{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 72,
  "input_formula": "H16O32Sn24",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -386.25217203226117,
  "input_cartesian_polarization_e_A2": [
    0.0009201482205886314,
    -8.515602769206225e-18,
    -0.00037050227522163865
  ],
  "input_reduced_polarization": [
    0.10223052946290177,
    -9.380649876460369e-16,
    -0.04096957800615419
  ],
  "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": 5.969722426203534e-15,
      "parent_symmetrization_rmsd_A": 0.3154477119332875,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -360.3921435474018,
      "reduced_polarization": [
        -6.600864114348962e-16,
        5.3789485744038655e-15,
        -2.5037539833767678e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.0741413577450824e-18,
        4.8829228229222836e-17,
        -1.78146195297824e-17
      ],
      "ranking_score": 0.31544771193329946
    },
    {
      "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": 0.0006852138794074538,
      "parent_symmetrization_rmsd_A": 0.01632705765787538,
      "parent_cell_rmsd_A": 0.025479951201660227,
      "energy_eV": -386.16327733010223,
      "reduced_polarization": [
        -0.00031544819103562375,
        -2.560257081117665e-15,
        0.0006082848833441163
      ],
      "cartesian_polarization_e_A2": [
        -2.801930515593527e-06,
        -2.3236093181202645e-17,
        4.65275178444814e-06
      ],
      "ranking_score": 0.5240674732171053
    },
    {
      "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": 4.061439559955196e-15,
      "parent_symmetrization_rmsd_A": 0.3154619857333285,
      "parent_cell_rmsd_A": 0.025479951201660227,
      "energy_eV": -360.4313838218049,
      "reduced_polarization": [
        -1.5581910249333844e-15,
        -7.668884885377321e-16,
        3.671404918438501e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.3795759848119391e-17,
        -6.9622458331489e-18,
        2.78489833325956e-17
      ],
      "ranking_score": 0.32183197353375165
    },
    {
      "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": 4.141916678042453e-05,
      "parent_symmetrization_rmsd_A": 0.05687490337692125,
      "parent_cell_rmsd_A": 0.12133095836361626,
      "energy_eV": -385.4089672980526,
      "reduced_polarization": [
        0.49996754160292334,
        5.72373172386658e-15,
        -2.57293574734843e-05
      ],
      "cartesian_polarization_e_A2": [
        0.004511739538010613,
        -1.432238670701846e-17,
        -0.00040774555488810865
      ],
      "ranking_score": 0.5872904813013862
    },
    {
      "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": 0.0001604060467949926,
      "parent_symmetrization_rmsd_A": 0.05119175102089729,
      "parent_cell_rmsd_A": 0.1389276264006841,
      "energy_eV": -385.4311583891506,
      "reduced_polarization": [
        0.00015156006038897382,
        2.7987647172754165e-16,
        -0.4999474676486031
      ],
      "cartesian_polarization_e_A2": [
        -5.950823201551885e-05,
        8.480008371165927e-17,
        -0.0036504724996351073
      ],
      "ranking_score": 0.5862444697146583
    },
    {
      "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": 3.3954110583510184e-05,
      "parent_symmetrization_rmsd_A": 0.07076923700249253,
      "parent_cell_rmsd_A": 0.22516404466480022,
      "energy_eV": -384.6448622467233,
      "reduced_polarization": [
        -5.0175832123242016e-06,
        -0.49998141017184006,
        -2.796647588110519e-05
      ],
      "cartesian_polarization_e_A2": [
        3.9231686966795804e-05,
        -0.004543221570136586,
        9.889340061566823e-05
      ],
      "ranking_score": 0.6271281563898596
    },
    {
      "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": 0.00030811371109471956,
      "parent_symmetrization_rmsd_A": 0.08583453213862922,
      "parent_cell_rmsd_A": 0.10921002326335429,
      "energy_eV": -384.4188495824592,
      "reduced_polarization": [
        0.4997434846762383,
        3.1994432102136263e-15,
        -0.49982931330561525
      ],
      "cartesian_polarization_e_A2": [
        0.004546830521248086,
        -3.6471972954996296e-17,
        -0.004028386492867098
      ],
      "ranking_score": 0.6137532653766572
    },
    {
      "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": 4.585017033367105e-05,
      "parent_symmetrization_rmsd_A": 0.090309695268871,
      "parent_cell_rmsd_A": 0.2595837242991826,
      "energy_eV": -383.73020059062475,
      "reduced_polarization": [
        0.49998362134346547,
        -0.4999700630320051,
        -3.062279668844635e-05
      ],
      "cartesian_polarization_e_A2": [
        0.004549124099016956,
        -0.0045901225700745165,
        -0.0003104088365306181
      ],
      "ranking_score": 0.655297326684334
    },
    {
      "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": 0.0004001608566256751,
      "parent_symmetrization_rmsd_A": 0.08269380114304381,
      "parent_cell_rmsd_A": 0.24548077702415178,
      "energy_eV": -383.76966969038506,
      "reduced_polarization": [
        9.283521610108297e-05,
        -0.5002965299706099,
        -0.5002521513639799
      ],
      "cartesian_polarization_e_A2": [
        -2.086309232691799e-05,
        -0.004425611898784488,
        -0.0035608560719781464
      ],
      "ranking_score": 0.6448643171123332
    },
    {
      "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": 3.151836235077906e-05,
      "parent_symmetrization_rmsd_A": 0.10813989941689385,
      "parent_cell_rmsd_A": 0.23472199890990458,
      "energy_eV": -382.6200985565221,
      "reduced_polarization": [
        0.4999731332107983,
        -0.49999314758835295,
        -0.49998501242988724
      ],
      "cartesian_polarization_e_A2": [
        0.004586330143548655,
        -0.004468636834166737,
        -0.0039399714848873295
      ],
      "ranking_score": 0.6668834358690716
    }
  ],
  "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "target_residual": 0.11013440641446968,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.016553277914528944,
            "max_log_strain_component": 0.002611114488310848,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0025927586409222,
