{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 42,
  "input_formula": "As6Ca10Cl2O24",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -259.34544570050303,
  "input_cartesian_polarization_e_A2": [
    0.0016040237694058541,
    -1.8835755057007783e-09,
    1.1066998053396127e-08
  ],
  "input_reduced_polarization": [
    0.1460695898578209,
    2.7466432762017844e-07,
    7.789583897686856e-07
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        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": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 6.248223871217329e-15,
      "parent_symmetrization_rmsd_A": 0.17809875824524132,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -259.1021132042888,
      "reduced_polarization": [
        2.7739707442618284e-15,
        -5.292000946498004e-15,
        1.8275978324275206e-15
      ],
      "cartesian_polarization_e_A2": [
        3.0461610892201616e-17,
        -1.0180818152671952e-16,
        2.5965471223530362e-17
      ],
      "ranking_score": 0.1780987582452538
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00011170441412076733,
      "parent_symmetrization_rmsd_A": 0.015994079095192567,
      "parent_cell_rmsd_A": 0.002421551488005506,
      "energy_eV": -259.2753747005156,
      "reduced_polarization": [
        0.00011170441410509375,
        -1.0607765492909867e-10,
        -1.8682514214768923e-09
      ],
      "cartesian_polarization_e_A2": [
        1.226966611248051e-06,
        1.3571536478476728e-11,
        -2.654334151480826e-11
      ],
      "ranking_score": 0.5168228757954355
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 1.5653601969981336e-15,
      "parent_symmetrization_rmsd_A": 0.17810004145014963,
      "parent_cell_rmsd_A": 0.002421551488005506,
      "energy_eV": -259.09638099085566,
      "reduced_polarization": [
        2.1011636912994508e-16,
        -1.150804243211263e-15,
        -1.040121748439401e-15
      ],
      "cartesian_polarization_e_A2": [
        2.3079284170054824e-18,
        -1.0343167092936416e-17,
        -1.4771196781865203e-17
      ],
      "ranking_score": 0.17870542932215414
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "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": 5.410570548444842e-07,
      "parent_symmetrization_rmsd_A": 0.03869906417687477,
      "parent_cell_rmsd_A": 0.00584272521870679,
      "energy_eV": -259.00141468371555,
      "reduced_polarization": [
        0.5000005410570548,
        8.107484330472569e-13,
        4.413297135374104e-12
      ],
      "cartesian_polarization_e_A2": [
        0.0054872200188387085,
        6.957023916228751e-12,
        9.707251876892144e-11
      ],
      "ranking_score": 0.5401608275956612
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 6.487656826876142e-06,
      "parent_symmetrization_rmsd_A": 0.07981050027868576,
      "parent_cell_rmsd_A": 0.01644388638015073,
      "energy_eV": -256.36058597019826,
      "reduced_polarization": [
        -1.6922924113988138e-06,
        -3.236659763442556e-07,
        0.5000062546844711
      ],
      "cartesian_polarization_e_A2": [
        5.067380875792208e-06,
        -0.0040997163678119,
        0.007100922873811539
      ],
      "ranking_score": 0.5839344471873772
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.99043453157689e-06,
      "parent_symmetrization_rmsd_A": 0.08773338895341315,
      "parent_cell_rmsd_A": 0.01735408014103967,
      "energy_eV": -256.0276322772355,
      "reduced_polarization": [
        0.49999562397397723,
        -2.3710288512884507e-06,
        0.5000003647673894
      ],
      "cartesian_polarization_e_A2": [
        0.005492203514276199,
        -0.00409357922618901,
        0.007121980091345433
      ],
      "ranking_score": 0.5920818898577362
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "target_residual": 0.14606958986015614,
            "energy_eV": -259.34544570050303,
            "max_atomic_step_A": 0.014336681713847041,
            "max_log_strain_component": 0.0005521099191314935,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0005522623600456,
              0.9998717344632077,
              0.9998717282807948
            ],
            "cell_volume_ratio": 1.0002955998901053,
            "cell_rmsd_from_input_A": 0.002421551488005506
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00011170441410509375,
              -1.0607765492909867e-10,
              -1.8682514214768923e-09
            ],
            "branch_aligned_reduced_polarization": [
              0.00011170441410509375,
              -1.0607765492909867e-10,
              -1.8682514214768923e-09
            ],
            "target_residual": 0.00011170441412076733,
            "energy_eV": -259.2753747005156
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P6_3/m",
        "spacegroup_number": 176,
        "pointgroup": "6/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": 6.248223871217329e-15,
        "parent_symmetrization_rmsd_A": 0.17809875824524132,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -259.1021132042888,
        "reduced_polarization": [
