{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 12,
  "input_formula": "Hf4O8",
  "input_spacegroup": "Pca2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -116.88169873957682,
  "input_cartesian_polarization_e_A2": [
    -1.7153365226830372e-16,
    3.799274771128696e-17,
    -0.003984740338383719
  ],
  "input_reduced_polarization": [
    -4.388953861305899e-15,
    1.0156156472174635e-15,
    -0.10584040097888446
  ],
  "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": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbca",
      "spacegroup_number": 61,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.8024672623973145e-16,
      "parent_symmetrization_rmsd_A": 0.39600949533021934,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -116.242558159053,
      "reduced_polarization": [
        2.265606435007847e-16,
        3.467955868547436e-16,
        7.766835873187673e-16
      ],
      "cartesian_polarization_e_A2": [
        8.854678328375822e-18,
        1.2973133364829692e-17,
        2.924103075882248e-17
      ],
      "ranking_score": 0.3960094953302211
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcn",
      "spacegroup_number": 60,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.082717944988012e-15,
      "parent_symmetrization_rmsd_A": 0.3978548657660782,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -116.81743489220061,
      "reduced_polarization": [
        5.901114435369276e-16,
        -1.995450797378485e-15,
        8.751364364155124e-17
      ],
      "cartesian_polarization_e_A2": [
        2.3063348204141675e-17,
        -7.46469975357264e-17,
        3.2947640291630963e-18
      ],
      "ranking_score": 0.39785486576608237
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1412486966844346e-15,
      "parent_symmetrization_rmsd_A": 0.40050128934825874,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -114.45802629371669,
      "reduced_polarization": [
        4.026898238146746e-16,
        -2.069764137418787e-15,
        3.726436666628868e-16
      ],
      "cartesian_polarization_e_A2": [
        1.573834184478262e-17,
        -7.742695468533277e-17,
        1.402950325831685e-17
      ],
      "ranking_score": 0.400501289348263
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pca2_1",
      "spacegroup_number": 29,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1086963781186384e-06,
      "parent_symmetrization_rmsd_A": 0.01859360493193892,
      "parent_cell_rmsd_A": 0.009075409735988058,
      "energy_eV": -116.88255023818638,
      "reduced_polarization": [
        -4.006367176315256e-15,
        -2.529064039267526e-15,
        -2.1086963781186384e-06
      ],
      "cartesian_polarization_e_A2": [
        -1.5615930867683188e-16,
        -9.42906732417927e-17,
        -7.931448877974515e-08
      ],
      "ranking_score": 0.5208666747586922
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.100368373537244e-15,
      "parent_symmetrization_rmsd_A": 0.400515863789893,
      "parent_cell_rmsd_A": 0.009075409735988058,
      "energy_eV": -114.32891974513436,
      "reduced_polarization": [
        -3.8192477754986866e-16,
        8.888847378360318e-16,
        -1.864286644186226e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.4886583022081566e-17,
        3.31402475050044e-17,
        -7.012149480451109e-17
      ],
      "ranking_score": 0.4027847162238942
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pbca",
      "spacegroup_number": 61,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.3281409702001067e-15,
      "parent_symmetrization_rmsd_A": 0.3960153976823908,
      "parent_cell_rmsd_A": 0.009075409735988058,
      "energy_eV": -116.23164855343022,
      "reduced_polarization": [
        -1.263505896927815e-16,
        1.6621869401020765e-15,
        2.8805715443576277e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.924866502291675e-18,
        6.197123682050358e-17,
        1.0834706305041685e-16
      ],
      "ranking_score": 0.39828425011639446
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pca2_1",
      "spacegroup_number": 29,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.4701361764755134e-05,
      "parent_symmetrization_rmsd_A": 0.06687567361942275,
      "parent_cell_rmsd_A": 0.03197618334758259,
      "energy_eV": -116.59158712232964,
      "reduced_polarization": [
        5.138750416589389e-15,
        6.906139454603837e-15,
        -0.5000347013617648
      ],
      "cartesian_polarization_e_A2": [
        1.8442502451465755e-16,
        3.23186871676336e-18,
        -0.01888901153034174
      ],
      "ranking_score": 0.5749391221798479
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0001025977856262976,
      "parent_symmetrization_rmsd_A": 0.09868752215648446,
      "parent_cell_rmsd_A": 0.03620935312644676,
      "energy_eV": -116.46441126700897,
      "reduced_polarization": [
        -0.500089458187765,
        6.3537712246541205e-15,
        -5.023483111576492e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.01948842685818363,
        3.046869996432925e-16,
        -0.0001394784321899225
      ],
      "ranking_score": 0.6079450560093488
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.6220032542427477e-05,
      "parent_symmetrization_rmsd_A": 0.08720813577056426,
      "parent_cell_rmsd_A": 0.011175688938634815,
      "energy_eV": -116.53093746242139,
      "reduced_polarization": [
        3.896033771825707e-15,
        0.5000149357213646,
        6.3256369637568896e-06
      ],
      "cartesian_polarization_e_A2": [
        1.5617483193886354e-16,
        0.018643832439693902,
        -2.6906464682595052e-05
      ],
      "ranking_score": 0.5900344980703078
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.955961904654889e-05,
      "parent_symmetrization_rmsd_A": 0.11775639521840307,
      "parent_cell_rmsd_A": 0.04676723145307011,
      "energy_eV": -116.12914229001778,
      "reduced_polarization": [
        -0.49997147445205425,
        6.797913608061897e-15,
        -0.5000274090600624
      ],
      "cartesian_polarization_e_A2": [
        -0.0198586802865187,
        9.532356982273594e-17,
        -0.019031118962795492
      ],
      "ranking_score": 0.6295273223197637
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 5.0071427374574785e-05,
      "parent_symmetrization_rmsd_A": 0.10914627734416774,
      "parent_cell_rmsd_A": 0.032810283298599155,
      "energy_eV": -116.238202689474,
