{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 60,
  "input_formula": "H36Na4O20",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -285.9164748747859,
  "input_cartesian_polarization_e_A2": [
    -1.462091494631496e-13,
    -0.0027469650044720257,
    9.504338571633929e-11
  ],
  "input_reduced_polarization": [
    1.651802509099901e-09,
    -0.3596805571681754,
    6.037464076102951e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.613100367302385e-15,
      "parent_symmetrization_rmsd_A": 0.08342433770900803,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -284.11199120835147,
      "reduced_polarization": [
        -4.992612013732481e-17,
        -3.601401173053346e-15,
        -2.862013931808258e-16
      ],
      "cartesian_polarization_e_A2": [
        8.285902384670315e-19,
        -2.7504747733184873e-17,
        -4.5054594216644845e-18
      ],
      "ranking_score": 0.08342433770901526
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0008606529204013874,
      "parent_symmetrization_rmsd_A": 0.014195752046929916,
      "parent_cell_rmsd_A": 0.006624661889519915,
      "energy_eV": -285.8333191108862,
      "reduced_polarization": [
        -3.298269529905709e-11,
        -0.5008606529204014,
        -7.58862412632905e-11
      ],
      "cartesian_polarization_e_A2": [
        -5.784126755128176e-13,
        -0.003820089179418954,
        -1.4993915683441437e-12
      ],
      "ranking_score": 0.5175732233601127
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999944,
      "parent_symmetrization_rmsd_A": 0.08343749012371585,
      "parent_cell_rmsd_A": 0.006624661889519915,
      "energy_eV": -284.03716622050763,
      "reduced_polarization": [
        -1.986377645977618e-16,
        -5.397891246097205e-16,
        -4.699383487768999e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.0155842435724718e-18,
        -4.116998575197716e-18,
        -7.39047555976573e-18
      ],
      "ranking_score": 1.0850936555960948
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4096848664999123e-05,
      "parent_symmetrization_rmsd_A": 0.03700744687122194,
      "parent_cell_rmsd_A": 0.01719107927676703,
      "energy_eV": -284.86575072438404,
      "reduced_polarization": [
        6.661594326875055e-13,
        -2.4096848664999062e-05,
        1.5607352325776707e-12
      ],
      "cartesian_polarization_e_A2": [
        6.897279023183436e-15,
        -1.8467317444531492e-07,
        2.46048922233475e-14
      ],
      "ranking_score": 0.5413534103877436
    },
    {
      "candidate_id": "bec_projection_02",
      "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": 0.00021690449392064147,
      "parent_symmetrization_rmsd_A": 0.13312953381185333,
      "parent_cell_rmsd_A": 0.02599509941023754,
      "energy_eV": -276.261255305109,
      "reduced_polarization": [
        1.7392071269899913e-05,
        -0.49985891462212706,
        0.4998361708466409
      ],
      "cartesian_polarization_e_A2": [
        -0.003949519136552317,
        -0.003835903215306674,
        0.007881649592526373
      ],
      "ranking_score": 0.6400621176522541
    },
    {
      "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": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 9.780488207403179e-05,
      "parent_symmetrization_rmsd_A": 0.19649168137934764,
      "parent_cell_rmsd_A": 0.03380842891625636,
      "energy_eV": -265.9457376437799,
      "reduced_polarization": [
        0.4999595959418535,
        -0.5000864423438851,
        2.147156786217338e-05
      ],
      "cartesian_polarization_e_A2": [
        0.01444949047767265,
        -0.0038018016893864434,
        4.265073081036056e-05
      ],
      "ranking_score": 0.7051393983725598
    },
    {
      "candidate_id": "bec_projection_04",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0002565740383916758,
      "parent_symmetrization_rmsd_A": 0.14034573899158545,
      "parent_cell_rmsd_A": 0.03182706810937664,
      "energy_eV": -274.4940552071538,
      "reduced_polarization": [
        7.291344900036988e-05,
        0.00016872043246596923,
        0.49982098245393264
      ],
      "cartesian_polarization_e_A2": [
        -0.003992465762429472,
        -2.232806548208981e-05,
        0.007893706347000583
      ],
      "ranking_score": 0.648815654095713
    },
    {
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.047112427758981e-05,
      "parent_symmetrization_rmsd_A": 0.20117346867540936,
      "parent_cell_rmsd_A": 0.03721894111787763,
      "energy_eV": -265.0095218629461,
      "reduced_polarization": [
        0.49999851331378087,
        -9.54501783071282e-06,
        4.0406487516174746e-06
      ],
      "cartesian_polarization_e_A2": [
        0.01454178084086142,
        1.4212399204127336e-05,
        -9.89072920191942e-06
      ],
      "ranking_score": 0.7104991462034339
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.400627209009289e-05,
      "parent_symmetrization_rmsd_A": 0.18453383285357622,
      "parent_cell_rmsd_A": 0.045613214096812876,
      "energy_eV": -265.26266112112575,
      "reduced_polarization": [
        0.5000005983048106,
        -0.49996809777048384,
        0.500011760796092
      ],
      "cartesian_polarization_e_A2": [
        0.010512749280511826,
        -0.00397128658227395,
        0.007932058947229233
      ],
      "ranking_score": 0.6960051489219596
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.012289623508865435,
      "parent_symmetrization_rmsd_A": 0.20304089668194827,
      "parent_cell_rmsd_A": 0.051178204287502874,
      "energy_eV": -259.45938325911675,
      "reduced_polarization": [
        0.4970311644688505,
        -0.011215123498572658,
        0.49594514285203467
      ],
      "cartesian_polarization_e_A2": [
        0.010509226020613858,
        -0.00022070560137375908,
        0.00784019275574045
      ],
      "ranking_score": 0.7404146947715549
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "target_residual": 0.14031944283182476,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.01898170370442874,
            "max_log_strain_component": 0.0009748864433245912,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0010373504787915,
              1.0007000101380794,
              1.000297759446631
            ],
            "cell_volume_ratio": 1.0020363637511092,
            "cell_rmsd_from_input_A": 0.006624661889519915
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.298269529905709e-11,
              -0.5008606529204014,
              -7.58862412632905e-11
            ],
            "branch_aligned_reduced_polarization": [
              -3.298269529905709e-11,
              -0.5008606529204014,
              -7.58862412632905e-11