          2.7739707442618284e-15,
          -5.292000946498004e-15,
          1.8275978324275206e-15
        ],
        "cartesian_polarization_e_A2": [
          3.0461610892201616e-17,
          -1.0180818152671952e-16,
          2.5965471223530362e-17
        ],
        "ranking_score": 0.1780987582452538
      },
      "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": [
          -259.345445700503,
          -259.31052689558624,
          -259.2768052373399,
          -259.24307399979523,
          -259.2069115053814,
          -259.16961227391414,
          -259.1360034692426,
          -259.11147369299624,
          -259.1021132042888
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.001604023769405849,
            -1.8835755278252693e-09,
            1.106699805646003e-08
          ],
          [
            0.0014129092986316194,
            -1.517809408244312e-09,
            1.0039409865109601e-08
          ],
          [
            0.0012364198155286798,
            -1.089396286802156e-09,
            9.003845632524118e-09
          ],
          [
            0.0010620952849243288,
            -7.125484492306224e-10,
            7.899561340712477e-09
          ],
          [
            0.0008799110737986062,
            -4.28254855839399e-10,
            6.666155917011241e-09
          ],
          [
            0.0006836414219943666,
            -2.386742670861869e-10,
            5.240699723145869e-09
          ],
          [
            0.00047046105980310803,
            -1.238637950837873e-10,
            3.6325595490891203e-09
          ],
          [
            0.00024052392190982954,
            -5.1850161490449076e-11,
            1.8876249115674625e-09
          ],
          [
            1.125869653486158e-17,
            -2.6642638279808837e-17,
            1.528621371304032e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.0269562977782698e-15,
            -1.0860581010822774e-15,
            1.075930842816007e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.14606958985782037,
            2.7466432639400296e-07,
            7.789583900130737e-07
          ],
          [
            0.1286658500290605,
            2.6079613923979394e-07,
            7.06630877256309e-07
          ],
          [
            0.11259392709202443,
            2.5046595097943936e-07,
            6.337419652391318e-07
          ],
          [
            0.09671915442767243,
            2.3457410447402793e-07,
            5.560161439044364e-07
          ],
          [
            0.08012864404666853,
            2.084963989235078e-07,
            4.692020414420739e-07
          ],
          [
            0.06225545034006785,
            1.6988657203231838e-07,
            3.688703112958436e-07
          ],
          [
            0.04284229159208175,
            1.2028990248325044e-07,
            2.5568024164535075e-07
          ],
          [
            0.02190318578469508,
            6.327033019726258e-08,
            1.3286179811888843e-07
          ],
          [
            9.992007221626409e-16,
            -1.1102230246251565e-15,
            1.1102230246251565e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -259.1021132042888,
          -259.1114736929962,
          -259.1360034692426,
          -259.16961227391425,
          -259.2069115053814,
          -259.2430739997951,
          -259.2768052373399,
          -259.3105268955864,
          -259.3454457005031
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.125869653486158e-17,
            -2.6642638279808837e-17,
            1.528621371304032e-17
          ],
          [
            -0.00024052392190979801,
            5.18501471478288e-11,
            -1.8876248941165344e-09
          ],
          [
            -0.00047046105980311063,
            1.2386387817551542e-10,
            -3.6325595402748474e-09
          ],
          [
            -0.0006836414219943293,
            2.3867423725753317e-10,
            -5.240699759057925e-09
          ],
          [
            -0.0008799110737985509,
            4.2825490793685795e-10,
            -6.66615591640068e-09
          ],
          [
            -0.0010620952849242581,
            7.125483333351458e-10,
            -7.899561336716081e-09
          ],
          [
            -0.0012364198155286627,
            1.0893962442294402e-09,
            -9.003845619247202e-09
          ],
          [
            -0.0014129092986315387,
            1.5178093947120721e-09,
            -1.0039409842607673e-08
          ],
          [
            -0.0016040237694058027,
            1.88357549552107e-09,
            -1.1066998006527286e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.14606958985781837,
          -2.74664328551506e-07,
          -7.789583878324789e-07
        ],
        "actual_opposite_endpoint_branch_residual": 3.204230099818658e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.0269562977782698e-15,
            -1.0860581010822774e-15,
            1.075930842816007e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.14606958985782037,
            2.7466432639400296e-07,