              1.0004571067143182,
              0.9973343316820013
            ],
            "cell_volume_ratio": 1.0003772491159102,
            "cell_rmsd_from_input_A": 0.025479951201660227
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00031544819103562375,
              -2.560257081117665e-15,
              0.0006082848833441163
            ],
            "branch_aligned_reduced_polarization": [
              -0.00031544819103562375,
              -2.560257081117665e-15,
              0.0006082848833441163
            ],
            "target_residual": 0.0006852138794074538,
            "energy_eV": -386.16327733010223
          }
        ],
        "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": 5.969722426203534e-15,
        "parent_symmetrization_rmsd_A": 0.3154477119332875,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -360.3921435474018,
        "reduced_polarization": [
          -6.600864114348962e-16,
          5.3789485744038655e-15,
          -2.5037539833767678e-15
        ],
        "cartesian_polarization_e_A2": [
          -6.0741413577450824e-18,
          4.8829228229222836e-17,
          -1.78146195297824e-17
        ],
        "ranking_score": 0.31544771193329946
      },
      "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": [
          -386.2521720322612,
          -385.0988974905332,
          -381.8123052263876,
          -377.56886877516115,
          -373.3492455767681,
          -368.9186917903515,
          -364.818206363274,
          -361.69508665503764,
          -360.3921435474018
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009201482205886444,
            -1.1327307779328507e-17,
            -0.0003705022752216098
          ],
          [
            0.0009079782488542959,
            -6.5436531676414564e-18,
            -0.00041383405847446515
          ],
          [
            0.0009328304837374283,
            -3.398192333798552e-17,
            -0.0005260545677351445
          ],
          [
            0.0009577202296723675,
            -1.3634622959390685e-17,
            -0.0006083564068138557
          ],
          [
            0.0008175548600585213,
            -1.9161447693027994e-17,
            -0.0004984585444013875
          ],
          [
            0.0008000695169074103,
            -2.0325836981571e-17,
            -0.00010870879478778396
          ],
          [
            0.0014129064911815655,
            1.9724861864903643e-17,
            0.0005256771571638817
          ],
          [
            0.0013162387284187142,
            -3.4556069208373086e-18,
            0.0007279353678431381
          ],
          [
            3.131509625777412e-17,
            4.0490698485463245e-17,
            4.7616546297376204e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.501967948083541e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.006396848021395747
          ],
          [
            0.15617941943269073,
            2.172858786759188e-15,
            0.08696991026393895
          ],
          [
            0.14532038809091177,
            -3.8066405295781204e-16,
            0.11363900778477488
          ],
          [
            3.435289251326909e-15,
            4.460389664005667e-15,
            6.852250238264099e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.5019679480835411e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.00639684802139575
          ],
          [
            0.15617941943269073,
            2.1728587867591876e-15,
            0.08696991026393894
          ],
          [
            0.14532038809091177,
            -3.806640529578121e-16,
            0.11363900778477488
          ],
          [
            3.4416913763379853e-15,
            4.460389664005667e-15,
            6.855627177060342e-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": [
          [
            0.10223052946290323,
            -1.2212453270876722e-15,
            -0.04096957800615009
          ],
          [
            0.10091356635885018,
            -7.216449660063518e-16,
            -0.04703200569801552
          ],
          [
            0.10374919120335746,
            -3.7192471324942744e-15,
            -0.06213440137369963
          ],
          [
            0.1065671700549452,
            -1.4988010832439613e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1094237467877974e-15,
            -0.05957876986714339
          ],
          [
            0.08873397451959109,
            -2.220446049250313e-15,
            -0.006396848021395729
          ],
          [
            0.15617941943269076,
            2.220446049250313e-15,
            0.08696991026393897
          ],
          [
            0.14532038809091175,
            -3.885780586188048e-16,
            0.11363900778477487
          ],
          [
            3.4416913763379853e-15,
            4.440892098500626e-15,
            6.8833827526759706e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -360.39214354740176,
          -361.6950866550376,
          -364.81820636327404,
          -368.9186917903516,
          -373.349245576768,
          -377.5688687751611,
          -381.8123052263875,
          -385.0988974905331,
          -386.25217203226134
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.846435047981766e-17,
            5.092190943904667e-17,
            3.735704251998345e-17
          ],
          [
            -0.001316238728418665,
            3.397655748872956e-17,
            -0.0007279353678431433
          ],
          [
            -0.001412906491181603,
            1.1973892614671512e-17,
            -0.000525677157163926
          ],
          [
            -0.0008000695169073905,
            8.410968708715033e-18,
            0.00010870879478778611
          ],
          [
            -0.0008175548600585213,
            4.932020343614305e-17,
            0.0004984585444013495
          ],
          [
            -0.0009577202296723475,
            5.3990504482297975e-17,
            0.0006083564068138778
          ],
          [
            -0.0009328304837374641,
            4.85622772287389e-17,
            0.0005260545677351333