            ],
            "target_residual": 0.0008606529204013874,
            "energy_eV": -285.8333191108862
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0008606529204013874,
        "parent_symmetrization_rmsd_A": 0.014195752046929916,
        "parent_cell_rmsd_A": 0.006624661889519915,
        "energy_eV": -285.8333191108862,
        "reduced_polarization": [
          -3.298269529905709e-11,
          -0.5008606529204014,
          -7.58862412632905e-11
        ],
        "cartesian_polarization_e_A2": [
          -5.784126755128176e-13,
          -0.003820089179418954,
          -1.4993915683441437e-12
        ],
        "ranking_score": 0.5175732233601127
      },
      "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,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "target_residual": 0.35968055716817543,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.04865576444067442,
            "max_log_strain_component": 0.002498924539851179,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              0.9992371585057209,
              0.9982079008273215,
              0.9973458681954036
            ],
            "cell_volume_ratio": 0.994799072136909,
            "cell_rmsd_from_input_A": 0.016943217718529177
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.241493306312448e-10,
              -0.005131061542941453,
              2.1142992190862765e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.241493306312448e-10,
              -0.005131061542941453,
              2.1142992190862765e-10
            ],
            "target_residual": 0.005131061542941459,
            "energy_eV": -284.8920127024109,
            "max_atomic_step_A": 0.0007216268175199639,
            "max_log_strain_component": 3.661608252922583e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              0.9992259851173689,
              0.9981816655589113,
              0.9973070303136591
            ],
            "cell_volume_ratio": 0.9947230657358698,
            "cell_rmsd_from_input_A": 0.01719107927676703
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.661594326875055e-13,
              -2.4096848664999062e-05,
              1.5607352325776707e-12
            ],
            "branch_aligned_reduced_polarization": [
              6.661594326875055e-13,
              -2.4096848664999062e-05,
              1.5607352325776707e-12
            ],
            "target_residual": 2.4096848664999123e-05,
            "energy_eV": -284.86575072438404
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.613100367302385e-15,
        "parent_symmetrization_rmsd_A": 0.08342433770900803,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -284.11199120835147,
        "reduced_polarization": [
          -4.992612013732481e-17,
          -3.601401173053346e-15,
          -2.862013931808258e-16
        ],
        "cartesian_polarization_e_A2": [
          8.285902384670315e-19,
          -2.7504747733184873e-17,
          -4.5054594216644845e-18
        ],
        "ranking_score": 0.08342433770901526
      },
      "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": [
          -285.9164748747859,
          -285.910644540082,
          -285.81283776732147,
          -285.65465506201616,
          -285.4384786391438,
          -285.1442174283263,
          -284.76028029439806,
          -284.33509654903594,
          -284.11199120835136
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.462116870207549e-13,
            -0.0027469650044720253,
            9.504339622907794e-11
          ],
          [
            -5.496085659952734e-13,
            -0.0029560214883654692,
            8.066404035034394e-11
          ],
          [
            -7.139099833153507e-13,
            -0.0032017036985374603,
            6.69953890018009e-11
          ],
          [
            -7.013905026810128e-13,
            -0.0034690347746048904,
            5.513932577061363e-11
          ],
          [
            -6.884301084660308e-13,
            -0.0037151989315277367,
            4.658087115942694e-11
          ],
          [
            -4.636669275270234e-13,
            -0.003848885058627344,
            4.2411799229479893e-11
          ],
          [
            4.620857184175788e-13,
            -0.0036597495413117627,
            3.9317770155955455e-11
          ],
          [
            1.1339191126202249e-12,
            -0.00256893575663055,
            2.735014936729084e-11
          ],
          [
            -2.0766542851579978e-17,
            -3.617894857833078e-17,
            2.1232624860717685e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294984569e-16,
            -4.73717879959446e-15,
            1.3487651862544665e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294645906e-16,
            -4.718447854656915e-15,
            1.3487651856255124e-16
          ]
        ],
        "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": [
          [
            1.651802583602091e-09,
            -0.3596805571681753,
            6.037464750363597e-09
          ],
          [
            1.387201797875548e-09,
            -0.38705387735390734,
            5.12404141339573e-09
          ],
          [
            1.143247607693354e-09,
            -0.4192228762662014,
            4.255764407545826e-09
          ],
          [
            9.369981457396648e-10,
            -0.4542265221924378,
            3.5026287426020986e-09
          ],
          [
            7.882497987665715e-10,
            -0.4864586259770513,
            2.9589679595432017e-09
          ],
          [
            7.233343923829239e-10,
            0.4960368551803127,
            2.6941350261822095e-09
          ],
          [
            7.013686298407151e-10,
            -0.47919822493988906,
            2.497592244132818e-09
          ],
          [
            5.159441762714323e-10,
            -0.3363698637477615,
            1.737370136645211e-09
          ],
          [
            -6.661338147750939e-16,
            -4.718447854656915e-15,
            1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -284.1119912083514,
          -284.3350965490359,
          -284.76028029439806,
          -285.1442174283263,
          -285.4384786391437,
          -285.65465506201616,
          -285.8128377673214,
          -285.9106445400821,
          -285.9164748747858
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.5215085134848844e-17,
            -7.262778499063129e-17,
            1.455211606307724e-17
          ],
          [
            -1.1339285378341876e-12,
            0.002568935756630546,
            -2.735006397070939e-11
          ],
          [
            -4.620497265290953e-13,
            0.003659749541311844,