      "reduced_polarization": [
        5.7616123888166484e-15,
        0.5000196774656375,
        -0.5000460428624807
      ],
      "cartesian_polarization_e_A2": [
        9.779464313566377e-17,
        0.018959257813774062,
        -0.01891742065779679
      ],
      "ranking_score": 0.6174489910235667
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00011277263466282792,
      "parent_symmetrization_rmsd_A": 0.13006604112865275,
      "parent_cell_rmsd_A": 0.036694533365630146,
      "energy_eV": -116.09417156809694,
      "reduced_polarization": [
        -0.5000321696909148,
        0.4999471945744903,
        -9.430994195724405e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.01948865179760266,
        0.018637128824260135,
        -0.00016798130928822477
      ],
      "ranking_score": 0.639465219739386
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 4.2318653123274095e-05,
      "parent_symmetrization_rmsd_A": 0.14519013544521722,
      "parent_cell_rmsd_A": 0.04728141565731832,
      "energy_eV": -115.77776141565121,
      "reduced_polarization": [
        -0.4999654675341893,
        0.4999882889884746,
        -0.5000214762523791
      ],
      "cartesian_polarization_e_A2": [
        -0.019859555498046542,
        0.01894635771158782,
        -0.01905816131978343
      ],
      "ranking_score": 0.6570951266657934
    }
  ],
  "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": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "target_residual": 0.10584040097888446,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.015286412012098705,
            "max_log_strain_component": 0.0025300848105006385,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0025332881761007,
              1.0007973057202983,
              1.0001368477077601
            ],
            "cell_volume_ratio": 1.003469917469859,
            "cell_rmsd_from_input_A": 0.008975210889777142
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.9991919744258467e-14,
              6.4105058854976285e-15,
              -0.0011379634767031785
            ],
            "branch_aligned_reduced_polarization": [
              1.9991919744258467e-14,
              6.4105058854976285e-15,
              -0.0011379634767031785
            ],
            "target_residual": 0.0011379634767031785,
            "energy_eV": -116.88273192886831,
            "max_atomic_step_A": 0.00016662312686991886,
            "max_log_strain_component": 2.8178853388513627e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0025615388126787,
              1.0008061893019387,
              1.0001383719563786
            ],
            "cell_volume_ratio": 1.003508631441061,
            "cell_rmsd_from_input_A": 0.009075409735988058
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.006367176315256e-15,
              -2.529064039267526e-15,
              -2.1086963781186384e-06
            ],
            "branch_aligned_reduced_polarization": [
              -4.006367176315256e-15,
              -2.529064039267526e-15,
              -2.1086963781186384e-06
            ],
            "target_residual": 2.1086963781186384e-06,
            "energy_eV": -116.88255023818638
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pbca",
        "spacegroup_number": 61,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 8.8024672623973145e-16,
        "parent_symmetrization_rmsd_A": 0.39600949533021934,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -116.242558159053,
        "reduced_polarization": [
          2.265606435007847e-16,
          3.467955868547436e-16,
          7.766835873187673e-16
        ],
        "cartesian_polarization_e_A2": [
          8.854678328375822e-18,
          1.2973133364829692e-17,
          2.924103075882248e-17
        ],
        "ranking_score": 0.3960094953302211
      },
      "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": [
          -116.88169873957683,
          -116.55585987911734,
          -116.12322860849332,
          -115.84120539733574,
          -115.85617123242571,
          -116.0310057157511,
          -116.17088934478198,
          -116.22989352686541,
          -116.24255815905296
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5094137708603436e-16,
            -3.541871331350329e-17,
            -0.003984740338383591
          ],
          [
            9.472446583843902e-17,
            -3.974309110177985e-17,
            -0.007477561783124653
          ],
          [
            7.09918686908736e-17,
            -4.993626731700318e-17,
            -0.007702732947958729
          ],
          [
            7.516180441528314e-17,
            -5.59080271198613e-17,
            -0.0037010687475718985
          ],
          [
            -2.736713371723597e-16,
            -6.69248943423754e-18,
            0.001390326502793077
          ],
          [
            -2.740831826760051e-16,
            -1.2190626907903457e-16,
            0.003754873415875355
          ],
          [
            -1.468229220495805e-16,
            -1.1202197699154528e-16,
            0.0033930656058581915
          ],
          [
            -5.683467950306341e-17,
            -3.0888412773404026e-17,
            0.001866963926234684
          ],
          [
            -1.0378506691863754e-16,
            -4.4685237145524495e-17,
            6.5895280583261926e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.0023045398265786e-15,
            -1.78902485282209e-16,
            0.036929059876176805
          ],
          [
            -7.012842244175452e-15,
            -3.2587775780636223e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445712e-15,
            -8.2570377822558e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.7502728728310247e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.002304539826579e-15,
            -1.7890248528220903e-16,
            0.03692905987617681
          ],
          [
            -7.012842244175452e-15,
            -3.258777578063622e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445714e-15,
            -8.257037782255798e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.734723475976807e-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": [
          [
            -3.885780586188048e-15,
            -9.43689570931383e-16,
            -0.10584040097888103
          ],
          [
            2.4424906541753444e-15,
            -1.0547118733938987e-15,