          ],
          [
            -0.0009079782488543163,
            1.4426756455801567e-17,
            0.0004138340584744641
          ],
          [
            -0.0009201482205886399,
            2.084900728402696e-17,
            0.0003705022752216245
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.3430541772026e-15,
            5.609474941878317e-15,
            5.629388380906405e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.319024587228816e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396252
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.58922808910512e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.3430541772026e-15,
            5.609474941878317e-15,
            5.629388380906405e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.3190245872288159e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396256
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.5892280891051205e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.1022305294628963,
          1.0168577178623043e-14,
          0.04096957800616381
        ],
        "actual_opposite_endpoint_branch_residual": 1.5447605186379978e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.501967948083541e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.006396848021395747
          ],
          [
            0.15617941943269073,
            2.172858786759188e-15,
            0.08696991026393895
          ],
          [
            0.14532038809091177,
            -3.8066405295781204e-16,
            0.11363900778477488
          ],
          [
            3.435289251326909e-15,
            4.460389664005667e-15,
            6.852250238264099e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.319024587228816e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396252
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.58922808910512e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.5019679480835411e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.00639684802139575
          ],
          [
            0.15617941943269073,
            2.1728587867591876e-15,
            0.08696991026393894
          ],
          [
            0.14532038809091177,
            -3.806640529578121e-16,
            0.11363900778477488
          ],
          [
            3.4416913763379853e-15,
            4.460389664005667e-15,
            6.855627177060342e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.3190245872288159e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396256
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.5892280891051205e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "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": [
          [
            0.10223052946290323,
            -1.2212453270876722e-15,
            -0.04096957800615009
          ],
          [
            0.10091356635885018,
            -7.216449660063518e-16,
            -0.04703200569801552
          ],
          [
            0.10374919120335746,
            -3.7192471324942744e-15,
            -0.06213440137369963
          ],
          [
            0.1065671700549452,
            -1.4988010832439613e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1094237467877974e-15,
            -0.05957876986714339
          ],
          [
            0.08873397451959109,
            -2.220446049250313e-15,
            -0.006396848021395729
          ],
          [
            0.15617941943269076,
            2.220446049250313e-15,
            0.08696991026393897
          ],
          [
            0.14532038809091175,
            -3.885780586188048e-16,
            0.11363900778477487
          ],
          [
            3.4416913763379853e-15,
            4.440892098500626e-15,
            6.8833827526759706e-15
          ],
          [
            -0.1453203880909063,
            3.774758283725532e-15,
            -0.11363900778477509
          ],
          [
            -0.15617941943269487,
            1.3322676295501878e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958887,
            8.881784197001252e-16,
            0.006396848021396284
          ],
          [
            -0.09095552591810407,
            5.440092820663267e-15,
            0.05957876986713817
          ],
          [
            -0.10656717005494298,
            5.995204332975845e-15,
            0.0731397123261841
          ],
          [
            -0.1037491912033614,
            5.329070518200751e-15,
            0.062134401373697745
          ],
          [
            -0.10091356635885246,
            1.5543122344752192e-15,
            0.047032005698015134
          ],
          [
            -0.10223052946290268,
            2.3314683517128287e-15,
            0.040969578006152196
          ]
        ]
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290179,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "target_residual": 0.3998738026094806,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.05733000508375456,
            "max_log_strain_component": 0.012986463115826016,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0112232425661114,
              1.0021153674713852,
              0.985271307678177
            ],
            "cell_volume_ratio": 0.9984368490366365,
            "cell_rmsd_from_input_A": 0.1227516799392388
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49892696408981374,
              3.4638362497706875e-14,
              0.012883107088817347
            ],
            "branch_aligned_reduced_polarization": [
              0.49892696408981374,
              3.4638362497706875e-14,
              0.012883107088817347
            ],
            "target_residual": 0.012927716516325884,
            "energy_eV": -385.4140848263667,
            "max_atomic_step_A": 0.0016472135496622196,
            "max_log_strain_component": 0.00023962458548474757,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0112147474367368,
              1.001875264760252,
              0.9855149944964111
            ],
            "cell_volume_ratio": 0.9984361237866913,
            "cell_rmsd_from_input_A": 0.12133095836361626
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996754160292334,
              5.72373172386658e-15,