            -3.931774079278888e-11
          ],
          [
            4.637100660063136e-13,
            0.003848885058627324,
            -4.2411752517705206e-11
          ],
          [
            6.884576073045699e-13,
            0.0037151989315277753,
            -4.658089006164175e-11
          ],
          [
            7.014099745516168e-13,
            0.0034690347746048956,
            -5.5139316915055456e-11
          ],
          [
            7.139397089901557e-13,
            0.003201703698537418,
            -6.699538993396492e-11
          ],
          [
            5.496473025889218e-13,
            0.002956021488365533,
            -8.066400166553718e-11
          ],
          [
            1.4625555051650374e-13,
            0.0027469650044720717,
            -9.504341186871869e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.624855750967944e-16,
            -9.50969602044187e-15,
            9.243976032622073e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.624855750967944e-16,
            -9.50969602044187e-15,
            9.243976032622073e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.6518039650618371e-09,
          0.3596805571681658,
          -6.037464474153164e-09
        ],
        "actual_opposite_endpoint_branch_residual": 1.586462490993078e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294984569e-16,
            -4.73717879959446e-15,
            1.3487651862544665e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294645906e-16,
            -4.718447854656915e-15,
            1.3487651856255124e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "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": [
          [
            1.651802583602091e-09,
            -0.3596805571681753,
            6.037464750363597e-09
          ],
          [
            1.387201797875548e-09,
            -0.38705387735390734,
            5.12404141339573e-09
          ],
          [
            1.143247607693354e-09,
            -0.4192228762662014,
            4.255764407545826e-09
          ],
          [
            9.369981457396648e-10,
            -0.4542265221924378,
            3.5026287426020986e-09
          ],
          [
            7.882497987665715e-10,
            -0.4864586259770513,
            2.9589679595432017e-09
          ],
          [
            7.233343923829239e-10,
            0.4960368551803127,
            2.6941350261822095e-09
          ],
          [
            7.013686298407151e-10,
            -0.47919822493988906,
            2.497592244132818e-09
          ],
          [
            5.159441762714323e-10,
            -0.3363698637477615,
            1.737370136645211e-09
          ],
          [
            -6.661338147750939e-16,
            -4.718447854656915e-15,
            1.1102230246251565e-16
          ],
          [
            -5.159429550261052e-10,
            0.336369863747761,
            -1.7373647520635416e-09
          ],
          [
            -7.01366908995027e-10,
            0.4791982249398996,
            -2.4975904122648274e-09
          ],
          [
            -7.233320609145721e-10,
            -0.4960368551803154,
            -2.694132084091194e-09
          ],
          [
            -7.88249188143908e-10,
            0.48645862597705636,
            -2.9589691807885288e-09
          ],
          [
            -9.369973685835475e-10,
            0.45422652219243853,
            -3.5026282430017375e-09
          ],
          [
            -1.143246664003783e-09,
            0.4192228762661959,
            -4.255764407545826e-09
          ],
          [
            -1.3871997994741037e-09,
            0.3870538773539156,
            -5.124038970905076e-09
          ],
          [
            -1.651801362356764e-09,
            0.35968055716818137,
            -6.037465749564319e-09
          ]
        ]
      },
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464084229782e-09
            ],
            "target_residual": 0.5193164160694034,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0035180470596872407,
            "step_scale": 0.6696070314451699,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0052970745058767,
              1.0002900076470993,
              0.9957979707424979
            ],
            "cell_volume_ratio": 1.001363105549793,
            "cell_rmsd_from_input_A": 0.019206243895401657
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.000423511652811438,
              -0.47614762259474264,
              0.34034132596252314
            ],
            "branch_aligned_reduced_polarization": [
              -0.000423511652811438,
              -0.47614762259474264,
              0.34034132596252314
            ],
            "target_residual": 0.16143112297635853,
            "energy_eV": -280.60483826225516,
            "max_atomic_step_A": 0.054638536297125326,
            "max_log_strain_component": 0.0014993285530710775,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.007218608310553,
              1.0002608437641352,
              0.9938092538770333
            ],
            "cell_volume_ratio": 1.001244273835016,
            "cell_rmsd_from_input_A": 0.02648837015297158
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0013355271189408168,
              -0.4993325546542496,
              0.5137333793257998
            ],
            "branch_aligned_reduced_polarization": [
              -0.0013355271189408168,
              -0.4993325546542496,
              0.5137333793257998
            ],
            "target_residual": 0.013814297799066542,
            "energy_eV": -275.82629900641155,
            "max_atomic_step_A": 0.005571884504674346,
            "max_log_strain_component": 9.110316538049149e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0071044961241886,
              1.0002679557029674,
              0.9939501893213728
            ],
            "cell_volume_ratio": 1.001279931384025,
            "cell_rmsd_from_input_A": 0.02599509941023754
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.7392071269899913e-05,
              -0.49985891462212706,
              0.4998361708466409
            ],
            "branch_aligned_reduced_polarization": [
              1.7392071269899913e-05,
              -0.49985891462212706,
              0.4998361708466409
            ],
            "target_residual": 0.00021690449392064147,
            "energy_eV": -276.261255305109
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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": 0.00021690449392064147,
        "parent_symmetrization_rmsd_A": 0.13312953381185333,
        "parent_cell_rmsd_A": 0.02599509941023754,
        "energy_eV": -276.261255305109,