            -0.19861473277109765
          ],
          [
            1.7763568394002505e-15,
            -1.3322676295501878e-15,
            -0.2045956008706707
          ],
          [
            1.887379141862766e-15,
            -1.4988010832439613e-15,
            -0.09830567791835515
          ],
          [
            -6.994405055138486e-15,
            -1.6653345369377348e-16,
            0.036929059876176784
          ],
          [
            -6.994405055138486e-15,
            -3.2751579226442118e-15,
            0.09973480684124092
          ],
          [
            -3.774758283725532e-15,
            -2.9976021664879227e-15,
            0.09012467407533997
          ],
          [
            -1.4432899320127035e-15,
            -8.326672684688674e-16,
            0.049589231364054576
          ],
          [
            -2.6645352591003757e-15,
            -1.2212453270876722e-15,
            2.220446049250313e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -116.24255815905299,
          -116.2298935268654,
          -116.17088934478194,
          -116.0310057157511,
          -115.85617123242582,
          -115.84120539733571,
          -116.12322860849325,
          -116.5558598791173,
          -116.88169873957679
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.127476520385069e-17,
            -2.0180429678623967e-17,
            1.2849579713736075e-16
          ],
          [
            1.6473820145815483e-17,
            7.33084996488789e-17,
            -0.0018669639262346093
          ],
          [
            3.2947640291630966e-17,
            1.017258394004106e-16,
            -0.003393065605858195
          ],
          [
            -4.9833305941091835e-17,
            6.218867105045344e-17,
            -0.0037548734158749826
          ],
          [
            -1.779172575748072e-16,
            8.030987321085047e-18,
            -0.001390326502793358
          ],
          [
            7.629437955030795e-17,
            1.9356738671333192e-17,
            0.0037010687475721262
          ],
          [
            8.669347851735397e-17,
            -6.198274829863075e-17,
            0.007702732947959227
          ],
          [
            -5.353991547390032e-18,
            1.6659150622455907e-16,
            0.00747756178312532
          ],
          [
            -1.413659691262791e-16,
            3.80957090871983e-17,
            0.003984740338383991
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3119441914347765e-15,
            -5.394598017740456e-16,
            3.413032102020498e-15
          ],
          [
            4.2150817395494824e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137186e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618427
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.369901565353582e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3119441914347765e-15,
            -5.394598017740456e-16,
            3.413032102020498e-15
          ],
          [
            4.215081739549482e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137188e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618428
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.3699015653535826e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4489343479701343e-15,
          -1.4422292659673463e-15,
          0.1058404009788814
        ],
        "actual_opposite_endpoint_branch_residual": 1.0780503786927878e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.0023045398265786e-15,
            -1.78902485282209e-16,
            0.036929059876176805
          ],
          [
            -7.012842244175452e-15,
            -3.2587775780636223e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445712e-15,
            -8.2570377822558e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.7502728728310247e-16
          ],
          [
            4.2150817395494824e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137186e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618427
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.369901565353582e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.002304539826579e-15,
            -1.7890248528220903e-16,
            0.03692905987617681
          ],
          [
            -7.012842244175452e-15,
            -3.258777578063622e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445714e-15,
            -8.257037782255798e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.734723475976807e-16
          ],
          [
            4.215081739549482e-16,
            1.9596703003220435e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137188e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618428
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.3699015653535826e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "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": [
          [
            -3.885780586188048e-15,
            -9.43689570931383e-16,
            -0.10584040097888103
          ],
          [
            2.4424906541753444e-15,
            -1.0547118733938987e-15,
            -0.19861473277109765
          ],
          [
            1.7763568394002505e-15,
            -1.3322676295501878e-15,
            -0.2045956008706707
          ],
          [
            1.887379141862766e-15,
            -1.4988010832439613e-15,
            -0.09830567791835515
          ],
          [
            -6.994405055138486e-15,
            -1.6653345369377348e-16,
            0.036929059876176784
          ],
          [
            -6.994405055138486e-15,
            -3.2751579226442118e-15,
            0.09973480684124092
          ],
          [
            -3.774758283725532e-15,
            -2.9976021664879227e-15,
            0.09012467407533997
          ],
          [
            -1.4432899320127035e-15,
            -8.326672684688674e-16,
            0.049589231364054576
          ],
          [
            -2.6645352591003757e-15,
            -1.2212453270876722e-15,
            2.220446049250313e-16
          ],
          [
            4.440892098500626e-16,
            1.9984014443252818e-15,
            -0.04958923136405258
          ],
          [
            8.881784197001252e-16,
            2.6645352591003757e-15,
            -0.09012467407534008
          ],
          [
            -1.27675647831893e-15,
            1.6653345369377348e-15,
            -0.09973480684123104
          ],
          [