              -2.57293574734843e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49996754160292334,
              5.72373172386658e-15,
              -2.57293574734843e-05
            ],
            "target_residual": 4.141916678042453e-05,
            "energy_eV": -385.4089672980526
          }
        ],
        "iterations": 2
      },
      "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": 4.141916678042453e-05,
        "parent_symmetrization_rmsd_A": 0.05687490337692125,
        "parent_cell_rmsd_A": 0.12133095836361626,
        "energy_eV": -385.4089672980526,
        "reduced_polarization": [
          0.49996754160292334,
          5.72373172386658e-15,
          -2.57293574734843e-05
        ],
        "cartesian_polarization_e_A2": [
          0.004511739538010613,
          -1.432238670701846e-17,
          -0.00040774555488810865
        ],
        "ranking_score": 0.5872904813013862
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.040969578006154195
            ],
            "target_residual": 0.47027652447269086,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.05092075468623991,
            "max_log_strain_component": 0.0096649184745461,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0155704686081692,
              0.9944366288656935,
              0.9907898323932258
            ],
            "cell_volume_ratio": 1.000618936350776,
            "cell_rmsd_from_input_A": 0.13563533087541654
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.007898213184557936,
              -6.72512639871895e-14,
              -0.49457253662099726
            ],
            "branch_aligned_reduced_polarization": [
              0.007898213184557936,
              -6.72512639871895e-14,
              -0.49457253662099726
            ],
            "target_residual": 0.00958327346156524,
            "energy_eV": -385.4545745550938,
            "max_atomic_step_A": 0.0011621390257041762,
            "max_log_strain_component": 0.00034272076810728256,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0160049739220067,
              0.9941894364327046,
              0.9906470323432699
            ],
            "cell_volume_ratio": 1.0006539665958099,
            "cell_rmsd_from_input_A": 0.1389276264006841
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00015156006038897382,
              2.7987647172754165e-16,
              -0.4999474676486031
            ],
            "branch_aligned_reduced_polarization": [
              0.00015156006038897382,
              2.7987647172754165e-16,
              -0.4999474676486031
            ],
            "target_residual": 0.0001604060467949926,
            "energy_eV": -385.4311583891506
          }
        ],
        "iterations": 2
      },
      "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": 0.0001604060467949926,
        "parent_symmetrization_rmsd_A": 0.05119175102089729,
        "parent_cell_rmsd_A": 0.1389276264006841,
        "energy_eV": -385.4311583891506,
        "reduced_polarization": [
          0.00015156006038897382,
          2.7987647172754165e-16,
          -0.4999474676486031
        ],
        "cartesian_polarization_e_A2": [
          -5.950823201551885e-05,
          8.480008371165927e-17,
          -0.0036504724996351073
        ],
        "ranking_score": 0.5862444697146583
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290177,
              -9.43689570931383e-16,
              -0.04096957800615419
            ],
            "target_residual": 0.5119859250763312,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.06819448531438053,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9316367472531845,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.022967814027931,
              0.99810173959507,
              0.9797512491946045
            ],
            "cell_volume_ratio": 1.0003514546078545,
            "cell_rmsd_from_input_A": 0.20657255885063744
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00010070419226857146,
              -0.46147861096527615,
              -0.02526747815049437
            ],
            "branch_aligned_reduced_polarization": [
              0.00010070419226857146,
              -0.46147861096527615,
              -0.02526747815049437
            ],
            "target_residual": 0.04606900266539959,
            "energy_eV": -384.882443365972,
            "max_atomic_step_A": 0.006800227088164782,
            "max_log_strain_component": 0.0017914937227427171,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0249808152316755,
              0.997915112997347,
              0.9779910554410239
            ],
            "cell_volume_ratio": 1.0003321325517813,
            "cell_rmsd_from_input_A": 0.22482384697496655
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0003614534291217684,
              -0.4993594568116482,
              -0.0013591015356979991
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003614534291217684,
              -0.4993594568116482,
              -0.0013591015356979991
            ],
            "target_residual": 0.0015453482267451793,
            "energy_eV": -384.64847603737564,
            "max_atomic_step_A": 0.00018896284371979974,
            "max_log_strain_component": 3.377781073014079e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0250167231177096,
              0.9979119474736838,
              0.9779576871898601
            ],
            "cell_volume_ratio": 1.000329872027215,
            "cell_rmsd_from_input_A": 0.22516404466480022
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.0175832123242016e-06,
              -0.49998141017184006,
              -2.796647588110519e-05
            ],
            "branch_aligned_reduced_polarization": [
              -5.0175832123242016e-06,
              -0.49998141017184006,
              -2.796647588110519e-05
            ],
            "target_residual": 3.3954110583510184e-05,
            "energy_eV": -384.6448622467233
          }
        ],
        "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": 3.3954110583510184e-05,
        "parent_symmetrization_rmsd_A": 0.07076923700249253,
        "parent_cell_rmsd_A": 0.22516404466480022,
