{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "Bi8Mo4O24",
  "input_spacegroup": "Pca2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -225.1007202789811,
  "input_cartesian_polarization_e_A2": [
    5.281408783138899e-17,
    -4.68371916858161e-17,
    0.04690742957403356
  ],
  "input_reduced_polarization": [
    4.9520776135869594e-15,
    -1.4752580002832295e-15,
    4.378376163503677
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        4.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        4.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        4.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        4.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        4.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        4.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbca",
      "spacegroup_number": 61,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3933595811519085e-15,
      "parent_symmetrization_rmsd_A": 0.41604347364402255,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -223.31544596907565,
      "reduced_polarization": [
        1.5474274432196972e-15,
        -1.82492411773185e-15,
        -5.736163511283064e-17
      ],
      "cartesian_polarization_e_A2": [
        1.6503369954193806e-17,
        -5.793855766100953e-17,
        -6.145399021982078e-19
      ],
      "ranking_score": 0.41604347364402733
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.308947215953567e-15,
      "parent_symmetrization_rmsd_A": 0.44194091248380646,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -223.48538017525598,
      "reduced_polarization": [
        6.360426318376483e-15,
        -2.577538808621263e-15,
        -2.5143548166777236e-15
      ],
      "cartesian_polarization_e_A2": [
        6.783417798262157e-17,
        -8.183292633142587e-17,
        -2.6937366065199512e-17
      ],
      "ranking_score": 0.44194091248382106
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pca2_1",
      "spacegroup_number": 29,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0007025191486560445,
      "parent_symmetrization_rmsd_A": 0.0052217822057415925,
      "parent_cell_rmsd_A": 0.005853854659316254,
      "energy_eV": -225.12517211311763,
      "reduced_polarization": [
        -2.440000481184685e-15,
        2.4579636565606216e-15,
        4.499297480851344
      ],
      "cartesian_polarization_e_A2": [
        -6.386126423863832e-17,
        9.410646180061034e-17,
        0.048201889168305485
      ],
      "ranking_score": 0.5080902841678827
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pbca",
      "spacegroup_number": 61,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999556,
      "parent_symmetrization_rmsd_A": 0.4160443520501261,
      "parent_cell_rmsd_A": 0.005853854659316254,
      "energy_eV": -223.37194620024385,
      "reduced_polarization": [
        2.47906319048696e-17,
        2.2871200884834224e-15,
        4.626133349594557e-15
      ],
      "cartesian_polarization_e_A2": [
        2.646413436462608e-19,
        7.272344123399247e-17,
        4.9560707631353495e-17
      ],
      "ranking_score": 1.4175078157149463
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pca2_1",
      "spacegroup_number": 29,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.5669982294473925e-05,
      "parent_symmetrization_rmsd_A": 0.015927180116404836,
      "parent_cell_rmsd_A": 0.017944864923005056,
      "energy_eV": -224.94441125779036,
      "reduced_polarization": [
        -6.307591883108747e-15,
        2.3132268986649997e-15,
        3.9999743300177055
      ],
      "cartesian_polarization_e_A2": [
        4.896623568370209e-17,
        2.91769772183608e-17,
        0.04285623491369119
      ],
      "ranking_score": 0.5204647363117451
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        4.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.2145421757023927e-05,
      "parent_symmetrization_rmsd_A": 0.020217238853334846,
      "parent_cell_rmsd_A": 0.021622817558041907,
      "energy_eV": -225.00056669405873,
      "reduced_polarization": [
        0.4999781247590337,
        2.7334050428383295e-15,
        4.500003448700837
      ],
      "cartesian_polarization_e_A2": [
        0.004978100091656983,
        -2.9641829618766907e-18,
        0.048170962833804266
      ],
      "ranking_score": 0.5256672340863594
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        4.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 9.011443625588015e-05,
      "parent_symmetrization_rmsd_A": 0.079055984368704,
      "parent_cell_rmsd_A": 0.03759148398567664,
      "energy_eV": -224.18423745923678,
      "reduced_polarization": [
        -2.714550916785634e-15,
        -0.5000800291149163,
        4.499958575944339
      ],
      "cartesian_polarization_e_A2": [
        -3.787843639120192e-16,
        -0.015720812963162054,
        0.04814026521807003
      ],
      "ranking_score": 0.588634084237635
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        4.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 4.7133969958165427e-05,
      "parent_symmetrization_rmsd_A": 0.02475185903919966,
      "parent_cell_rmsd_A": 0.027409945595534006,
      "energy_eV": -224.8526897379686,
      "reduced_polarization": [
        0.4999751537883876,
        3.632063441875169e-16,
        3.999959946574522
      ],
      "cartesian_polarization_e_A2": [
        0.004999038322373762,
        -1.3930635893042233e-16,
        0.04281765099883122
      ],
      "ranking_score": 0.5316986133779995
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        4.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00039637303382060213,
      "parent_symmetrization_rmsd_A": 0.07981828244114338,
      "parent_cell_rmsd_A": 0.03797473232659249,
      "energy_eV": -223.98843520255465,
      "reduced_polarization": [
        1.7755596110227306e-14,
        -0.5001116263178784,
        3.999619669686855
      ],
      "cartesian_polarization_e_A2": [
        5.416211732720478e-17,
        -0.01564093294000952,
        0.04278349959156348
      ],
      "ranking_score": 0.5901047115904328
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        4.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00046619733601880155,
      "parent_symmetrization_rmsd_A": 0.081654681393786,
      "parent_cell_rmsd_A": 0.043197152102066455,
      "energy_eV": -224.03748899513258,
      "reduced_polarization": [
        0.4995698764693209,
        -0.5000853731693757,
        4.499841743479067
      ],
      "cartesian_polarization_e_A2": [
        0.004973719955786658,
        -0.015722046159822162,
        0.04809988116536811
      ],
      "ranking_score": 0.5933863640913403
    },
    {
      "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,
        4.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0005993791110239097,
      "parent_symmetrization_rmsd_A": 0.08221145310893668,