            -4.551914400963142e-15,
            2.220446049250313e-16,
            -0.03692905987618428
          ],
          [
            1.9984014443252818e-15,
            5.551115123125783e-16,
            0.0983056779183612
          ],
          [
            2.220446049250313e-15,
            -1.6653345369377348e-15,
            0.20459560087068396
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-15,
            0.1986147327711154
          ],
          [
            -3.608224830031759e-15,
            9.992007221626409e-16,
            0.10584040097889169
          ]
        ]
      },
      "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": [
        0.0,
        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": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888447
            ],
            "target_residual": 0.3941595990211155,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.05692803479044197,
            "max_log_strain_component": 0.009422273585256949,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              0.9994905309681478,
              0.9970363419735762,
              0.990621976945242
            ],
            "cell_volume_ratio": 0.9871829166847741,
            "cell_rmsd_from_input_A": 0.03305677318019655
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.934764238216375e-14,
              -4.285300045543816e-15,
              -0.5148523647998204
            ],
            "branch_aligned_reduced_polarization": [
              -4.934764238216375e-14,
              -4.285300045543816e-15,
              -0.5148523647998204
            ],
            "target_residual": 0.014852364799820439,
            "energy_eV": -116.57160164778749,
            "max_atomic_step_A": 0.002002891827586718,
            "max_log_strain_component": 0.00031061752863028783,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              0.9995073221407352,
              0.9971339026765957,
              0.9909297292896893
            ],
            "cell_volume_ratio": 0.987602818362085,
            "cell_rmsd_from_input_A": 0.03197618334758259
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.138750416589389e-15,
              6.906139454603837e-15,
              -0.5000347013617648
            ],
            "branch_aligned_reduced_polarization": [
              5.138750416589389e-15,
              6.906139454603837e-15,
              -0.5000347013617648
            ],
            "target_residual": 3.4701361764755134e-05,
            "energy_eV": -116.59158712232964
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pca2_1",
        "spacegroup_number": 29,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.4701361764755134e-05,
        "parent_symmetrization_rmsd_A": 0.06687567361942275,
        "parent_cell_rmsd_A": 0.03197618334758259,
        "energy_eV": -116.59158712232964,
        "reduced_polarization": [
          5.138750416589389e-15,
          6.906139454603837e-15,
          -0.5000347013617648
        ],
        "cartesian_polarization_e_A2": [
          1.8442502451465755e-16,
          3.23186871676336e-18,
          -0.01888901153034174
        ],
        "ranking_score": 0.5749391221798479
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.385380947269368e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "target_residual": 0.5110794365647738,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.08485611792208987,
            "max_log_strain_component": 0.007130843275104043,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0088860876599532,
              1.0001368477077675,
              0.9944954400439204
            ],
            "cell_volume_ratio": 1.0034699174698876,
            "cell_rmsd_from_input_A": 0.03633963645185846
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5058741346015125,
              -8.31108675521239e-15,
              -0.010781378363397855
            ],
            "branch_aligned_reduced_polarization": [
              -0.5058741346015125,
              -8.31108675521239e-15,
              -0.010781378363397855
            ],
            "target_residual": 0.012277767579304889,
            "energy_eV": -116.45470150197774,
            "max_atomic_step_A": 0.0020712139340017814,
            "max_log_strain_component": 0.00024489670289608545,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0089811857718425,
              1.0001500947211772,
              0.9947219961921424
            ],
            "cell_volume_ratio": 1.0038064226656238,
            "cell_rmsd_from_input_A": 0.03620935312644676
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.500089458187765,
              6.3537712246541205e-15,
              -5.023483111576492e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.500089458187765,
              6.3537712246541205e-15,
              -5.023483111576492e-05
            ],
            "target_residual": 0.0001025977856262976,
            "energy_eV": -116.46441126700897
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0001025977856262976,
        "parent_symmetrization_rmsd_A": 0.09868752215648446,
        "parent_cell_rmsd_A": 0.03620935312644676,
        "energy_eV": -116.46441126700897,
        "reduced_polarization": [
          -0.500089458187765,
          6.3537712246541205e-15,
          -5.023483111576492e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.01948842685818363,
          3.046869996432925e-16,
          -0.0001394784321899225
        ],
        "ranking_score": 0.6079450560093488
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.388953861305899e-15,
              9.992007221626409e-16,
              -0.10584040097888446
            ],
            "target_residual": 0.5110794365647772,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.07132315379681473,
            "max_log_strain_component": 0.0025300848104976743,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0032173719412318,
              1.0007973057202948,
              0.9994548645209069
            ],
            "cell_volume_ratio": 1.003469917469859,
            "cell_rmsd_from_input_A": 0.011284110182053523
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.7762215020767376e-14,
              0.4980836212752487,
              0.0017799672189474922
            ],
            "branch_aligned_reduced_polarization": [
              1.7762215020767376e-14,
              0.4980836212752487,
              0.0017799672189474922