        "energy_eV": -384.6448622467233,
        "reduced_polarization": [
          -5.0175832123242016e-06,
          -0.49998141017184006,
          -2.796647588110519e-05
        ],
        "cartesian_polarization_e_A2": [
          3.9231686966795804e-05,
          -0.004543221570136586,
          9.889340061566823e-05
        ],
        "ranking_score": 0.6271281563898596
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290179,
              -9.380649876460369e-16,
              -0.040969578006154195
            ],
            "target_residual": 0.6073956535959173,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.08235982000917837,
            "max_log_strain_component": 0.007596712477904997,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.010271689151085,
              0.9960623844130841,
              0.9924320696131248
            ],
            "cell_volume_ratio": 0.9986780674784245,
            "cell_rmsd_from_input_A": 0.10670653166103611
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48775225247201026,
              -1.9876034757597117e-14,
              -0.49448267405248625
            ],
            "branch_aligned_reduced_polarization": [
              0.48775225247201026,
              -1.9876034757597117e-14,
              -0.49448267405248625
            ],
            "target_residual": 0.013433101098424268,
            "energy_eV": -384.49814440682144,
            "max_atomic_step_A": 0.002318914564025904,
            "max_log_strain_component": 0.00031762078958263106,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0105802301838909,
              0.99578406212965,
              0.9923596108432051
            ],
            "cell_volume_ratio": 0.9986310126977436,
            "cell_rmsd_from_input_A": 0.10921002326335429
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4997434846762383,
              3.1994432102136263e-15,
              -0.49982931330561525
            ],
            "branch_aligned_reduced_polarization": [
              0.4997434846762383,
              3.1994432102136263e-15,
              -0.49982931330561525
            ],
            "target_residual": 0.00030811371109471956,
            "energy_eV": -384.4188495824592
          }
        ],
        "iterations": 2
      },
      "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": 0.00030811371109471956,
        "parent_symmetrization_rmsd_A": 0.08583453213862922,
        "parent_cell_rmsd_A": 0.10921002326335429,
        "energy_eV": -384.4188495824592,
        "reduced_polarization": [
          0.4997434846762383,
          3.1994432102136263e-15,
          -0.49982931330561525
        ],
        "cartesian_polarization_e_A2": [
          0.004546830521248086,
          -3.6471972954996296e-17,
          -0.004028386492867098
        ],
        "ranking_score": 0.6137532653766572
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290179,
              -9.43689570931383e-16,
              -0.04096957800615419
            ],
            "target_residual": 0.6402335964422399,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.08677235452418366,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9316367472524384,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0209965106174408,
              1.005474267132006,
              0.972684127109906
            ],
            "cell_volume_ratio": 0.9985436332667014,
            "cell_rmsd_from_input_A": 0.23247123765094466
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.46115451017163345,
              -0.4543260594541301,
              -0.016605349288865767
            ],
            "branch_aligned_reduced_polarization": [
              0.46115451017163345,
              -0.4543260594541301,
              -0.016605349288865767
            ],
            "target_residual": 0.062215902709826694,
            "energy_eV": -384.2139266547136,
            "max_atomic_step_A": 0.010330099761664659,
            "max_log_strain_component": 0.002170377435462219,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0234851683175277,
              1.0060230262310164,
              0.9696251795736733
            ],
            "cell_volume_ratio": 0.9983742232239535,
            "cell_rmsd_from_input_A": 0.2588893496166928
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4992622526094132,
              -0.4988863451569192,
              -0.0011084822716276052
            ],
            "branch_aligned_reduced_polarization": [
              0.4992622526094132,
              -0.4988863451569192,
              -0.0011084822716276052
            ],
            "target_residual": 0.0017358661435570497,
            "energy_eV": -383.7411942287616,
            "max_atomic_step_A": 0.0002477698550119982,
            "max_log_strain_component": 5.5893930038296635e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0235552675424877,
              1.006031202129271,
              0.9695474694695516
            ],
            "cell_volume_ratio": 0.998370696563243,
            "cell_rmsd_from_input_A": 0.2595837242991826
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49998362134346547,
              -0.4999700630320051,
              -3.062279668844635e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49998362134346547,
              -0.4999700630320051,
              -3.062279668844635e-05
            ],
            "target_residual": 4.585017033367105e-05,
            "energy_eV": -383.73020059062475
          }
        ],
        "iterations": 3
      },
      "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": 4.585017033367105e-05,
        "parent_symmetrization_rmsd_A": 0.090309695268871,
        "parent_cell_rmsd_A": 0.2595837242991826,
        "energy_eV": -383.73020059062475,
        "reduced_polarization": [
          0.49998362134346547,
          -0.4999700630320051,
          -3.062279668844635e-05
        ],
        "cartesian_polarization_e_A2": [
          0.004549124099016956,
          -0.0045901225700745165,
          -0.0003104088365306181
        ],
        "ranking_score": 0.655297326684334
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290177,
              -9.43689570931383e-16,
              -0.040969578006154195
            ],