      "parent_cell_rmsd_A": 0.04343139124998367,
      "energy_eV": -223.87954228616405,
      "reduced_polarization": [
        0.49961383608654514,
        -0.5001176946729221,
        3.999556964206138
      ],
      "cartesian_polarization_e_A2": [
        0.0049953949078432895,
        -0.015641719852904967,
        0.04274382710499355
      ],
      "ranking_score": 0.5942680591434805
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "target_residual": 0.12162383649632336,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.007449356115943948,
            "max_log_strain_component": 0.0012428806571556398,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.000304035491583,
              0.9997172645430367,
              0.9987578913991171
            ],
            "cell_volume_ratio": 0.9987790791219409,
            "cell_rmsd_from_input_A": 0.005853854659316254
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.440000481184685e-15,
              2.4579636565606216e-15,
              4.499297480851344
            ],
            "branch_aligned_reduced_polarization": [
              -2.440000481184685e-15,
              2.4579636565606216e-15,
              4.499297480851344
            ],
            "target_residual": 0.0007025191486560445,
            "energy_eV": -225.12517211311763
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pca2_1",
        "spacegroup_number": 29,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          4.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0007025191486560445,
        "parent_symmetrization_rmsd_A": 0.0052217822057415925,
        "parent_cell_rmsd_A": 0.005853854659316254,
        "energy_eV": -225.12517211311763,
        "reduced_polarization": [
          -2.440000481184685e-15,
          2.4579636565606216e-15,
          4.499297480851344
        ],
        "cartesian_polarization_e_A2": [
          -6.386126423863832e-17,
          9.410646180061034e-17,
          0.048201889168305485
        ],
        "ranking_score": 0.5080902841678827
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "target_residual": 0.37837616350367664,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.02317521687295831,
            "max_log_strain_component": 0.0038666467716769954,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.003874131894638,
              1.0008801116958823,
              0.9990547253791446
            ],
            "cell_volume_ratio": 1.0038078813495763,
            "cell_rmsd_from_input_A": 0.018209699151444415
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.246451803644515e-16,
              4.226451213815871e-15,
              3.994068988487879
            ],
            "branch_aligned_reduced_polarization": [
              7.246451803644515e-16,
              4.226451213815871e-15,
              3.994068988487879
            ],
            "target_residual": 0.005931011512120943,
            "energy_eV": -224.94115993508152,
            "max_atomic_step_A": 0.0003579005874555345,
            "max_log_strain_component": 5.623887510359603e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0038176767302172,
              1.0008673052636683,
              0.999068467625605
            ],
            "cell_volume_ratio": 1.0037523934138246,
            "cell_rmsd_from_input_A": 0.017944864923005056
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.307591883108747e-15,
              2.3132268986649997e-15,
              3.9999743300177055
            ],
            "branch_aligned_reduced_polarization": [
              -6.307591883108747e-15,
              2.3132268986649997e-15,
              3.9999743300177055
            ],
            "target_residual": 2.5669982294473925e-05,
            "energy_eV": -224.94441125779036
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pbca",
        "spacegroup_number": 61,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.3933595811519085e-15,
        "parent_symmetrization_rmsd_A": 0.41604347364402255,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -223.31544596907565,
        "reduced_polarization": [
          1.5474274432196972e-15,
          -1.82492411773185e-15,
          -5.736163511283064e-17
        ],
        "cartesian_polarization_e_A2": [
          1.6503369954193806e-17,
          -5.793855766100953e-17,
          -6.145399021982078e-19
        ],
        "ranking_score": 0.41604347364402733
      },
      "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": [
          -225.10072027898107,
          -224.85091148681556,
          -224.57030174642586,
          -224.2931996300777,
          -224.01467418569393,
          -223.74553047732977,
          -223.5192443858337,
          -223.36843637393324,
          -223.31544596907565
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.833515497403916e-17,
            -5.270505655841834e-17,
            0.04690742957403359
          ],
          [
            -1.5726935131524029e-18,
            -5.497819340095795e-18,
            0.041291375274081735
          ],
          [
            -9.621183845167641e-18,
            1.0509293123183115e-16,
            0.03569229453856427
          ],
          [
            -2.3382252085251167e-17,
            4.646714615330965e-17,
            0.030099471611363542
          ],
          [
            5.159161598293019e-18,
            -1.1735729745204486e-17,
            0.024369577422088784
          ],
          [
            -2.5286995384268727e-17,
            -1.2793002695222906e-17,
            0.018438910475864337
          ],
          [
            4.831324384338088e-17,
            -4.017637210070004e-17,
            0.012355417274512505
          ],
          [
            -7.758731464150814e-17,
            -4.519841861328754e-17,
            0.0061929039118598555
          ],
          [
            6.938353734495895e-19,
            -6.650246855615875e-17,
            -3.268295006744447e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966483e-16,
            -1.7316798197455516e-16,
            3.8541692627387882
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            3.331546687753504
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            2.8095082214908373
          ],
          [
            4.837453358533648e-16,
            -3.69647038445685e-16,
            2.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            1.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            1.1532643117757466
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            0.578050494703845
          ],
          [
            6.505700962485214e-17,
            -2.0946665511922154e-15,
            -3.0506521211619393e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966562e-16,
            -1.7316798197455511e-16,
            4.854169262738788
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            5.331546687753503