            ],
            "target_residual": 0.002615490530896094,
            "energy_eV": -116.5334444257176,
            "max_atomic_step_A": 0.00039813672277582123,
            "max_log_strain_component": 4.442536517822037e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0031851286769151,
              1.0007833004717481,
              0.9994401849220722
            ],
            "cell_volume_ratio": 1.003408886000368,
            "cell_rmsd_from_input_A": 0.011175688938634815
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.896033771825707e-15,
              0.5000149357213646,
              6.3256369637568896e-06
            ],
            "branch_aligned_reduced_polarization": [
              3.896033771825707e-15,
              0.5000149357213646,
              6.3256369637568896e-06
            ],
            "target_residual": 1.6220032542427477e-05,
            "energy_eV": -116.53093746242139
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.6220032542427477e-05,
        "parent_symmetrization_rmsd_A": 0.08720813577056426,
        "parent_cell_rmsd_A": 0.011175688938634815,
        "energy_eV": -116.53093746242139,
        "reduced_polarization": [
          3.896033771825707e-15,
          0.5000149357213646,
          6.3256369637568896e-06
        ],
        "cartesian_polarization_e_A2": [
          1.5617483193886354e-16,
          0.018643832439693902,
          -2.6906464682595052e-05
        ],
        "ranking_score": 0.5900344980703078
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.385380947269368e-15,
              1.0156156472174635e-15,
              -0.10584040097888447
            ],
            "target_residual": 0.6366802882927052,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.1118227327058511,
            "max_log_strain_component": 0.009422273585239293,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0016332442802511,
              0.9994905309681551,
              0.9860756098224996
            ],
            "cell_volume_ratio": 0.9871829166848023,
            "cell_rmsd_from_input_A": 0.047709689599389066
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.482741251100012,
              -1.2038245194680681e-14,
              -0.5408009559099428
            ],
            "branch_aligned_reduced_polarization": [
              -0.482741251100012,
              -1.2038245194680681e-14,
              -0.5408009559099428
            ],
            "target_residual": 0.04430104306625223,
            "energy_eV": -116.09220800863002,
            "max_atomic_step_A": 0.006855224687910638,
            "max_log_strain_component": 0.0008501970385632878,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0023440554557799,
              0.9995364910708513,
              0.9864786149293913
            ],
            "cell_volume_ratio": 0.9883326620625167,
            "cell_rmsd_from_input_A": 0.046804949016996424
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5011945108321468,
              -6.013490309969325e-15,
              -0.49941660261686266
            ],
            "branch_aligned_reduced_polarization": [
              -0.5011945108321468,
              -6.013490309969325e-15,
              -0.49941660261686266
            ],
            "target_residual": 0.0013293639963409636,
            "energy_eV": -116.12815748507883,
            "max_atomic_step_A": 0.0002299872858280576,
            "max_log_strain_component": 1.817722139250733e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.002319941931967,
              0.9995357624021183,
              0.9864848617523224
            ],
            "cell_volume_ratio": 0.9883144235373782,
            "cell_rmsd_from_input_A": 0.04676723145307011
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49997147445205425,
              6.797913608061897e-15,
              -0.5000274090600624
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997147445205425,
              6.797913608061897e-15,
              -0.5000274090600624
            ],
            "target_residual": 3.955961904654889e-05,
            "energy_eV": -116.12914229001778
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.955961904654889e-05,
        "parent_symmetrization_rmsd_A": 0.11775639521840307,
        "parent_cell_rmsd_A": 0.04676723145307011,
        "energy_eV": -116.12914229001778,
        "reduced_polarization": [
          -0.49997147445205425,
          6.797913608061897e-15,
          -0.5000274090600624
        ],
        "cartesian_polarization_e_A2": [
          -0.0198586802865187,
          9.532356982273594e-17,
          -0.019031118962795492
        ],
        "ranking_score": 0.6295273223197637
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.388953861305899e-15,
              9.992007221626409e-16,
              -0.10584040097888447
            ],
            "target_residual": 0.6366802882927078,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.09228830019701206,
            "max_log_strain_component": 0.009422273585259914,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              0.999719902939973,
              0.9970363419735726,
              0.990394692367318
            ],
            "cell_volume_ratio": 0.9871829166847741,
            "cell_rmsd_from_input_A": 0.03373107086028881
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.078124656390987e-14,
              0.4924642453397587,
              -0.513367100813668
            ],
            "branch_aligned_reduced_polarization": [
              -5.078124656390987e-14,
              0.4924642453397587,
              -0.513367100813668
            ],
            "target_residual": 0.015344933445998129,
            "energy_eV": -116.23156913624156,
            "max_atomic_step_A": 0.002132076269449456,
            "max_log_strain_component": 0.00027662606698556106,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              0.9997485053545572,
              0.9971232259598057,
              0.9906551778670698
            ],
            "cell_volume_ratio": 0.9875568590282352,
            "cell_rmsd_from_input_A": 0.032810283298599155
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.7616123888166484e-15,
              0.5000196774656375,
              -0.5000460428624807
            ],
            "branch_aligned_reduced_polarization": [
              5.7616123888166484e-15,
              0.5000196774656375,
              -0.5000460428624807