        "reduced_polarization": [
          1.7392071269899913e-05,
          -0.49985891462212706,
          0.4998361708466409
        ],
        "cartesian_polarization_e_A2": [
          -0.003949519136552317,
          -0.003835903215306674,
          0.007881649592526373
        ],
        "ranking_score": 0.6400621176522541
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6518025280909399e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "target_residual": 0.5193164202919365,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005321940772765241,
            "step_scale": 0.4858091482399006,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0057780789675415,
              1.0002058173576993,
              0.9950334065125298
            ],
            "cell_volume_ratio": 1.00098876657978,
            "cell_rmsd_from_input_A": 0.017950745480406784
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24732871578467786,
              -0.4321794499079311,
              -0.002996356181783745
            ],
            "branch_aligned_reduced_polarization": [
              0.24732871578467786,
              -0.4321794499079311,
              -0.002996356181783745
            ],
            "target_residual": 0.2616321521376512,
            "energy_eV": -279.2099041776515,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00415307284753651,
            "step_scale": 0.8999035017644863,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0102743939266774,
              1.0003485813027073,
              0.9911812672519299
            ],
            "cell_volume_ratio": 1.001714111179444,
            "cell_rmsd_from_input_A": 0.03152837639378457
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.469196986195621,
              -0.4762051421285451,
              -0.03272181159791904
            ],
            "branch_aligned_reduced_polarization": [
              0.469196986195621,
              -0.4762051421285451,
              -0.03272181159791904
            ],
            "target_residual": 0.05085015117780095,
            "energy_eV": -266.58591989486246,
            "max_atomic_step_A": 0.01727974741808586,
            "max_log_strain_component": 0.0008304192459879481,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0112071155412494,
              1.0003892278514201,
              0.9905004077348032
            ],
            "cell_volume_ratio": 1.0019909112766023,
            "cell_rmsd_from_input_A": 0.033613941414073055
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4967440458054517,
              -0.5012206683125044,
              0.0024871174510522395
            ],
            "branch_aligned_reduced_polarization": [
              0.4967440458054517,
              -0.5012206683125044,
              0.0024871174510522395
            ],
            "target_residual": 0.0042751633958806635,
            "energy_eV": -266.151045318029,
            "max_atomic_step_A": 0.0028006695257726637,
            "max_log_strain_component": 5.036485906098238e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0112607252421495,
              1.000390695452161,
              0.9904503462345494
            ],
            "cell_volume_ratio": 1.0019948573956572,
            "cell_rmsd_from_input_A": 0.03380842891625636
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999595959418535,
              -0.5000864423438851,
              2.147156786217338e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999595959418535,
              -0.5000864423438851,
              2.147156786217338e-05
            ],
            "target_residual": 9.780488207403179e-05,
            "energy_eV": -265.9457376437799
          }
        ],
        "iterations": 4
      },
      "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": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 9.780488207403179e-05,
        "parent_symmetrization_rmsd_A": 0.19649168137934764,
        "parent_cell_rmsd_A": 0.03380842891625636,
        "energy_eV": -265.9457376437799,
        "reduced_polarization": [
          0.4999595959418535,
          -0.5000864423438851,
          2.147156786217338e-05
        ],
        "cartesian_polarization_e_A2": [
          0.01444949047767265,
          -0.0038018016893864434,
          4.265073081036056e-05
        ],
        "ranking_score": 0.7051393983725598
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464084229782e-09
            ],
            "target_residual": 0.6159302697281122,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003282874927495133,
            "step_scale": 0.624845582411041,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0031770669366817,
              0.99930276388748,
              0.9942835929446727
            ],
            "cell_volume_ratio": 0.9967470455434043,
            "cell_rmsd_from_input_A": 0.020268379454073917
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00414656566517472,
              -0.1539474584311204,
              0.31032827832222054
            ],
            "branch_aligned_reduced_polarization": [
              -0.00414656566517472,
              -0.1539474584311204,
              0.31032827832222054
            ],
            "target_residual": 0.24432023241727277,
            "energy_eV": -280.6955371457592,
            "max_atomic_step_A": 0.06345099314464273,
            "max_log_strain_component": 0.0020845672159281537,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0048397307953516,
              0.9988237986433585,
              0.9906810144940906
            ],
            "cell_volume_ratio": 0.9943047641054398,
            "cell_rmsd_from_input_A": 0.032569560326331994
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0007729585619653893,
              0.006847219498189,
              0.5176695157870606
            ],
            "branch_aligned_reduced_polarization": [
              -0.0007729585619653893,
              0.006847219498189,
              0.5176695157870606
            ],
            "target_residual": 0.018965591684523775,
            "energy_eV": -273.84130408558156,
            "max_atomic_step_A": 0.006833296892831384,
            "max_log_strain_component": 0.0001318848965642756,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0046917273149,
              0.9988435263973476,
              0.9908939067592207
            ],
            "cell_volume_ratio": 0.9943915916711205,
            "cell_rmsd_from_input_A": 0.03182706810937664
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.291344900036988e-05,
              0.00016872043246596923,
              0.49982098245393264
            ],
            "branch_aligned_reduced_polarization": [
              7.291344900036988e-05,
