ],
          [
            -0.07186928738838369,
            1.248827705990216e-10,
            -0.06800743133216626
          ],
          [
            -0.0867536760894542,
            1.3338647531578856e-10,
            -0.08193362970193559
          ],
          [
            -0.10242410916452456,
            1.370414005643626e-10,
            -0.09655106496095979
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1024241091645276,
            -1.370412672230259e-10,
            0.09655106496096566
          ],
          [
            0.08675367608945372,
            -1.333942400982835e-10,
            0.08193362970192908
          ],
          [
            0.07186928738838083,
            -1.2488804435051293e-10,
            0.0680074313321598
          ],
          [
            0.05787890144940866,
            -1.1388312515236976e-10,
            0.055014414391337696
          ],
          [
            0.04470450162314321,
            -1.0111866899364941e-10,
            0.04277435174327704
          ],
          [
            0.032439856499767106,
            -8.186118449771129e-11,
            0.031190583223562496
          ],
          [
            0.02109465943538158,
            -5.704758887503658e-11,
            0.020280274650407604
          ],
          [
            0.01037272254197441,
            -2.9790614419766825e-11,
            0.009912039672163697
          ],
          [
            -2.1094237467877974e-15,
            1.1102230246251565e-16,
            -1.7763568394002505e-15
          ],
          [
            -0.010372722541972856,
            2.9790170330556975e-11,
            -0.009912039672175355
          ],
          [
            -0.021094659435381302,
            5.705869110528283e-11,
            -0.020280274650412433
          ],
          [
            -0.03243985649976794,
            8.185663258331033e-11,
            -0.031190583223563717
          ],
          [
            -0.04470450162314038,
            1.011181138821371e-10,
            -0.04277435174327637
          ],
          [
            -0.05787890144941016,
            1.1388623377683871e-10,
            -0.05501441439134014
          ],
          [
            -0.07186928738838372,
            1.2488277079114596e-10,
            -0.06800743133216625
          ],
          [
            -0.08675367608945417,
            1.3338652404826234e-10,
            -0.08193362970193557
          ],
          [
            -0.10242410916452455,
            1.3704137824532836e-10,
            -0.09655106496095978
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.9353468624887845e-15,
        "parent_symmetrization_rmsd_A": 0.3011718178440193,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -146.33957834659947,
        "reduced_polarization": [
          -6.799517031214874e-16,
          1.924961072905051e-15,
          -3.3643937756039708e-15
        ],
        "cartesian_polarization_e_A2": [
          1.2406070044338021e-17,
          1.6218179061405924e-17,
          -2.6680042947754052e-17
        ],
        "ranking_score": 0.3011718178440272
      }
    }
  ],
  "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": 845.9014183229883
  }
}