            ],
            "target_residual": 5.0071427374574785e-05,
            "energy_eV": -116.238202689474
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 5.0071427374574785e-05,
        "parent_symmetrization_rmsd_A": 0.10914627734416774,
        "parent_cell_rmsd_A": 0.032810283298599155,
        "energy_eV": -116.238202689474,
        "reduced_polarization": [
          5.7616123888166484e-15,
          0.5000196774656375,
          -0.5000460428624807
        ],
        "cartesian_polarization_e_A2": [
          9.779464313566377e-17,
          0.018959257813774062,
          -0.01891742065779679
        ],
        "ranking_score": 0.6174489910235667
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.385380947269368e-15,
              9.992007221626409e-16,
              -0.10584040097888446
            ],
            "target_residual": 0.714984049108346,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.10913134251978618,
            "max_log_strain_component": 0.00713084327510512,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0090211570599537,
              1.0001637690382401,
              0.994335549909526
            ],
            "cell_volume_ratio": 1.0034699174698876,
            "cell_rmsd_from_input_A": 0.03697779734769792
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5064104708150039,
              0.4999222047673542,
              -0.005808154132702766
            ],
            "branch_aligned_reduced_polarization": [
              -0.5064104708150039,
              0.4999222047673542,
              -0.005808154132702766
            ],
            "target_residual": 0.00865071341552079,
            "energy_eV": -116.08364956427899,
            "max_atomic_step_A": 0.0015415497615270373,
            "max_log_strain_component": 0.00013034584555699123,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0090271928868122,
              1.000172985791217,
              0.9944978964063867
            ],
            "cell_volume_ratio": 1.0036490077324003,
            "cell_rmsd_from_input_A": 0.036694533365630146
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000321696909148,
              0.4999471945744903,
              -9.430994195724405e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000321696909148,
              0.4999471945744903,
              -9.430994195724405e-05
            ],
            "target_residual": 0.00011277263466282792,
            "energy_eV": -116.09417156809694
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00011277263466282792,
        "parent_symmetrization_rmsd_A": 0.13006604112865275,
        "parent_cell_rmsd_A": 0.036694533365630146,
        "energy_eV": -116.09417156809694,
        "reduced_polarization": [
          -0.5000321696909148,
          0.4999471945744903,
          -9.430994195724405e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.01948865179760266,
          0.018637128824260135,
          -0.00016798130928822477
        ],
        "ranking_score": 0.639465219739386
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.388953861305899e-15,
              1.0156156472174635e-15,
              -0.10584040097888446
            ],
            "branch_aligned_reduced_polarization": [
              -4.385380947269368e-15,
              9.992007221626409e-16,
              -0.10584040097888447
            ],
            "target_residual": 0.809544186255748,
            "energy_eV": -116.88169873957682,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008519304166637707,
            "step_scale": 0.904166503929706,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0017177768892225,
              0.9993972467371061,
              0.9873042264708229
            ],
            "cell_volume_ratio": 0.9884040717592357,
            "cell_rmsd_from_input_A": 0.04361964186876396
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4369104004830464,
              0.44690949354082526,
              -0.49083163338197205
            ],
            "branch_aligned_reduced_polarization": [
              -0.4369104004830464,
              0.44690949354082526,
              -0.49083163338197205
            ],
            "target_residual": 0.08296359677439155,
            "energy_eV": -115.95369800105246,
            "max_atomic_step_A": 0.013419174093959207,
            "max_log_strain_component": 0.0009183586966188752,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.002484646603724,
              0.999408052568246,
              0.9863480764286945
            ],
            "cell_volume_ratio": 0.9882134859150287,
            "cell_rmsd_from_input_A": 0.04729833194798943
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.500986945122176,
              0.500710228022978,
              -0.4991822880392616
            ],
            "branch_aligned_reduced_polarization": [
              -0.500986945122176,
              0.500710228022978,
              -0.4991822880392616
            ],
            "target_residual": 0.0014653113558370167,
            "energy_eV": -115.77629260118242,
            "max_atomic_step_A": 0.00024204655114144267,
            "max_log_strain_component": 1.737034019923704e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.806861655951811,
            "cell_principal_stretches": [
              1.0024623497870704,
              0.9994062918121772,
              0.9863482954581729
            ],
            "cell_volume_ratio": 0.9881899849548456,
            "cell_rmsd_from_input_A": 0.04728141565731832
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999654675341893,
              0.4999882889884746,
              -0.5000214762523791
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999654675341893,
              0.4999882889884746,
              -0.5000214762523791
            ],
            "target_residual": 4.2318653123274095e-05,
            "energy_eV": -115.77776141565121
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.2318653123274095e-05,
        "parent_symmetrization_rmsd_A": 0.14519013544521722,
        "parent_cell_rmsd_A": 0.04728141565731832,
        "energy_eV": -115.77776141565121,
        "reduced_polarization": [
          -0.4999654675341893,
          0.4999882889884746,
          -0.5000214762523791
        ],
        "cartesian_polarization_e_A2": [
          -0.019859555498046542,
          0.01894635771158782,
          -0.01905816131978343
        ],
        "ranking_score": 0.6570951266657934