              0.00016872043246596923,
              0.49982098245393264
            ],
            "target_residual": 0.0002565740383916758,
            "energy_eV": -274.4940552071538
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0002565740383916758,
        "parent_symmetrization_rmsd_A": 0.14034573899158545,
        "parent_cell_rmsd_A": 0.03182706810937664,
        "energy_eV": -274.4940552071538,
        "reduced_polarization": [
          7.291344900036988e-05,
          0.00016872043246596923,
          0.49982098245393264
        ],
        "cartesian_polarization_e_A2": [
          -0.003992465762429472,
          -2.232806548208981e-05,
          0.007893706347000583
        ],
        "ranking_score": 0.648815654095713
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6518025280909399e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "target_residual": 0.6159302732883054,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005258644732972112,
            "step_scale": 0.48003122243382346,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0043361007801528,
              0.9994776929966338,
              0.9937124435455996
            ],
            "cell_volume_ratio": 0.9975000073428103,
            "cell_rmsd_from_input_A": 0.019165601913760495
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24500880957970905,
              -0.18834917951961608,
              -0.004338914965408622
            ],
            "branch_aligned_reduced_polarization": [
              0.24500880957970905,
              -0.18834917951961608,
              -0.004338914965408622
            ],
            "target_residual": 0.3170406074949181,
            "energy_eV": -279.1263272431363,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0040519228312317,
            "step_scale": 0.8699098983248644,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.007764452211947,
              0.9991625739733629,
              0.9890267615056693
            ],
            "cell_volume_ratio": 0.9958713449759173,
            "cell_rmsd_from_input_A": 0.03294331925777532
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4511072319013178,
              -0.12268138470742794,
              -0.046475280585975845
            ],
            "branch_aligned_reduced_polarization": [
              0.4511072319013178,
              -0.12268138470742794,
              -0.046475280585975845
            ],
            "target_residual": 0.14000420219275075,
            "energy_eV": -266.69194472686786,
            "max_atomic_step_A": 0.03197124812463064,
            "max_log_strain_component": 0.0008133726896984828,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0083913785606475,
              0.9991081950105142,
              0.9880678104665468
            ],
            "cell_volume_ratio": 0.9954705035253895,
            "cell_rmsd_from_input_A": 0.03532961810120566
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48331159090588804,
              -0.0604928048899199,
              -0.006725657603480029
            ],
            "branch_aligned_reduced_polarization": [
              0.48331159090588804,
              -0.0604928048899199,
              -0.006725657603480029
            ],
            "target_residual": 0.06311193953398679,
            "energy_eV": -266.3677721006882,
            "max_atomic_step_A": 0.014962422786702045,
            "max_log_strain_component": 0.0005346842411744498,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0085192549243325,
              0.9989182281339083,
              0.9871301901735712
            ],
            "cell_volume_ratio": 0.9944628569557232,
            "cell_rmsd_from_input_A": 0.03810674441641662
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4990989256294404,
              -0.0045911886132884265,
              0.0008079918644670193
            ],
            "branch_aligned_reduced_polarization": [
              0.4990989256294404,
              -0.0045911886132884265,
              0.0008079918644670193
            ],
            "target_residual": 0.004748031040032652,
            "energy_eV": -265.075980877713,
            "max_atomic_step_A": 0.0009802045600349099,
            "max_log_strain_component": 0.00014522890703626642,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.829686939175012,
            "cell_principal_stretches": [
              1.0085340750903413,
              0.9990104864315901,
              0.9873214409786727
            ],
            "cell_volume_ratio": 0.9947620108141073,
            "cell_rmsd_from_input_A": 0.03721894111787763
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49999851331378087,
              -9.54501783071282e-06,
              4.0406487516174746e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999851331378087,
              -9.54501783071282e-06,
              4.0406487516174746e-06
            ],
            "target_residual": 1.047112427758981e-05,
            "energy_eV": -265.0095218629461
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.047112427758981e-05,
        "parent_symmetrization_rmsd_A": 0.20117346867540936,
        "parent_cell_rmsd_A": 0.03721894111787763,
        "energy_eV": -265.0095218629461,
        "reduced_polarization": [
          0.49999851331378087,
          -9.54501783071282e-06,
          4.0406487516174746e-06
        ],
        "cartesian_polarization_e_A2": [
          0.01454178084086142,
          1.4212399204127336e-05,
          -9.89072920191942e-06
        ],
        "ranking_score": 0.7104991462034339
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6518025280909399e-09,
              -0.3596805571681754,
              6.037464084229782e-09
            ],
            "target_residual": 0.7208949565279029,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007886449509201239,
            "step_scale": 0.4865567082981461,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0085057375738464,
              1.0001479531658257,
              0.9924011079311325
            ],
            "cell_volume_ratio": 1.0009902890968463,
            "cell_rmsd_from_input_A": 0.02348459147631839
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24955505590989452,
              -0.44570863806451305,
              0.25011929567631597
            ],
            "branch_aligned_reduced_polarization": [
              0.24955505590989452,
              -0.44570863806451305,
              0.25011929567631597
            ],
            "target_residual": 0.35792539501187465,
            "energy_eV": -279.40831130850165,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005130624432216706,
            "step_scale": 0.8660723037277948,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.013717152272768,