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            5.809508221490837
          ],
          [
            4.837453358533646e-16,
            -3.69647038445685e-16,
            6.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            6.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            7.153264311775747
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            7.578050494703845
          ],
          [
            6.505700962485252e-17,
            -2.0946665511922154e-15,
            7.999999999999997
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ]
        ],
        "folded_reduced_polarization": [
          [
            8.326672684688674e-15,
            -1.6653345369377348e-15,
            0.3783761635036802
          ],
          [
            -1.6653345369377348e-16,
            -1.6653345369377348e-16,
            -0.1458307372612122
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-15,
            0.3315466877535034
          ],
          [
            -2.1649348980190553e-15,
            1.4432899320127035e-15,
            -0.19049177850916266
          ],
          [
            4.440892098500626e-16,
            -3.885780586188048e-16,
            0.27467541642051785
          ],
          [
            -2.3869795029440866e-15,
            -3.885780586188048e-16,
            -0.27889767481112315
          ],
          [
            4.551914400963142e-15,
            -1.27675647831893e-15,
            0.15326431177574662
          ],
          [
            -7.271960811294775e-15,
            -1.4432899320127035e-15,
            -0.4219495052961548
          ],
          [
            1.1102230246251565e-16,
            -2.1094237467877974e-15,
            -3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -223.31544596907568,
          -223.36843637393326,
          -223.51924438583364,
          -223.7455304773298,
          -224.01467418569396,
          -224.29319963007765,
          -224.57030174642588,
          -224.85091148681553,
          -225.10072027898104
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.322708507748994e-18,
            -5.053764701088057e-17,
            -9.409729255163956e-18
          ],
          [
            -8.33725800648902e-17,
            -1.3638821055237644e-16,
            -0.006192903911859653
          ],
          [
            -1.19002678480511e-16,
            -9.155983747159534e-17,
            -0.012355417274512502
          ],
          [
            -7.646065815414476e-17,
            -1.4289043919498974e-16,
            -0.018438910475864108
          ],
          [
            -9.325147419162483e-17,
            -1.255511628146876e-16,
            -0.024369577422088617
          ],
          [
            -6.434827492049621e-17,
            -1.7228262720550189e-16,
            -0.030099471611363546
          ],
          [
            -7.992322706545509e-17,
            -1.3839702915741144e-16,
            -0.03569229453856428
          ],
          [
            -1.917562733536537e-16,
            -6.227337675608506e-17,
            -0.04129137527408174
          ],
          [
            -1.2011281507803035e-16,
            -8.521619977148482e-17,
            -0.046907429574033564
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.990802024077943e-16,
            -1.5918133727661028e-15,
            -8.783114881792563e-16
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            -0.5780504947038261
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            -1.1532643117757464
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            -1.7211023251888555
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            -2.2746754164205027
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            -2.809508221490838
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            -3.331546687753505
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            -3.8541692627387887
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            -4.3783761635036775
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.990802024077943e-16,
            -1.5918133727661028e-15,
            7.999999999999999
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            8.421949505296174
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            8.846735688224253
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            9.278897674811144
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            9.725324583579498
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            10.190491778509163
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            10.668453312246495
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            11.14583073726121
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            11.621623836496322
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          8
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.152572691845756e-15,
          -2.5292515828783585e-15,
          -4.3783761635036855
        ],
        "actual_opposite_endpoint_branch_residual": 7.757671497808989e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966483e-16,
            -1.7316798197455516e-16,
            3.8541692627387882
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            3.331546687753504
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            2.8095082214908373
          ],
          [
            4.837453358533648e-16,
            -3.69647038445685e-16,
            2.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            1.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            1.1532643117757466
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            0.578050494703845
          ],
          [
            6.505700962485214e-17,
            -2.0946665511922154e-15,
            -3.0506521211619393e-15
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            -0.5780504947038261
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            -1.1532643117757464
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            -1.7211023251888555
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            -2.2746754164205027
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            -2.809508221490838
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            -3.331546687753505
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            -3.8541692627387887
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            -4.3783761635036775
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966562e-16,
            -1.7316798197455511e-16,
            4.854169262738788
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            5.331546687753503
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            5.809508221490837
          ],
          [