            7.789583900130737e-07
          ],
          [
            0.1286658500290605,
            2.6079613923979394e-07,
            7.06630877256309e-07
          ],
          [
            0.11259392709202443,
            2.5046595097943936e-07,
            6.337419652391318e-07
          ],
          [
            0.09671915442767243,
            2.3457410447402793e-07,
            5.560161439044364e-07
          ],
          [
            0.08012864404666853,
            2.084963989235078e-07,
            4.692020414420739e-07
          ],
          [
            0.06225545034006785,
            1.6988657203231838e-07,
            3.688703112958436e-07
          ],
          [
            0.04284229159208175,
            1.2028990248325044e-07,
            2.5568024164535075e-07
          ],
          [
            0.02190318578469508,
            6.327033019726258e-08,
            1.3286179811888843e-07
          ],
          [
            9.992007221626409e-16,
            -1.1102230246251565e-15,
            1.1102230246251565e-15
          ],
          [
            -0.021903185784692247,
            -6.327033047481834e-08,
            -1.3286179695315425e-07
          ],
          [
            -0.04284229159208203,
            -1.2028989709866877e-07,
            -2.5568024109023924e-07
          ],
          [
            -0.06225545034006447,
            -1.698865750854317e-07,
            -3.6887031384935653e-07
          ],
          [
            -0.08012864404666348,
            -2.0849639575937218e-07,
            -4.6920204138656274e-07
          ],
          [
            -0.0967191544276661,
            -2.34574111468433e-07,
            -5.560161435713695e-07
          ],
          [
            -0.11259392709202282,
            -2.504659530888631e-07,
            -6.337419642954423e-07
          ],
          [
            -0.12866585002905317,
            -2.6079613923979394e-07,
            -7.066308756464856e-07
          ],
          [
            -0.14606958985781626,
            -2.7466432661604756e-07,
            -7.7895838646036e-07
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.14606958985782093,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "target_residual": 0.3539304101431428,
            "energy_eV": -259.34544570050303,
            "max_atomic_step_A": 0.03473814345133191,
            "max_log_strain_component": 0.0013377766742650897,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0003108739537558,
              1.0003108589673004,
              0.9986631177498683
            ],
            "cell_volume_ratio": 0.9992841159959813,
            "cell_rmsd_from_input_A": 0.005861893354245675
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5011752656275666,
              5.232124090276774e-09,
              -3.3057685701193393e-09
            ],
            "branch_aligned_reduced_polarization": [
              0.5011752656275666,
              5.232124090276774e-09,
              -3.3057685701193393e-09
            ],
            "target_residual": 0.0011752656275829418,
            "energy_eV": -258.99907021204797,
            "max_atomic_step_A": 0.00011440631311002763,
            "max_log_strain_component": 4.377409381341191e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0003098565691688,
              1.0003098416317666,
              0.9986674893167363
            ],
            "cell_volume_ratio": 0.9992864576417342,
            "cell_rmsd_from_input_A": 0.00584272521870679
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000005410570548,
              8.107484330472569e-13,
              4.413297135374104e-12
            ],
            "branch_aligned_reduced_polarization": [
              0.5000005410570548,
              8.107484330472569e-13,
              4.413297135374104e-12
            ],
            "target_residual": 5.410570548444842e-07,
            "energy_eV": -259.00141468371555
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "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": 5.410570548444842e-07,
        "parent_symmetrization_rmsd_A": 0.03869906417687477,
        "parent_cell_rmsd_A": 0.00584272521870679,
        "energy_eV": -259.00141468371555,
        "reduced_polarization": [
          0.5000005410570548,
          8.107484330472569e-13,
          4.413297135374104e-12
        ],
        "cartesian_polarization_e_A2": [
          0.0054872200188387085,
          6.957023916228751e-12,
          9.707251876892144e-11
        ],
        "ranking_score": 0.5401608275956612
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.78958389791029e-07
            ],
            "target_residual": 0.520898786832456,
            "energy_eV": -259.34544570050303,
            "max_atomic_step_A": 0.11093157228715234,
            "max_log_strain_component": 0.002175435289518733,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0031700239404546,
              0.9998717428126693,
              0.9972625805452665
            ],
            "cell_volume_ratio": 1.0002956152415252,
            "cell_rmsd_from_input_A": 0.016386911530660107