              1.0001279401717982,
              0.9871834572925733
            ],
            "cell_volume_ratio": 1.0008528360006443,
            "cell_rmsd_from_input_A": 0.03841314249820913
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.34140173874392554,
              -0.4951693485502953,
              0.28694901496956426
            ],
            "branch_aligned_reduced_polarization": [
              0.34140173874392554,
              -0.4951693485502953,
              0.28694901496956426
            ],
            "target_residual": 0.2656453761865949,
            "energy_eV": -267.9787471291462,
            "max_atomic_step_A": 0.07208592693225999,
            "max_log_strain_component": 0.0006099124287096725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0142859710307959,
              1.0001120960459262,
              0.9865393217355121
            ],
            "cell_volume_ratio": 1.0007451609086062,
            "cell_rmsd_from_input_A": 0.04012773337736782
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.453663800942715,
              -0.497440479774368,
              0.4146604087858652
            ],
            "branch_aligned_reduced_polarization": [
              0.453663800942715,
              -0.497440479774368,
              0.4146604087858652
            ],
            "target_residual": 0.09714134194799552,
            "energy_eV": -268.1944972100491,
            "max_atomic_step_A": 0.032349178950440406,
            "max_log_strain_component": 0.001724065074218176,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0159746636898912,
              1.000061860323922,
              0.9846233866222357
            ],
            "cell_volume_ratio": 1.0004142962090996,
            "cell_rmsd_from_input_A": 0.04528787994795994
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4989943974194531,
              -0.5008304277643416,
              0.4930034496022024
            ],
            "branch_aligned_reduced_polarization": [
              0.4989943974194531,
              -0.5008304277643416,
              0.4930034496022024
            ],
            "target_residual": 0.007117061492688817,
            "energy_eV": -265.37606846853885,
            "max_atomic_step_A": 0.00193305499565917,
            "max_log_strain_component": 0.00026933584583822476,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.2597254760730054,
            "cell_principal_stretches": [
              1.0162366927000208,
              0.9999802660998607,
              0.9847510450358741
            ],
            "cell_volume_ratio": 1.0007203966340565,
            "cell_rmsd_from_input_A": 0.045613214096812876
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000005983048106,
              -0.49996809777048384,
              0.500011760796092
            ],
            "branch_aligned_reduced_polarization": [
              0.5000005983048106,
              -0.49996809777048384,
              0.500011760796092
            ],
            "target_residual": 3.400627209009289e-05,
            "energy_eV": -265.26266112112575
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.400627209009289e-05,
        "parent_symmetrization_rmsd_A": 0.18453383285357622,
        "parent_cell_rmsd_A": 0.045613214096812876,
        "energy_eV": -265.26266112112575,
        "reduced_polarization": [
          0.5000005983048106,
          -0.49996809777048384,
          0.500011760796092
        ],
        "cartesian_polarization_e_A2": [
          0.010512749280511826,
          -0.00397128658227395,
          0.007932058947229233
        ],
        "ranking_score": 0.6960051489219596
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.651802509099901e-09,
              -0.3596805571681754,
              6.037464076102951e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6518025280909399e-09,
              -0.3596805571681754,
              6.037464084229782e-09
            ],
            "target_residual": 0.7933284915566454,
            "energy_eV": -285.9164748747859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007788914056266876,
            "step_scale": 0.4805392333146277,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0069100525701655,
              0.9996254938298383,
              0.9910230526801699
            ],
            "cell_volume_ratio": 0.9974973651981698,
            "cell_rmsd_from_input_A": 0.024234940077558918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24441037860141077,
              -0.20197478993655718,
              0.24140574792637673
            ],
            "branch_aligned_reduced_polarization": [
              0.2444103786014108,
              -0.20197478993655718,
              0.2414057479263767
            ],
            "target_residual": 0.4159216964070367,
            "energy_eV": -278.95755912650174,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0051760293658660635,
            "step_scale": 0.8280645915154521,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0112527019800743,
              0.9992814706841137,
              0.9848414726843977
            ],
            "cell_volume_ratio": 0.9952079999709528,
            "cell_rmsd_from_input_A": 0.04090878218827806
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.31625969028487855,
              -0.16405093768406256,
              0.261395556287384
            ],
            "branch_aligned_reduced_polarization": [
              0.31625969028487855,
              -0.16405093768406256,
              0.261395556287384
            ],
            "target_residual": 0.34293627998308357,
            "energy_eV": -266.58491483416844,
            "max_atomic_step_A": 0.07024081905921434,
            "max_log_strain_component": 0.0006321325372518494,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0115045403473897,
              0.9991486228744052,
              0.9838993768537094
            ],
            "cell_volume_ratio": 0.9943713805074755,
            "cell_rmsd_from_input_A": 0.04350908608832015
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.43197142909860076,
              -0.06860938233118956,
              0.38532698845755026
            ],
            "branch_aligned_reduced_polarization": [
              0.43197142909860076,
              -0.06860938233118956,
              0.38532698845755026
            ],
            "target_residual": 0.14995010296418226,
            "energy_eV": -266.9573981743301,
            "max_atomic_step_A": 0.05742546872706867,
            "max_log_strain_component": 0.0029222017039188123,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7244107170062667,
            "cell_principal_stretches": [