            4.837453358533646e-16,
            -3.69647038445685e-16,
            6.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            6.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            7.153264311775747
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            7.578050494703845
          ],
          [
            6.505700962485252e-17,
            -2.0946665511922154e-15,
            7.999999999999997
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            8.421949505296173
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            8.846735688224253
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            9.278897674811144
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            9.725324583579496
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            10.190491778509163
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            10.668453312246495
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            11.14583073726121
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            11.621623836496322
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ],
          [
            0,
            0,
            9
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            11
          ],
          [
            0,
            0,
            12
          ],
          [
            0,
            0,
            13
          ],
          [
            0,
            0,
            14
          ],
          [
            0,
            0,
            15
          ],
          [
            0,
            0,
            16
          ]
        ],
        "folded_reduced_polarization": [
          [
            8.326672684688674e-15,
            -1.6653345369377348e-15,
            0.3783761635036802
          ],
          [
            -1.6653345369377348e-16,
            -1.6653345369377348e-16,
            -0.1458307372612122
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-15,
            0.3315466877535034
          ],
          [
            -2.1649348980190553e-15,
            1.4432899320127035e-15,
            -0.19049177850916266
          ],
          [
            4.440892098500626e-16,
            -3.885780586188048e-16,
            0.27467541642051785
          ],
          [
            -2.3869795029440866e-15,
            -3.885780586188048e-16,
            -0.27889767481112315
          ],
          [
            4.551914400963142e-15,
            -1.27675647831893e-15,
            0.15326431177574662
          ],
          [
            -7.271960811294775e-15,
            -1.4432899320127035e-15,
            -0.4219495052961548
          ],
          [
            1.1102230246251565e-16,
            -2.1094237467877974e-15,
            -3.552713678800501e-15
          ],
          [
            -7.827072323607354e-15,
            -4.274358644806853e-15,
            0.4219495052961726
          ],
          [
            -1.1157741397482823e-14,
            -2.886579864025407e-15,
            -0.15326431177574662
          ],
          [
            -7.16093850883226e-15,
            -4.496403249731884e-15,
            0.27889767481114447
          ],
          [
            -8.770761894538737e-15,
            -3.941291737419306e-15,
            -0.27467541642050364
          ],
          [
            -6.050715484207103e-15,
            -5.440092820663267e-15,
            0.19049177850916266
          ],
          [
            -7.494005416219807e-15,
            -4.385380947269368e-15,
            -0.33154668775350515
          ],
          [
            -1.7985612998927536e-14,
            -1.942890293094024e-15,
            0.14583073726121043
          ],
          [
            -1.1268763699945339e-14,
            -2.6645352591003757e-15,
            -0.37837616350367753
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "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,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9404924595819466e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "target_residual": 0.5145797874033525,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.027400719353423336,
            "max_log_strain_component": 0.007439925350532445,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0067150139211312,
              1.0003040354915815,
              0.991815452559168
            ],
            "cell_volume_ratio": 0.9987790791219386,
            "cell_rmsd_from_input_A": 0.021493648168804915
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49916128125843584,
              8.771679047426003e-15,
              4.493547421327346
            ],
            "branch_aligned_reduced_polarization": [
              0.49916128125843584,
              8.771679047426003e-15,
              4.493547421327346
            ],
            "target_residual": 0.0065068595077995995,
            "energy_eV": -225.00049062351096,
            "max_atomic_step_A": 0.0004046619496899619,
            "max_log_strain_component": 6.86163185579364e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0066900002839911,
              1.0003208232194694,
              0.9917565597700079
            ],
            "cell_volume_ratio": 0.9987117185834267,
            "cell_rmsd_from_input_A": 0.021622817558041907
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999781247590337,
              2.7334050428383295e-15,
              4.500003448700837
            ],
            "branch_aligned_reduced_polarization": [
              0.4999781247590337,
              2.7334050428383295e-15,
              4.500003448700837
            ],
            "target_residual": 2.2145421757023927e-05,
            "energy_eV": -225.00056669405873
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          4.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.2145421757023927e-05,
        "parent_symmetrization_rmsd_A": 0.020217238853334846,
        "parent_cell_rmsd_A": 0.021622817558041907,
        "energy_eV": -225.00056669405873,
        "reduced_polarization": [
          0.4999781247590337,
          2.7334050428383295e-15,
          4.500003448700837
        ],
        "cartesian_polarization_e_A2": [
          0.004978100091656983,
          -2.9641829618766907e-18,
          0.048170962833804266
        ],
        "ranking_score": 0.5256672340863594
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9520776135869594e-15,
              -1.4988010832439613e-15,
              4.378376163503677
            ],
            "target_residual": 0.5145797874033559,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.10602945437769891,
            "max_log_strain_component": 0.004272113398022035,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0038796219393646,
              0.9997172645430287,
              0.9952005473679794
            ],
            "cell_volume_ratio": 0.9987790791219474,
            "cell_rmsd_from_input_A": 0.03592406542753302