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0059279035409763965,
              0.0001753061619193922,
              0.4979256785257635
            ],
            "branch_aligned_reduced_polarization": [
              -0.0059279035409763965,
              0.0001753061619193922,
              0.4979256785257635
            ],
            "target_residual": 0.00628280050773586,
            "energy_eV": -256.38099435301706,
            "max_atomic_step_A": 0.000812750481074925,
            "max_log_strain_component": 2.2643040393525482e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0031731740665915,
              0.9998770029445017,
              0.9972421147125148
            ],
            "cell_volume_ratio": 1.0002834904706166,
            "cell_rmsd_from_input_A": 0.01644388638015073
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.6922924113988138e-06,
              -3.236659763442556e-07,
              0.5000062546844711
            ],
            "branch_aligned_reduced_polarization": [
              -1.6922924113988138e-06,
              -3.236659763442556e-07,
              0.5000062546844711
            ],
            "target_residual": 6.487656826876142e-06,
            "energy_eV": -256.36058597019826
          }
        ],
        "iterations": 2
      },
      "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 6.487656826876142e-06,
        "parent_symmetrization_rmsd_A": 0.07981050027868576,
        "parent_cell_rmsd_A": 0.01644388638015073,
        "energy_eV": -256.36058597019826,
        "reduced_polarization": [
          -1.6922924113988138e-06,
          -3.236659763442556e-07,
          0.5000062546844711
        ],
        "cartesian_polarization_e_A2": [
          5.067380875792208e-06,
          -0.0040997163678119,
          0.007100922873811539
        ],
        "ranking_score": 0.5839344471873772
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.1460695898578209,
              2.7466432762017844e-07,
              7.789583897686856e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.14606958985782093,
              2.7466432762017844e-07,
              7.78958389791029e-07
            ],
            "target_residual": 0.6125895495890404,
            "energy_eV": -259.34544570050303,
            "max_atomic_step_A": 0.11548753983140671,
            "max_log_strain_component": 0.0021754423632800723,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0025368072069578,
              1.0003108683772832,
              0.9964457911710963
            ],
            "cell_volume_ratio": 0.9992841313318779,
            "cell_rmsd_from_input_A": 0.017207201930022065
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4959531814803515,
              -0.000769012465995383,
              0.49599941179521123
            ],
            "branch_aligned_reduced_polarization": [
              0.4959531814803515,
              -0.000769012465995383,
              0.49599941179521123
            ],
            "target_residual": 0.005742196991406807,
            "energy_eV": -256.07873427805583,
            "max_atomic_step_A": 0.001011941081261769,
            "max_log_strain_component": 1.9000905576506118e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6195737499693691,
            "cell_principal_stretches": [
              1.0025546980471158,
              1.000314422162502,
              0.9964163133678748
            ],
            "cell_volume_ratio": 0.9992759519248269,
            "cell_rmsd_from_input_A": 0.01735408014103967
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999562397397723,
              -2.3710288512884507e-06,
              0.5000003647673894
            ],
            "branch_aligned_reduced_polarization": [
              0.49999562397397723,
              -2.3710288512884507e-06,
              0.5000003647673894
            ],
            "target_residual": 4.99043453157689e-06,
            "energy_eV": -256.0276322772355
          }
        ],
        "iterations": 2
      },
      "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.99043453157689e-06,
        "parent_symmetrization_rmsd_A": 0.08773338895341315,
        "parent_cell_rmsd_A": 0.01735408014103967,
        "energy_eV": -256.0276322772355,
        "reduced_polarization": [
          0.49999562397397723,
          -2.3710288512884507e-06,
          0.5000003647673894
        ],
        "cartesian_polarization_e_A2": [
          0.005492203514276199,
          -0.00409357922618901,
          0.007121980091345433
        ],
        "ranking_score": 0.5920818898577362
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41
        ],
        "endpoint_rmsd_A": 0.17809875824524132,
        "minimum_distance_A_by_image": [
          1.7048761015921727,
          1.7048758977513032,
          1.7048757211137489,
          1.7048755716795176,
          1.70487544944862,
          1.7048753544210595,
          1.7048752865968402,
          1.7048752459759673,
          1.7048752325584415
        ],
        "minimum_distance_A": 1.7048752325584415,
        "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": [