      },
      "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
        ],
        "endpoint_rmsd_A": 0.39600949533021934,
        "minimum_distance_A_by_image": [
          2.0398614813937073,
          2.044370064769418,
          2.049957031307114,
          2.056613592465587,
          2.064329401343571,
          2.073092630785557,
          2.082890060567727,
          2.0937071722270164,
          2.1022477057593405
        ],
        "minimum_distance_A": 2.0398614813937073,
        "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": [
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814,
          134.78634764713814
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.655501495916174e-15,
        -1.1945181324996723e-15,
        1.7502728728310247e-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": [
          -116.88169873957683,
          -116.55585987911734,
          -116.12322860849332,
          -115.84120539733574,
          -115.85617123242571,
          -116.0310057157511,
          -116.17088934478198,
          -116.22989352686541,
          -116.24255815905296
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5094137708603436e-16,
            -3.541871331350329e-17,
            -0.003984740338383591
          ],
          [
            9.472446583843902e-17,
            -3.974309110177985e-17,
            -0.007477561783124653
          ],
          [
            7.09918686908736e-17,
            -4.993626731700318e-17,
            -0.007702732947958729
          ],
          [
            7.516180441528314e-17,
            -5.59080271198613e-17,
            -0.0037010687475718985
          ],
          [
            -2.736713371723597e-16,
            -6.69248943423754e-18,
            0.001390326502793077
          ],
          [
            -2.740831826760051e-16,
            -1.2190626907903457e-16,
            0.003754873415875355
          ],
          [
            -1.468229220495805e-16,
            -1.1202197699154528e-16,
            0.0033930656058581915
          ],
          [
            -5.683467950306341e-17,
            -3.0888412773404026e-17,
            0.001866963926234684
          ],
          [
            -1.0378506691863754e-16,
            -4.4685237145524495e-17,
            6.5895280583261926e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.0023045398265786e-15,
            -1.78902485282209e-16,
            0.036929059876176805
          ],
          [
            -7.012842244175452e-15,
            -3.2587775780636223e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445712e-15,
            -8.2570377822558e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.7502728728310247e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.002304539826579e-15,
            -1.7890248528220903e-16,
            0.03692905987617681
          ],
          [
            -7.012842244175452e-15,
            -3.258777578063622e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445714e-15,
            -8.257037782255798e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.734723475976807e-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": [
          [
            -3.885780586188048e-15,
            -9.43689570931383e-16,
            -0.10584040097888103
          ],
          [
            2.4424906541753444e-15,
            -1.0547118733938987e-15,
            -0.19861473277109765
          ],
          [
            1.7763568394002505e-15,
            -1.3322676295501878e-15,
            -0.2045956008706707
          ],
          [
            1.887379141862766e-15,
            -1.4988010832439613e-15,
            -0.09830567791835515
          ],
          [
            -6.994405055138486e-15,
            -1.6653345369377348e-16,
            0.036929059876176784
          ],
          [
            -6.994405055138486e-15,
            -3.2751579226442118e-15,
            0.09973480684124092
          ],
          [
            -3.774758283725532e-15,
            -2.9976021664879227e-15,
            0.09012467407533997
          ],
          [
            -1.4432899320127035e-15,
            -8.326672684688674e-16,
            0.049589231364054576
          ],
          [
            -2.6645352591003757e-15,
            -1.2212453270876722e-15,
            2.220446049250313e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -116.24255815905299,
          -116.2298935268654,
          -116.17088934478194,
          -116.0310057157511,
          -115.85617123242582,
          -115.84120539733571,
          -116.12322860849325,
          -116.5558598791173,
          -116.88169873957679
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.127476520385069e-17,
            -2.0180429678623967e-17,
            1.2849579713736075e-16
          ],
          [
            1.6473820145815483e-17,
            7.33084996488789e-17,
            -0.0018669639262346093
          ],
          [
            3.2947640291630966e-17,
            1.017258394004106e-16,
            -0.003393065605858195
          ],
          [
            -4.9833305941091835e-17,
            6.218867105045344e-17,
            -0.0037548734158749826
          ],
          [
            -1.779172575748072e-16,
            8.030987321085047e-18,
            -0.001390326502793358
          ],
          [
            7.629437955030795e-17,
            1.9356738671333192e-17,
            0.0037010687475721262
          ],
          [
            8.669347851735397e-17,
            -6.198274829863075e-17,
            0.007702732947959227
          ],
          [
            -5.353991547390032e-18,
            1.6659150622455907e-16,
            0.00747756178312532
          ],
          [
            -1.413659691262791e-16,
            3.80957090871983e-17,
            0.003984740338383991
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3119441914347765e-15,
            -5.394598017740456e-16,
            3.413032102020498e-15
          ],
          [
            4.2150817395494824e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137186e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618427
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.369901565353582e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3119441914347765e-15,
            -5.394598017740456e-16,
            3.413032102020498e-15
          ],
          [