              1.0136113679882943,
              0.9988230567472995,
              0.979992806919501
            ],
            "cell_volume_ratio": 0.9921627544222366,
            "cell_rmsd_from_input_A": 0.05429224722022703
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49237466139502534,
              -0.08525726424642896,
              0.4888174268194722
            ],
            "branch_aligned_reduced_polarization": [
              0.49237466139502534,
              -0.08525726424642896,
              0.4888174268194722
            ],
            "target_residual": 0.08632494910837649,
            "energy_eV": -260.2110461694431,
            "max_atomic_step_A": 0.017593258973583294,
            "max_log_strain_component": 0.0018250812347413092,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.5718233785537854,
            "cell_principal_stretches": [
              1.0121730629077363,
              0.9984894679965696,
              0.9826158123305474
            ],
            "cell_volume_ratio": 0.9930749156524648,
            "cell_rmsd_from_input_A": 0.051178204287502874
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4970311644688505,
              -0.011215123498572658,
              0.49594514285203467
            ],
            "branch_aligned_reduced_polarization": [
              0.4970311644688505,
              -0.011215123498572658,
              0.49594514285203467
            ],
            "target_residual": 0.012289623508865435,
            "energy_eV": -259.45938325911675
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.012289623508865435,
        "parent_symmetrization_rmsd_A": 0.20304089668194827,
        "parent_cell_rmsd_A": 0.051178204287502874,
        "energy_eV": -259.45938325911675,
        "reduced_polarization": [
          0.4970311644688505,
          -0.011215123498572658,
          0.49594514285203467
        ],
        "cartesian_polarization_e_A2": [
          0.010509226020613858,
          -0.00022070560137375908,
          0.00784019275574045
        ],
        "ranking_score": 0.7404146947715549
      },
      "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,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59
        ],
        "endpoint_rmsd_A": 0.08342433770900803,
        "minimum_distance_A_by_image": [
          0.9814518860079923,
          0.9814518807016583,
          0.9814518761028329,
          0.9814518722115216,
          0.9814518690277191,
          0.9814518665514305,
          0.981451864782653,
          0.9814518637213849,
          0.9814518633676292
        ],
        "minimum_distance_A": 0.9814518633676292,
        "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": [
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867,
          535.9575689325867
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.801666294984569e-16,
        -4.73717879959446e-15,
        1.3487651862544665e-16
      ],
      "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": [
          -285.9164748747859,
          -285.910644540082,
          -285.81283776732147,
          -285.65465506201616,
          -285.4384786391438,
          -285.1442174283263,
          -284.76028029439806,
          -284.33509654903594,
          -284.11199120835136
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.462116870207549e-13,
            -0.0027469650044720253,
            9.504339622907794e-11
          ],
          [
            -5.496085659952734e-13,
            -0.0029560214883654692,
            8.066404035034394e-11
          ],
          [
            -7.139099833153507e-13,
            -0.0032017036985374603,
            6.69953890018009e-11
          ],
          [
            -7.013905026810128e-13,
            -0.0034690347746048904,
            5.513932577061363e-11
          ],
          [
            -6.884301084660308e-13,
            -0.0037151989315277367,
            4.658087115942694e-11
          ],
          [
            -4.636669275270234e-13,
            -0.003848885058627344,
            4.2411799229479893e-11
          ],
          [
            4.620857184175788e-13,
            -0.0036597495413117627,
            3.9317770155955455e-11
          ],
          [
            1.1339191126202249e-12,
            -0.00256893575663055,
            2.735014936729084e-11
          ],
          [
            -2.0766542851579978e-17,
            -3.617894857833078e-17,
            2.1232624860717685e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294984569e-16,
            -4.73717879959446e-15,
            1.3487651862544665e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294645906e-16,
            -4.718447854656915e-15,
            1.3487651856255124e-16
          ]
        ],
        "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": [
          [
            1.651802583602091e-09,
            -0.3596805571681753,
            6.037464750363597e-09
          ],
          [
            1.387201797875548e-09,
            -0.38705387735390734,
            5.12404141339573e-09
          ],
          [
            1.143247607693354e-09,
            -0.4192228762662014,
            4.255764407545826e-09
          ],
          [
            9.369981457396648e-10,
            -0.4542265221924378,
            3.5026287426020986e-09
          ],
          [
            7.882497987665715e-10,
            -0.4864586259770513,
            2.9589679595432017e-09
          ],
          [
            7.233343923829239e-10,
            0.4960368551803127,
            2.6941350261822095e-09
          ],
          [
            7.013686298407151e-10,
            -0.47919822493988906,
            2.497592244132818e-09
          ],
          [
            5.159441762714323e-10,
            -0.3363698637477615,
            1.737370136645211e-09
          ],
          [
            -6.661338147750939e-16,
            -4.718447854656915e-15,
            1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -284.1119912083514,
          -284.3350965490359,
          -284.76028029439806,
          -285.1442174283263,
          -285.4384786391437,
          -285.65465506201616,
          -285.8128377673214,
          -285.9106445400821,
          -285.9164748747858
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.5215085134848844e-17,
            -7.262778499063129e-17,
            1.455211606307724e-17
          ],
          [
            -1.1339285378341876e-12,
            0.002568935756630546,
            -2.735006397070939e-11
          ],
          [
            -4.620497265290953e-13,
            0.003659749541311844,
            -3.931774079278888e-11
          ],
          [
            4.637100660063136e-13,