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0245965608510695e-14,
              -0.5034785497835803,
              4.371040855716082
            ],
            "branch_aligned_reduced_polarization": [
              -1.0245965608510695e-14,
              -0.5034785497835803,
              4.371040855716082
            ],
            "target_residual": 0.1290060510326445,
            "energy_eV": -224.1235236897099,
            "max_atomic_step_A": 0.008031838338487474,
            "max_log_strain_component": 0.0013600310262706706,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0036011584277065,
              0.9994079708480169,
              0.9944544638281786
            ],
            "cell_volume_ratio": 0.9974447857009197,
            "cell_rmsd_from_input_A": 0.03759148398567664
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.714550916785634e-15,
              -0.5000800291149163,
              4.499958575944339
            ],
            "branch_aligned_reduced_polarization": [
              -2.714550916785634e-15,
              -0.5000800291149163,
              4.499958575944339
            ],
            "target_residual": 9.011443625588015e-05,
            "energy_eV": -224.18423745923678
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          4.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 9.011443625588015e-05,
        "parent_symmetrization_rmsd_A": 0.079055984368704,
        "parent_cell_rmsd_A": 0.03759148398567664,
        "energy_eV": -224.18423745923678,
        "reduced_polarization": [
          -2.714550916785634e-15,
          -0.5000800291149163,
          4.499958575944339
        ],
        "cartesian_polarization_e_A2": [
          -3.787843639120192e-16,
          -0.015720812963162054,
          0.04814026521807003
        ],
        "ranking_score": 0.588634084237635
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9404924595819466e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "target_residual": 0.6270315152428594,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.03577156659055402,
            "max_log_strain_component": 0.007439925350528918,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.010011307605032,
              0.9990547253791436,
              0.994798420268998
            ],
            "cell_volume_ratio": 1.0038078813495739,
            "cell_rmsd_from_input_A": 0.027702654931116164
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5005253291963491,
              1.080477269795915e-14,
              3.990489272132595
            ],
            "branch_aligned_reduced_polarization": [
              0.5005253291963491,
              1.080477269795915e-14,
              3.990489272132595
            ],
            "target_residual": 0.009525225211635343,
            "energy_eV": -224.84775691746097,
            "max_atomic_step_A": 0.000579961642825929,
            "max_log_strain_component": 9.075248267299971e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.009943045183421,
              0.9990769012894081,
              0.994754837060027
            ],
            "cell_volume_ratio": 1.0037183421739755,
            "cell_rmsd_from_input_A": 0.027409945595534006
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999751537883876,
              3.632063441875169e-16,
              3.999959946574522
            ],
            "branch_aligned_reduced_polarization": [
              0.4999751537883876,
              3.632063441875169e-16,
              3.999959946574522
            ],
            "target_residual": 4.7133969958165427e-05,
            "energy_eV": -224.8526897379686
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          4.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 4.7133969958165427e-05,
        "parent_symmetrization_rmsd_A": 0.02475185903919966,
        "parent_cell_rmsd_A": 0.027409945595534006,
        "energy_eV": -224.8526897379686,
        "reduced_polarization": [
          0.4999751537883876,
          3.632063441875169e-16,
          3.999959946574522
        ],
        "cartesian_polarization_e_A2": [
          0.004999038322373762,
          -1.3930635893042233e-16,
          0.04281765099883122
        ],
        "ranking_score": 0.5316986133779995
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9520776135869594e-15,
              -1.4988010832439613e-15,
              4.378376163503677
            ],
            "target_residual": 0.627031515242862,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.10937925236763528,
            "max_log_strain_component": 0.0042721133980206235,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0063838823596645,
              1.000880111695874,
              0.9965632525867617
            ],
            "cell_volume_ratio": 1.003807881349583,
            "cell_rmsd_from_input_A": 0.03980624653628848
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.6817618307260946e-14,
              -0.49682241395209115,
              3.876438536409829
            ],
            "branch_aligned_reduced_polarization": [
              -4.6817618307260946e-14,
              -0.49682241395209115,
              3.876438536409829
            ],
            "target_residual": 0.12360231526001873,
            "energy_eV": -223.89907160577647,
            "max_atomic_step_A": 0.007386822321703917,
            "max_log_strain_component": 0.001201642858822657,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0056539447778825,
              1.00060651531209,
              0.9963817259581632
            ],
            "cell_volume_ratio": 1.0026229507841837,
            "cell_rmsd_from_input_A": 0.03797473232659249
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.7755596110227306e-14,
              -0.5001116263178784,
              3.999619669686855
            ],
            "branch_aligned_reduced_polarization": [
              1.7755596110227306e-14,
              -0.5001116263178784,
              3.999619669686855
            ],
            "target_residual": 0.00039637303382060213,
            "energy_eV": -223.98843520255465
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          4.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00039637303382060213,
        "parent_symmetrization_rmsd_A": 0.07981828244114338,
        "parent_cell_rmsd_A": 0.03797473232659249,
        "energy_eV": -223.98843520255465,
        "reduced_polarization": [
          1.7755596110227306e-14,
          -0.5001116263178784,
          3.999619669686855
        ],
        "cartesian_polarization_e_A2": [
          5.416211732720478e-17,
          -0.01564093294000952,
          0.04278349959156348
        ],
        "ranking_score": 0.5901047115904328
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9404924595819466e-15,
              -1.4988010832439613e-15,
              4.378376163503677
            ],