            "target_residual": 0.6864109625218062,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.07687948138360694,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9316367472518307,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0255020204599228,
              0.9998872314489938,
              0.9758044723339745
            ],
            "cell_volume_ratio": 1.000576611652139,
            "cell_rmsd_from_input_A": 0.23986097236380913
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.007847574690608069,
              -0.4891579292521983,
              -0.4910969911355316
            ],
            "branch_aligned_reduced_polarization": [
              0.007847574690608069,
              -0.4891579292521983,
              -0.4910969911355316
            ],
            "target_residual": 0.016074778177810476,
            "energy_eV": -383.88320712546437,
            "max_atomic_step_A": 0.001992715267800647,
            "max_log_strain_component": 0.0004186232302960096,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0261854678170674,
              0.9997574345658813,
              0.9753157811744112
            ],
            "cell_volume_ratio": 1.00061210837509,
            "cell_rmsd_from_input_A": 0.24548077702415178
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.283521610108297e-05,
              -0.5002965299706099,
              -0.5002521513639799
            ],
            "branch_aligned_reduced_polarization": [
              9.283521610108297e-05,
              -0.5002965299706099,
              -0.5002521513639799
            ],
            "target_residual": 0.0004001608566256751,
            "energy_eV": -383.76966969038506
          }
        ],
        "iterations": 2
      },
      "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": 0.0004001608566256751,
        "parent_symmetrization_rmsd_A": 0.08269380114304381,
        "parent_cell_rmsd_A": 0.24548077702415178,
        "energy_eV": -383.76966969038506,
        "reduced_polarization": [
          9.283521610108297e-05,
          -0.5002965299706099,
          -0.5002521513639799
        ],
        "cartesian_polarization_e_A2": [
          -2.086309232691799e-05,
          -0.004425611898784488,
          -0.0035608560719781464
        ],
        "ranking_score": 0.6448643171123332
      },
      "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": [
              0.10223052946290177,
              -9.380649876460369e-16,
              -0.04096957800615419
            ],
            "branch_aligned_reduced_polarization": [
              0.10223052946290179,
              -9.43689570931383e-16,
              -0.040969578006154195
            ],
            "target_residual": 0.7867207128372881,
            "energy_eV": -386.25217203226117,
            "max_atomic_step_A": 0.09791875671107103,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9316367472510847,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0166253408999033,
              1.0092219925227084,
              0.9734578445699711
            ],
            "cell_volume_ratio": 0.9987683834102853,
            "cell_rmsd_from_input_A": 0.22420010183619463
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4523511505271705,
              -0.48266190038600554,
              -0.4928089707277477
            ],
            "branch_aligned_reduced_polarization": [
              0.4523511505271705,
              -0.48266190038600554,
              -0.4928089707277477
            ],
            "target_residual": 0.051212629851468745,
            "energy_eV": -383.0084928147075,
            "max_atomic_step_A": 0.00978220524070854,
            "max_log_strain_component": 0.0015031412625484497,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.0172217572591462,
              1.0098364556442134,
              0.9721068033041769
            ],
            "cell_volume_ratio": 0.9985749520673336,
            "cell_rmsd_from_input_A": 0.23457418086351015
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4988095569673215,
              -0.49988443592847376,
              -0.499756078211025
            ],
            "branch_aligned_reduced_polarization": [
              0.4988095569673215,
              -0.49988443592847376,
              -0.499756078211025
            ],
            "target_residual": 0.0012206586368912844,
            "energy_eV": -382.6279187419085,
            "max_atomic_step_A": 0.00022833010671103907,
            "max_log_strain_component": 3.5539099772991985e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0539594854624927,
            "cell_principal_stretches": [
              1.017224571427847,
              1.0098498150355166,
              0.9720866467630465
            ],
            "cell_volume_ratio": 0.9985702194088106,
            "cell_rmsd_from_input_A": 0.23472199890990458
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999731332107983,
              -0.49999314758835295,
              -0.49998501242988724
            ],
            "branch_aligned_reduced_polarization": [
              0.4999731332107983,
              -0.49999314758835295,
              -0.49998501242988724
            ],
            "target_residual": 3.151836235077906e-05,
            "energy_eV": -382.6200985565221
          }
        ],
        "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": 3.151836235077906e-05,
        "parent_symmetrization_rmsd_A": 0.10813989941689385,
        "parent_cell_rmsd_A": 0.23472199890990458,
        "energy_eV": -382.6200985565221,
        "reduced_polarization": [
          0.4999731332107983,
          -0.49999314758835295,
          -0.49998501242988724
        ],
        "cartesian_polarization_e_A2": [
          0.004586330143548655,
          -0.004468636834166737,
          -0.0039399714848873295
        ],
        "ranking_score": 0.6668834358690716
      },
      "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,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71
        ],
        "endpoint_rmsd_A": 0.3154477119332875,
        "minimum_distance_A_by_image": [
          0.9765731061964062,
          1.0372093360620538,
          1.0955223752066474,
          1.1542116370414075,