            0.003848885058627324,
            -4.2411752517705206e-11
          ],
          [
            6.884576073045699e-13,
            0.0037151989315277753,
            -4.658089006164175e-11
          ],
          [
            7.014099745516168e-13,
            0.0034690347746048956,
            -5.5139316915055456e-11
          ],
          [
            7.139397089901557e-13,
            0.003201703698537418,
            -6.699538993396492e-11
          ],
          [
            5.496473025889218e-13,
            0.002956021488365533,
            -8.066400166553718e-11
          ],
          [
            1.4625555051650374e-13,
            0.0027469650044720717,
            -9.504341186871869e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.624855750967944e-16,
            -9.50969602044187e-15,
            9.243976032622073e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.624855750967944e-16,
            -9.50969602044187e-15,
            9.243976032622073e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.6518039650618371e-09,
          0.3596805571681658,
          -6.037464474153164e-09
        ],
        "actual_opposite_endpoint_branch_residual": 1.586462490993078e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294984569e-16,
            -4.73717879959446e-15,
            1.3487651862544665e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6518026047285782e-09,
            -0.3596805571681753,
            6.037464743906202e-09
          ],
          [
            1.3872017942499037e-09,
            -0.38705387735390734,
            5.124041427796035e-09
          ],
          [
            1.1432476550654707e-09,
            -0.4192228762662014,
            4.255764368181377e-09
          ],
          [
            9.36998190324793e-10,
            -0.4542265221924378,
            3.502628783808014e-09
          ],
          [
            7.882497952142548e-10,
            -0.4864586259770513,
            2.9589679927645163e-09
          ],
          [
            7.233343778148698e-10,
            -0.5039631448196873,
            2.6941350239257675e-09
          ],
          [
            7.013686784627948e-10,
            -0.47919822493988906,
            2.497592263574475e-09
          ],
          [
            5.159441379374665e-10,
            -0.3363698637477615,
            1.7373701813810795e-09
          ],
          [
            -6.801666294645906e-16,
            -4.718447854656915e-15,
            1.3487651856255124e-16
          ],
          [
            -5.1594297475771e-10,
            0.336369863747761,
            -1.737364756713294e-09
          ],
          [
            -7.013669235931191e-10,
            0.47919822493989966,
            -2.497590398330913e-09
          ],
          [
            -7.233320737038334e-10,
            0.5039631448196846,
            -2.694132056642358e-09
          ],
          [
            -7.882491750457041e-10,
            0.48645862597705636,
            -2.9589691934944986e-09
          ],
          [
            -9.369973634809458e-10,
            0.45422652219243853,
            -3.5026282212742414e-09
          ],
          [
            -1.1432466447278313e-09,
            0.4192228762661959,
            -4.25576442739546e-09
          ],
          [
            -1.38719978209049e-09,
            0.38705387735391567,
            -5.124038970411659e-09
          ],
          [
            -1.6518013625251668e-09,
            0.3596805571681814,
            -6.0374657373868995e-09
          ]
        ],
        "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": [
          [
            1.651802583602091e-09,
            -0.3596805571681753,
            6.037464750363597e-09
          ],
          [
            1.387201797875548e-09,
            -0.38705387735390734,
            5.12404141339573e-09
          ],
          [
            1.143247607693354e-09,
            -0.4192228762662014,
            4.255764407545826e-09
          ],
          [
            9.369981457396648e-10,
            -0.4542265221924378,
            3.5026287426020986e-09
          ],
          [
            7.882497987665715e-10,
            -0.4864586259770513,
            2.9589679595432017e-09
          ],
          [
            7.233343923829239e-10,
            0.4960368551803127,
            2.6941350261822095e-09
          ],
          [
            7.013686298407151e-10,
            -0.47919822493988906,
            2.497592244132818e-09
          ],
          [
            5.159441762714323e-10,
            -0.3363698637477615,
            1.737370136645211e-09
          ],
          [
            -6.661338147750939e-16,
            -4.718447854656915e-15,
            1.1102230246251565e-16
          ],
          [
            -5.159429550261052e-10,
            0.336369863747761,
            -1.7373647520635416e-09
          ],
          [
            -7.01366908995027e-10,
            0.4791982249398996,
            -2.4975904122648274e-09
          ],
          [
            -7.233320609145721e-10,
            -0.4960368551803154,
            -2.694132084091194e-09
          ],
          [
            -7.88249188143908e-10,
            0.48645862597705636,
            -2.9589691807885288e-09
          ],
          [
            -9.369973685835475e-10,
            0.45422652219243853,
            -3.5026282430017375e-09
          ],
          [
            -1.143246664003783e-09,
            0.4192228762661959,
            -4.255764407545826e-09
          ],
          [
            -1.3871997994741037e-09,
            0.3870538773539156,
            -5.124038970905076e-09
          ],
          [
            -1.651801362356764e-09,
            0.35968055716818137,
            -6.037465749564319e-09
          ]
        ]
      },
      "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": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.613100367302385e-15,
        "parent_symmetrization_rmsd_A": 0.08342433770900803,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -284.11199120835147,
        "reduced_polarization": [
          -4.992612013732481e-17,
          -3.601401173053346e-15,
          -2.862013931808258e-16
        ],
        "cartesian_polarization_e_A2": [
          8.285902384670315e-19,
          -2.7504747733184873e-17,
          -4.5054594216644845e-18
        ],
        "ranking_score": 0.08342433770901526
      }
    }
  ],
  "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": 97,
      "full_response": 29,
      "energy_polarization": 68
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 122,
      "full_response": 54,
      "energy_polarization": 68
    },
    "elapsed_seconds": 3162.1154625350027
  }
}