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513,
          625.0636740430513
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.025267341138005e-15,
        -1.0860581025861236e-15,
        1.0759308316599812e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -259.345445700503,
          -259.31052689558624,
          -259.2768052373399,
          -259.24307399979523,
          -259.2069115053814,
          -259.16961227391414,
          -259.1360034692426,
          -259.11147369299624,
          -259.1021132042888
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.001604023769405849,
            -1.8835755278252693e-09,
            1.106699805646003e-08
          ],
          [
            0.0014129092986316194,
            -1.517809408244312e-09,
            1.0039409865109601e-08
          ],
          [
            0.0012364198155286798,
            -1.089396286802156e-09,
            9.003845632524118e-09
          ],
          [
            0.0010620952849243288,
            -7.125484492306224e-10,
            7.899561340712477e-09
          ],
          [
            0.0008799110737986062,
            -4.28254855839399e-10,
            6.666155917011241e-09
          ],
          [
            0.0006836414219943666,
            -2.386742670861869e-10,
            5.240699723145869e-09
          ],
          [
            0.00047046105980310803,
            -1.238637950837873e-10,
            3.6325595490891203e-09
          ],
          [
            0.00024052392190982954,
            -5.1850161490449076e-11,
            1.8876249115674625e-09
          ],
          [
            1.125869653486158e-17,
            -2.6642638279808837e-17,
            1.528621371304032e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.0269562977782698e-15,
            -1.0860581010822774e-15,
            1.075930842816007e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.14606958985782037,
            2.7466432639400296e-07,
            7.789583900130737e-07
          ],
          [
            0.1286658500290605,
            2.6079613923979394e-07,
            7.06630877256309e-07
          ],
          [
            0.11259392709202443,
            2.5046595097943936e-07,
            6.337419652391318e-07
          ],
          [
            0.09671915442767243,
            2.3457410447402793e-07,
            5.560161439044364e-07
          ],
          [
            0.08012864404666853,
            2.084963989235078e-07,
            4.692020414420739e-07
          ],
          [
            0.06225545034006785,
            1.6988657203231838e-07,
            3.688703112958436e-07
          ],
          [
            0.04284229159208175,
            1.2028990248325044e-07,
            2.5568024164535075e-07
          ],
          [
            0.02190318578469508,
            6.327033019726258e-08,
            1.3286179811888843e-07
          ],
          [
            9.992007221626409e-16,
            -1.1102230246251565e-15,
            1.1102230246251565e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -259.1021132042888,
          -259.1114736929962,
          -259.1360034692426,
          -259.16961227391425,
          -259.2069115053814,
          -259.2430739997951,
          -259.2768052373399,
          -259.3105268955864,
          -259.3454457005031
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.125869653486158e-17,
            -2.6642638279808837e-17,
            1.528621371304032e-17
          ],
          [
            -0.00024052392190979801,
            5.18501471478288e-11,
            -1.8876248941165344e-09
          ],
          [
            -0.00047046105980311063,
            1.2386387817551542e-10,
            -3.6325595402748474e-09
          ],
          [
            -0.0006836414219943293,
            2.3867423725753317e-10,
            -5.240699759057925e-09
          ],
          [
            -0.0008799110737985509,
            4.2825490793685795e-10,
            -6.66615591640068e-09
          ],
          [
            -0.0010620952849242581,
            7.125483333351458e-10,
            -7.899561336716081e-09
          ],
          [
            -0.0012364198155286627,
            1.0893962442294402e-09,
            -9.003845619247202e-09
          ],
          [
            -0.0014129092986315387,
            1.5178093947120721e-09,
            -1.0039409842607673e-08
          ],
          [
            -0.0016040237694058027,
            1.88357549552107e-09,
            -1.1066998006527286e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.14606958985781837,
          -2.74664328551506e-07,
          -7.789583878324789e-07
        ],
        "actual_opposite_endpoint_branch_residual": 3.204230099818658e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.025267341138005e-15,
            -1.0860581025861236e-15,
            1.0759308316599812e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.14606958985782043,
            2.746643263793897e-07,
            7.789583899843405e-07
          ],
          [
            0.12866585002906056,
            2.6079613919099267e-07,