            "target_residual": 0.7174903188225454,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.11308424743016358,
            "max_log_strain_component": 0.007439925350540722,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.007942741528011,
              1.0001572773278298,
              0.9907527257009449
            ],
            "cell_volume_ratio": 0.998779079121945,
            "cell_rmsd_from_input_A": 0.04145391834557684
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4947337792363745,
              -0.5028394080025558,
              4.365934883756729
            ],
            "branch_aligned_reduced_polarization": [
              0.4947337792363745,
              -0.5028394080025558,
              4.365934883756729
            ],
            "target_residual": 0.1341985495907385,
            "energy_eV": -223.9890689906685,
            "max_atomic_step_A": 0.008531022745687034,
            "max_log_strain_component": 0.0014289802446708173,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0073431978306258,
              1.0003349431718498,
              0.9897751214428512
            ],
            "cell_volume_ratio": 0.9973771887913637,
            "cell_rmsd_from_input_A": 0.043197152102066455
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4995698764693209,
              -0.5000853731693757,
              4.499841743479067
            ],
            "branch_aligned_reduced_polarization": [
              0.4995698764693209,
              -0.5000853731693757,
              4.499841743479067
            ],
            "target_residual": 0.00046619733601880155,
            "energy_eV": -224.03748899513258
          }
        ],
        "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": [
          0.5,
          -0.5,
          4.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00046619733601880155,
        "parent_symmetrization_rmsd_A": 0.081654681393786,
        "parent_cell_rmsd_A": 0.043197152102066455,
        "energy_eV": -224.03748899513258,
        "reduced_polarization": [
          0.4995698764693209,
          -0.5000853731693757,
          4.499841743479067
        ],
        "cartesian_polarization_e_A2": [
          0.004973719955786658,
          -0.015722046159822162,
          0.04809988116536811
        ],
        "ranking_score": 0.5933863640913403
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.9520776135869594e-15,
              -1.4752580002832295e-15,
              4.378376163503677
            ],
            "branch_aligned_reduced_polarization": [
              4.9404924595819466e-15,
              -1.4988010832439613e-15,
              4.378376163503677
            ],
            "target_residual": 0.8019778806848444,
            "energy_eV": -225.1007202789811,
            "max_atomic_step_A": 0.11643380288562234,
            "max_log_strain_component": 0.007439925350537196,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.010978525514131,
              0.9995454986395657,
              0.993358706940809
            ],
            "cell_volume_ratio": 1.0038078813495805,
            "cell_rmsd_from_input_A": 0.044950662690622575
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4949654386055251,
              -0.4963427666159587,
              3.873617853536883
            ],
            "branch_aligned_reduced_polarization": [
              0.4949654386055251,
              -0.4963427666159587,
              3.873617853536883
            ],
            "target_residual": 0.12653524848470044,
            "energy_eV": -223.79848377789537,
            "max_atomic_step_A": 0.007727249984449244,
            "max_log_strain_component": 0.0012394376041643161,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 13.308980224935025,
            "cell_principal_stretches": [
              1.0102941680667217,
              0.9996766081120727,
              0.9926911082444569
            ],
            "cell_volume_ratio": 1.0025857043806652,
            "cell_rmsd_from_input_A": 0.04343139124998367
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49961383608654514,
              -0.5001176946729221,
              3.999556964206138
            ],
            "branch_aligned_reduced_polarization": [
              0.49961383608654514,
              -0.5001176946729221,
              3.999556964206138
            ],
            "target_residual": 0.0005993791110239097,
            "energy_eV": -223.87954228616405
          }
        ],
        "iterations": 2
      },
      "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,
          4.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0005993791110239097,
        "parent_symmetrization_rmsd_A": 0.08221145310893668,
        "parent_cell_rmsd_A": 0.04343139124998367,
        "energy_eV": -223.87954228616405,
        "reduced_polarization": [
          0.49961383608654514,
          -0.5001176946729221,
          3.999556964206138
        ],
        "cartesian_polarization_e_A2": [
          0.0049953949078432895,
          -0.015641719852904967,
          0.04274382710499355
        ],
        "ranking_score": 0.5942680591434805
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "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
        ],
        "endpoint_rmsd_A": 0.41604347364402255,
        "minimum_distance_A_by_image": [
          1.7979847195295178,
          1.8283274566842116,
          1.850895431633877,
          1.8395357211838015,
          1.8302395363053277,
          1.8230384447605479,
          1.8179573432758647,
          1.8150140365689207,
          1.8142189294541204
        ],
        "minimum_distance_A": 1.7979847195295178,
        "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": [
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592,
          525.0408726553592
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        6.505700962485214e-17,
        -2.0946665511922154e-15,
        -3.0506521211619393e-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": [
          -225.10072027898107,
          -224.85091148681556,
          -224.57030174642586,
          -224.2931996300777,
          -224.01467418569393,
          -223.74553047732977,
          -223.5192443858337,
          -223.36843637393324,
          -223.31544596907565
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.833515497403916e-17,
            -5.270505655841834e-17,
            0.04690742957403359
          ],
          [
            -1.5726935131524029e-18,
            -5.497819340095795e-18,
            0.041291375274081735
          ],
          [
            -9.621183845167641e-18,
            1.0509293123183115e-16,
            0.03569229453856427
          ],
          [
            -2.3382252085251167e-17,
            4.646714615330965e-17,
            0.030099471611363542
          ],
          [
            5.159161598293019e-18,
            -1.1735729745204486e-17,
            0.024369577422088784
          ],
          [