          1.2132225238283556,
          1.2725102916308129,
          1.3308495285653228,
          1.3883607786434586,
          1.4460781544012684
        ],
        "minimum_distance_A": 0.9765731061964062,
        "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": [
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403,
          1293.1585612849403
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        3.435289251326909e-15,
        4.460389664005667e-15,
        6.852250238264099e-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": [
          -386.2521720322612,
          -385.0988974905332,
          -381.8123052263876,
          -377.56886877516115,
          -373.3492455767681,
          -368.9186917903515,
          -364.818206363274,
          -361.69508665503764,
          -360.3921435474018
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009201482205886444,
            -1.1327307779328507e-17,
            -0.0003705022752216098
          ],
          [
            0.0009079782488542959,
            -6.5436531676414564e-18,
            -0.00041383405847446515
          ],
          [
            0.0009328304837374283,
            -3.398192333798552e-17,
            -0.0005260545677351445
          ],
          [
            0.0009577202296723675,
            -1.3634622959390685e-17,
            -0.0006083564068138557
          ],
          [
            0.0008175548600585213,
            -1.9161447693027994e-17,
            -0.0004984585444013875
          ],
          [
            0.0008000695169074103,
            -2.0325836981571e-17,
            -0.00010870879478778396
          ],
          [
            0.0014129064911815655,
            1.9724861864903643e-17,
            0.0005256771571638817
          ],
          [
            0.0013162387284187142,
            -3.4556069208373086e-18,
            0.0007279353678431381
          ],
          [
            3.131509625777412e-17,
            4.0490698485463245e-17,
            4.7616546297376204e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.501967948083541e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.006396848021395747
          ],
          [
            0.15617941943269073,
            2.172858786759188e-15,
            0.08696991026393895
          ],
          [
            0.14532038809091177,
            -3.8066405295781204e-16,
            0.11363900778477488
          ],
          [
            3.435289251326909e-15,
            4.460389664005667e-15,
            6.852250238264099e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.5019679480835411e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.00639684802139575
          ],
          [
            0.15617941943269073,
            2.1728587867591876e-15,
            0.08696991026393894
          ],
          [
            0.14532038809091177,
            -3.806640529578121e-16,
            0.11363900778477488
          ],
          [
            3.4416913763379853e-15,
            4.460389664005667e-15,
            6.855627177060342e-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": [
          [
            0.10223052946290323,
            -1.2212453270876722e-15,
            -0.04096957800615009
          ],
          [
            0.10091356635885018,
            -7.216449660063518e-16,
            -0.04703200569801552
          ],
          [
            0.10374919120335746,
            -3.7192471324942744e-15,
            -0.06213440137369963
          ],
          [
            0.1065671700549452,
            -1.4988010832439613e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1094237467877974e-15,
            -0.05957876986714339
          ],
          [
            0.08873397451959109,
            -2.220446049250313e-15,
            -0.006396848021395729
          ],
          [
            0.15617941943269076,
            2.220446049250313e-15,
            0.08696991026393897
          ],
          [
            0.14532038809091175,
            -3.885780586188048e-16,
            0.11363900778477487
          ],
          [
            3.4416913763379853e-15,
            4.440892098500626e-15,
            6.8833827526759706e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -360.39214354740176,
          -361.6950866550376,
          -364.81820636327404,
          -368.9186917903516,
          -373.349245576768,
          -377.5688687751611,
          -381.8123052263875,
          -385.0988974905331,
          -386.25217203226134
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.846435047981766e-17,
            5.092190943904667e-17,
            3.735704251998345e-17
          ],
          [
            -0.001316238728418665,
            3.397655748872956e-17,
            -0.0007279353678431433
          ],
          [
            -0.001412906491181603,
            1.1973892614671512e-17,
            -0.000525677157163926
          ],
          [
            -0.0008000695169073905,
            8.410968708715033e-18,
            0.00010870879478778611
          ],
          [
            -0.0008175548600585213,
            4.932020343614305e-17,
            0.0004984585444013495
          ],
          [
            -0.0009577202296723475,
            5.3990504482297975e-17,
            0.0006083564068138778
          ],
          [
            -0.0009328304837374641,
            4.85622772287389e-17,
            0.0005260545677351333
          ],
          [
            -0.0009079782488543163,
            1.4426756455801567e-17,
            0.0004138340584744641
          ],
          [
            -0.0009201482205886399,
            2.084900728402696e-17,
            0.0003705022752216245
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.3430541772026e-15,
            5.609474941878317e-15,
            5.629388380906405e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.319024587228816e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396252
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.58922808910512e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.3430541772026e-15,
            5.609474941878317e-15,
            5.629388380906405e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.3190245872288159e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396256