            7.066308772281588e-07
          ],
          [
            0.11259392709202437,
            2.504659509372158e-07,
            6.337419652373149e-07
          ],
          [
            0.09671915442767248,
            2.3457410452101026e-07,
            5.560161438676722e-07
          ],
          [
            0.08012864404666852,
            2.0849639895572917e-07,
            4.692020414215761e-07
          ],
          [
            0.062255450340067846,
            1.6988657199198246e-07,
            3.6887031134429196e-07
          ],
          [
            0.04284229159208178,
            1.2028990247952135e-07,
            2.5568024169200977e-07
          ],
          [
            0.021903185784695096,
            6.327033023731104e-08,
            1.3286179815949572e-07
          ],
          [
            1.0269562977782698e-15,
            -1.0860581010822774e-15,
            1.075930842816007e-15
          ],
          [
            -0.021903185784692223,
            -6.327033049742915e-08,
            -1.3286179693119993e-07
          ],
          [
            -0.04284229159208201,
            -1.202898971043986e-07,
            -2.55680241071611e-07
          ],
          [
            -0.06225545034006445,
            -1.6988657507405968e-07,
            -3.6887031387198714e-07
          ],
          [
            -0.08012864404666348,
            -2.084963957585992e-07,
            -4.6920204137860137e-07
          ],
          [
            -0.09671915442766607,
            -2.34574111444868e-07,
            -5.560161435863832e-07
          ],
          [
            -0.1125939270920228,
            -2.5046595306501754e-07,
            -6.337419643028098e-07
          ],
          [
            -0.1286658500290532,
            -2.607961392239544e-07,
            -7.06630875644345e-07
          ],
          [
            -0.14606958985781623,
            -2.746643265912427e-07,
            -7.789583864697894e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.14606958985782037,
            2.7466432639400296e-07,
            7.789583900130737e-07
          ],
          [
            0.1286658500290605,
            2.6079613923979394e-07,
            7.06630877256309e-07
          ],
          [
            0.11259392709202443,
            2.5046595097943936e-07,
            6.337419652391318e-07
          ],
          [
            0.09671915442767243,
            2.3457410447402793e-07,
            5.560161439044364e-07
          ],
          [
            0.08012864404666853,
            2.084963989235078e-07,
            4.692020414420739e-07
          ],
          [
            0.06225545034006785,
            1.6988657203231838e-07,
            3.688703112958436e-07
          ],
          [
            0.04284229159208175,
            1.2028990248325044e-07,
            2.5568024164535075e-07
          ],
          [
            0.02190318578469508,
            6.327033019726258e-08,
            1.3286179811888843e-07
          ],
          [
            9.992007221626409e-16,
            -1.1102230246251565e-15,
            1.1102230246251565e-15
          ],
          [
            -0.021903185784692247,
            -6.327033047481834e-08,
            -1.3286179695315425e-07
          ],
          [
            -0.04284229159208203,
            -1.2028989709866877e-07,
            -2.5568024109023924e-07
          ],
          [
            -0.06225545034006447,
            -1.698865750854317e-07,
            -3.6887031384935653e-07
          ],
          [
            -0.08012864404666348,
            -2.0849639575937218e-07,
            -4.6920204138656274e-07
          ],
          [
            -0.0967191544276661,
            -2.34574111468433e-07,
            -5.560161435713695e-07
          ],
          [
            -0.11259392709202282,
            -2.504659530888631e-07,
            -6.337419642954423e-07
          ],
          [
            -0.12866585002905317,
            -2.6079613923979394e-07,
            -7.066308756464856e-07
          ],
          [
            -0.14606958985781626,
            -2.7466432661604756e-07,
            -7.7895838646036e-07
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P6_3/m",
        "spacegroup_number": 176,
        "pointgroup": "6/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": 6.248223871217329e-15,
        "parent_symmetrization_rmsd_A": 0.17809875824524132,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -259.1021132042888,
        "reduced_polarization": [
          2.7739707442618284e-15,
          -5.292000946498004e-15,
          1.8275978324275206e-15
        ],
        "cartesian_polarization_e_A2": [
          3.0461610892201616e-17,
          -1.0180818152671952e-16,
          2.5965471223530362e-17
        ],
        "ranking_score": 0.1780987582452538
      }
    }
  ],
  "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": 40,
      "full_response": 8,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 65,
      "full_response": 33,
      "energy_polarization": 32
    },
    "elapsed_seconds": 798.3432951039867
  }
}