            -2.5286995384268727e-17,
            -1.2793002695222906e-17,
            0.018438910475864337
          ],
          [
            4.831324384338088e-17,
            -4.017637210070004e-17,
            0.012355417274512505
          ],
          [
            -7.758731464150814e-17,
            -4.519841861328754e-17,
            0.0061929039118598555
          ],
          [
            6.938353734495895e-19,
            -6.650246855615875e-17,
            -3.268295006744447e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966483e-16,
            -1.7316798197455516e-16,
            3.8541692627387882
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            3.331546687753504
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            2.8095082214908373
          ],
          [
            4.837453358533648e-16,
            -3.69647038445685e-16,
            2.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            1.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            1.1532643117757466
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            0.578050494703845
          ],
          [
            6.505700962485214e-17,
            -2.0946665511922154e-15,
            -3.0506521211619393e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966562e-16,
            -1.7316798197455511e-16,
            4.854169262738788
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            5.331546687753503
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            5.809508221490837
          ],
          [
            4.837453358533646e-16,
            -3.69647038445685e-16,
            6.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            6.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            7.153264311775747
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            7.578050494703845
          ],
          [
            6.505700962485252e-17,
            -2.0946665511922154e-15,
            7.999999999999997
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ]
        ],
        "folded_reduced_polarization": [
          [
            8.326672684688674e-15,
            -1.6653345369377348e-15,
            0.3783761635036802
          ],
          [
            -1.6653345369377348e-16,
            -1.6653345369377348e-16,
            -0.1458307372612122
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-15,
            0.3315466877535034
          ],
          [
            -2.1649348980190553e-15,
            1.4432899320127035e-15,
            -0.19049177850916266
          ],
          [
            4.440892098500626e-16,
            -3.885780586188048e-16,
            0.27467541642051785
          ],
          [
            -2.3869795029440866e-15,
            -3.885780586188048e-16,
            -0.27889767481112315
          ],
          [
            4.551914400963142e-15,
            -1.27675647831893e-15,
            0.15326431177574662
          ],
          [
            -7.271960811294775e-15,
            -1.4432899320127035e-15,
            -0.4219495052961548
          ],
          [
            1.1102230246251565e-16,
            -2.1094237467877974e-15,
            -3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -223.31544596907568,
          -223.36843637393326,
          -223.51924438583364,
          -223.7455304773298,
          -224.01467418569396,
          -224.29319963007765,
          -224.57030174642588,
          -224.85091148681553,
          -225.10072027898104
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.322708507748994e-18,
            -5.053764701088057e-17,
            -9.409729255163956e-18
          ],
          [
            -8.33725800648902e-17,
            -1.3638821055237644e-16,
            -0.006192903911859653
          ],
          [
            -1.19002678480511e-16,
            -9.155983747159534e-17,
            -0.012355417274512502
          ],
          [
            -7.646065815414476e-17,
            -1.4289043919498974e-16,
            -0.018438910475864108
          ],
          [
            -9.325147419162483e-17,
            -1.255511628146876e-16,
            -0.024369577422088617
          ],
          [
            -6.434827492049621e-17,
            -1.7228262720550189e-16,
            -0.030099471611363546
          ],
          [
            -7.992322706545509e-17,
            -1.3839702915741144e-16,
            -0.03569229453856428
          ],
          [
            -1.917562733536537e-16,
            -6.227337675608506e-17,
            -0.04129137527408174
          ],
          [
            -1.2011281507803035e-16,
            -8.521619977148482e-17,
            -0.046907429574033564
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.990802024077943e-16,
            -1.5918133727661028e-15,
            -8.783114881792563e-16
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            -0.5780504947038261
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            -1.1532643117757464
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            -1.7211023251888555
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            -2.2746754164205027
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            -2.809508221490838
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            -3.331546687753505
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            -3.8541692627387887
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            -4.3783761635036775
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.990802024077943e-16,
            -1.5918133727661028e-15,
            7.999999999999999
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            8.421949505296174
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            8.846735688224253
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            9.278897674811144
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            9.725324583579498
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            10.190491778509163
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            10.668453312246495
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            11.14583073726121
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            11.621623836496322
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          8
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.152572691845756e-15,
          -2.5292515828783585e-15,
          -4.3783761635036855
        ],
        "actual_opposite_endpoint_branch_residual": 7.757671497808989e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966483e-16,
            -1.7316798197455516e-16,
            3.8541692627387882
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            3.331546687753504
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            2.8095082214908373
          ],