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.5892280891051205e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.1022305294628963,
          1.0168577178623043e-14,
          0.04096957800616381
        ],
        "actual_opposite_endpoint_branch_residual": 1.5447605186379978e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.501967948083541e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.006396848021395747
          ],
          [
            0.15617941943269073,
            2.172858786759188e-15,
            0.08696991026393895
          ],
          [
            0.14532038809091177,
            -3.8066405295781204e-16,
            0.11363900778477488
          ],
          [
            3.435289251326909e-15,
            4.460389664005667e-15,
            6.852250238264099e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.319024587228816e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396252
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.58922808910512e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10223052946290319,
            -1.2477978506117098e-15,
            -0.04096957800615011
          ],
          [
            0.10091356635885018,
            -7.208382182951115e-16,
            -0.0470320056980155
          ],
          [
            0.10374919120335745,
            -3.74339355183513e-15,
            -0.06213440137369966
          ],
          [
            0.1065671700549452,
            -1.5019679480835411e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1107939955160663e-15,
            -0.05957876986714336
          ],
          [
            0.08873397451959109,
            -2.2390612307518506e-15,
            -0.00639684802139575
          ],
          [
            0.15617941943269073,
            2.1728587867591876e-15,
            0.08696991026393894
          ],
          [
            0.14532038809091177,
            -3.806640529578121e-16,
            0.11363900778477488
          ],
          [
            3.4416913763379853e-15,
            4.460389664005667e-15,
            6.855627177060342e-15
          ],
          [
            -0.1453203880909063,
            3.742802458585195e-15,
            -0.11363900778477508
          ],
          [
            -0.15617941943269487,
            1.3190245872288159e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958889,
            9.265386692723142e-16,
            0.006396848021396256
          ],
          [
            -0.09095552591810406,
            5.433033606772872e-15,
            0.059578769867138164
          ],
          [
            -0.106567170054943,
            5.947506394184604e-15,
            0.07313971232618412
          ],
          [
            -0.1037491912033614,
            5.3495416852196254e-15,
            0.06213440137369774
          ],
          [
            -0.10091356635885244,
            1.5892280891051205e-15,
            0.04703200569801515
          ],
          [
            -0.1022305294629027,
            2.296692822620464e-15,
            0.04096957800615216
          ]
        ],
        "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": [
          [
            0.10223052946290323,
            -1.2212453270876722e-15,
            -0.04096957800615009
          ],
          [
            0.10091356635885018,
            -7.216449660063518e-16,
            -0.04703200569801552
          ],
          [
            0.10374919120335746,
            -3.7192471324942744e-15,
            -0.06213440137369963
          ],
          [
            0.1065671700549452,
            -1.4988010832439613e-15,
            -0.07313971232618088
          ],
          [
            0.09095552591810407,
            -2.1094237467877974e-15,
            -0.05957876986714339
          ],
          [
            0.08873397451959109,
            -2.220446049250313e-15,
            -0.006396848021395729
          ],
          [
            0.15617941943269076,
            2.220446049250313e-15,
            0.08696991026393897
          ],
          [
            0.14532038809091175,
            -3.885780586188048e-16,
            0.11363900778477487
          ],
          [
            3.4416913763379853e-15,
            4.440892098500626e-15,
            6.8833827526759706e-15
          ],
          [
            -0.1453203880909063,
            3.774758283725532e-15,
            -0.11363900778477509
          ],
          [
            -0.15617941943269487,
            1.3322676295501878e-15,
            -0.0869699102639454
          ],
          [
            -0.08873397451958887,
            8.881784197001252e-16,
            0.006396848021396284
          ],
          [
            -0.09095552591810407,
            5.440092820663267e-15,
            0.05957876986713817
          ],
          [
            -0.10656717005494298,
            5.995204332975845e-15,
            0.0731397123261841
          ],
          [
            -0.1037491912033614,
            5.329070518200751e-15,
            0.062134401373697745
          ],
          [
            -0.10091356635885246,
            1.5543122344752192e-15,
            0.047032005698015134
          ],
          [
            -0.10223052946290268,
            2.3314683517128287e-15,
            0.040969578006152196
          ]
        ]
      },
      "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": 5.969722426203534e-15,
        "parent_symmetrization_rmsd_A": 0.3154477119332875,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -360.3921435474018,
        "reduced_polarization": [
          -6.600864114348962e-16,
          5.3789485744038655e-15,
          -2.5037539833767678e-15
        ],
        "cartesian_polarization_e_A2": [
          -6.0741413577450824e-18,
          4.8829228229222836e-17,
          -1.78146195297824e-17
        ],
        "ranking_score": 0.31544771193329946
      }
    }
  ],
  "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": 51,
      "full_response": 19,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 44,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1160.3519991409848
  }
}