            4.215081739549482e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137188e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618428
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.3699015653535826e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4489343479701343e-15,
          -1.4422292659673463e-15,
          0.1058404009788814
        ],
        "actual_opposite_endpoint_branch_residual": 1.0780503786927878e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.0023045398265786e-15,
            -1.78902485282209e-16,
            0.036929059876176805
          ],
          [
            -7.012842244175452e-15,
            -3.2587775780636223e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445712e-15,
            -8.2570377822558e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.7502728728310247e-16
          ],
          [
            4.2150817395494824e-16,
            1.959670300322043e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137186e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618427
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.369901565353582e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.862068643862213e-15,
            -9.468069990319985e-16,
            -0.10584040097888105
          ],
          [
            2.4236720002409527e-15,
            -1.0624055279835797e-15,
            -0.19861473277109765
          ],
          [
            1.8164367871371052e-15,
            -1.334887774798021e-15,
            -0.2045956008706707
          ],
          [
            1.923131043669451e-15,
            -1.4945238385882999e-15,
            -0.09830567791835515
          ],
          [
            -7.002304539826579e-15,
            -1.7890248528220903e-16,
            0.03692905987617681
          ],
          [
            -7.012842244175452e-15,
            -3.258777578063622e-15,
            0.0997348068412409
          ],
          [
            -3.756691600373477e-15,
            -2.9945523690314367e-15,
            0.09012467407533994
          ],
          [
            -1.4542032001445714e-15,
            -8.257037782255798e-16,
            0.04958923136405458
          ],
          [
            -2.655501495916174e-15,
            -1.1945181324996723e-15,
            1.734723475976807e-16
          ],
          [
            4.215081739549482e-16,
            1.9596703003220435e-15,
            -0.049589231364052605
          ],
          [
            8.430163479098965e-16,
            2.7193177762895767e-15,
            -0.09012467407534006
          ],
          [
            -1.2750622262137188e-15,
            1.6624169401608342e-15,
            -0.09973480684123101
          ],
          [
            -4.5522882787134404e-15,
            2.1468298233865075e-16,
            -0.03692905987618428
          ],
          [
            1.952109730628854e-15,
            5.174410343546968e-16,
            0.0983056779183612
          ],
          [
            2.218186765437915e-15,
            -1.656912248305997e-15,
            0.2045956008706839
          ],
          [
            -1.3699015653535826e-16,
            4.453295710563295e-15,
            0.19861473277111535
          ],
          [
            -3.6170670177509e-15,
            1.018367993144882e-15,
            0.10584040097889166
          ]
        ],
        "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": [
          [
            -3.885780586188048e-15,
            -9.43689570931383e-16,
            -0.10584040097888103
          ],
          [
            2.4424906541753444e-15,
            -1.0547118733938987e-15,
            -0.19861473277109765
          ],
          [
            1.7763568394002505e-15,
            -1.3322676295501878e-15,
            -0.2045956008706707
          ],
          [
            1.887379141862766e-15,
            -1.4988010832439613e-15,
            -0.09830567791835515
          ],
          [
            -6.994405055138486e-15,
            -1.6653345369377348e-16,
            0.036929059876176784
          ],
          [
            -6.994405055138486e-15,
            -3.2751579226442118e-15,
            0.09973480684124092
          ],
          [
            -3.774758283725532e-15,
            -2.9976021664879227e-15,
            0.09012467407533997
          ],
          [
            -1.4432899320127035e-15,
            -8.326672684688674e-16,
            0.049589231364054576
          ],
          [
            -2.6645352591003757e-15,
            -1.2212453270876722e-15,
            2.220446049250313e-16
          ],
          [
            4.440892098500626e-16,
            1.9984014443252818e-15,
            -0.04958923136405258
          ],
          [
            8.881784197001252e-16,
            2.6645352591003757e-15,
            -0.09012467407534008
          ],
          [
            -1.27675647831893e-15,
            1.6653345369377348e-15,
            -0.09973480684123104
          ],
          [
            -4.551914400963142e-15,
            2.220446049250313e-16,
            -0.03692905987618428
          ],
          [
            1.9984014443252818e-15,
            5.551115123125783e-16,
            0.0983056779183612
          ],
          [
            2.220446049250313e-15,
            -1.6653345369377348e-15,
            0.20459560087068396
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-15,
            0.1986147327711154
          ],
          [
            -3.608224830031759e-15,
            9.992007221626409e-16,
            0.10584040097889169
          ]
        ]
      },
      "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": "Pbca",
        "spacegroup_number": 61,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 8.8024672623973145e-16,
        "parent_symmetrization_rmsd_A": 0.39600949533021934,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -116.242558159053,
        "reduced_polarization": [
          2.265606435007847e-16,
          3.467955868547436e-16,
          7.766835873187673e-16
        ],
        "cartesian_polarization_e_A2": [
          8.854678328375822e-18,
          1.2973133364829692e-17,
          2.924103075882248e-17
        ],
        "ranking_score": 0.3960094953302211
      }
    }
  ],
  "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": 54,
      "full_response": 19,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 79,
      "full_response": 44,
      "energy_polarization": 35
    },
    "elapsed_seconds": 211.24226176796947
  }
}