          [
            4.837453358533648e-16,
            -3.69647038445685e-16,
            2.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            1.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            1.1532643117757466
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            0.578050494703845
          ],
          [
            6.505700962485214e-17,
            -2.0946665511922154e-15,
            -3.0506521211619393e-15
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            -0.5780504947038261
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            -1.1532643117757464
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            -1.7211023251888555
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            -2.2746754164205027
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            -2.809508221490838
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            -3.331546687753505
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            -3.8541692627387887
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            -4.3783761635036775
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.282686711095459e-15,
            -1.6600815195060718e-15,
            4.37837616350368
          ],
          [
            -1.4746255514966562e-16,
            -1.7316798197455511e-16,
            4.854169262738788
          ],
          [
            -9.021238667979495e-16,
            3.3101725785136116e-15,
            5.331546687753503
          ],
          [
            -2.192421224357517e-15,
            1.4636024630349419e-15,
            5.809508221490837
          ],
          [
            4.837453358533646e-16,
            -3.69647038445685e-16,
            6.274675416420518
          ],
          [
            -2.3710182055419324e-15,
            -4.0294857344079175e-16,
            6.721102325188877
          ],
          [
            4.530058988056222e-15,
            -1.2654583298140568e-15,
            7.153264311775747
          ],
          [
            -7.274922652478108e-15,
            -1.4236406210408139e-15,
            7.578050494703845
          ],
          [
            6.505700962485252e-17,
            -2.0946665511922154e-15,
            7.999999999999997
          ],
          [
            -7.817374194635805e-15,
            -4.2958980143687715e-15,
            8.421949505296173
          ],
          [
            -1.1158206536513924e-14,
            -2.883912930576245e-15,
            8.846735688224253
          ],
          [
            -7.169282460658706e-15,
            -4.500702454588678e-15,
            9.278897674811144
          ],
          [
            -8.743662093580126e-15,
            -3.954557280668927e-15,
            9.725324583579496
          ],
          [
            -6.0335729497791436e-15,
            -5.426485127452646e-15,
            10.190491778509163
          ],
          [
            -7.49394791821511e-15,
            -4.359170930859474e-15,
            10.668453312246495
          ],
          [
            -1.7979898688605563e-14,
            -1.961460411211788e-15,
            11.14583073726121
          ],
          [
            -1.1262297751913687e-14,
            -2.6841037206056047e-15,
            11.621623836496322
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ],
          [
            0,
            0,
            9
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            11
          ],
          [
            0,
            0,
            12
          ],
          [
            0,
            0,
            13
          ],
          [
            0,
            0,
            14
          ],
          [
            0,
            0,
            15
          ],
          [
            0,
            0,
            16
          ]
        ],
        "folded_reduced_polarization": [
          [
            8.326672684688674e-15,
            -1.6653345369377348e-15,
            0.3783761635036802
          ],
          [
            -1.6653345369377348e-16,
            -1.6653345369377348e-16,
            -0.1458307372612122
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-15,
            0.3315466877535034
          ],
          [
            -2.1649348980190553e-15,
            1.4432899320127035e-15,
            -0.19049177850916266
          ],
          [
            4.440892098500626e-16,
            -3.885780586188048e-16,
            0.27467541642051785
          ],
          [
            -2.3869795029440866e-15,
            -3.885780586188048e-16,
            -0.27889767481112315
          ],
          [
            4.551914400963142e-15,
            -1.27675647831893e-15,
            0.15326431177574662
          ],
          [
            -7.271960811294775e-15,
            -1.4432899320127035e-15,
            -0.4219495052961548
          ],
          [
            1.1102230246251565e-16,
            -2.1094237467877974e-15,
            -3.552713678800501e-15
          ],
          [
            -7.827072323607354e-15,
            -4.274358644806853e-15,
            0.4219495052961726
          ],
          [
            -1.1157741397482823e-14,
            -2.886579864025407e-15,
            -0.15326431177574662
          ],
          [
            -7.16093850883226e-15,
            -4.496403249731884e-15,
            0.27889767481114447
          ],
          [
            -8.770761894538737e-15,
            -3.941291737419306e-15,
            -0.27467541642050364
          ],
          [
            -6.050715484207103e-15,
            -5.440092820663267e-15,
            0.19049177850916266
          ],
          [
            -7.494005416219807e-15,
            -4.385380947269368e-15,
            -0.33154668775350515
          ],
          [
            -1.7985612998927536e-14,
            -1.942890293094024e-15,
            0.14583073726121043
          ],
          [
            -1.1268763699945339e-14,
            -2.6645352591003757e-15,
            -0.37837616350367753
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": "Pbca",
        "spacegroup_number": 61,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.3933595811519085e-15,
        "parent_symmetrization_rmsd_A": 0.41604347364402255,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -223.31544596907565,
        "reduced_polarization": [
          1.5474274432196972e-15,
          -1.82492411773185e-15,
          -5.736163511283064e-17
        ],
        "cartesian_polarization_e_A2": [
          1.6503369954193806e-17,
          -5.793855766100953e-17,
          -6.145399021982078e-19
        ],
        "ranking_score": 0.41604347364402733
      }
    }
  ],
  "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": 49,
      "full_response": 16,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 41,
      "energy_polarization": 33
    },
    "elapsed_seconds": 588.8989421979641
  }
}
