{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "O24Sb4Tl4W4",
  "input_spacegroup": "Ima2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -227.78634921458817,
  "input_cartesian_polarization_e_A2": [
    0.006639543238452723,
    6.4018642886778e-18,
    6.759032212565947e-08
  ],
  "input_reduced_polarization": [
    0.508284676616098,
    4.966597898483803e-16,
    3.6663750148076065e-06
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        1.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        1.0,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 8.310904796491584e-16,
      "parent_symmetrization_rmsd_A": 0.39959416637754125,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -227.64874936095634,
      "reduced_polarization": [
        -4.940250858165468e-16,
        6.486011590664666e-16,
        -1.6114321706189792e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.453275239372807e-18,
        8.360363940656917e-18,
        -2.970705916767843e-18
      ],
      "ranking_score": 0.3995941663775429
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.04208815456074e-06,
      "parent_symmetrization_rmsd_A": 0.0003482635349417854,
      "parent_cell_rmsd_A": 0.00019099028627861227,
      "energy_eV": -227.78610106199912,
      "reduced_polarization": [
        0.4999989579118466,
        -3.9478412575791017e-16,
        -4.960425204445827e-11
      ],
      "cartesian_polarization_e_A2": [
        0.006531088542241031,
        -5.380766326048256e-18,
        -1.4017302874547582e-11
      ],
      "ranking_score": 0.5003980952828205
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.4999999999999977,
      "parent_symmetrization_rmsd_A": 0.39959416644206075,
      "parent_cell_rmsd_A": 0.00019099028627861227,
      "energy_eV": -227.64867457503865,
      "reduced_polarization": [
        2.3036877226230787e-15,
        1.3085870281326041e-15,
        -9.84085497102601e-16
      ],
      "cartesian_polarization_e_A2": [
        3.009123973209409e-17,
        1.6866769734439516e-17,
        -1.8141000727332336e-17
      ],
      "ranking_score": 1.3996419140136258
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.6128855302815315e-06,
      "parent_symmetrization_rmsd_A": 0.021057847782772657,
      "parent_cell_rmsd_A": 0.011524419287186626,
      "energy_eV": -227.67501166810112,
      "reduced_polarization": [
        0.9999973871144704,
        2.6097638154130824e-15,
        5.936976201957929e-11
      ],
      "cartesian_polarization_e_A2": [
        0.013089376920930741,
        7.000379336574771e-17,
        1.1427721498764933e-11
      ],
      "ranking_score": 0.5239441783756299
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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": 4.1748262959867453e-07,
      "parent_symmetrization_rmsd_A": 0.03918006504995782,
      "parent_cell_rmsd_A": 0.002322024773789459,
      "energy_eV": -227.2033164176995,
      "reduced_polarization": [
        0.5000004052302824,
        5.731841911770361e-15,
        0.49999989959997904
      ],
      "cartesian_polarization_e_A2": [
        0.00653356061455948,
        9.549949674374643e-17,
        0.009218889822620813
      ],
      "ranking_score": 0.5397614062086644
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.9539804698513355e-06,
      "parent_symmetrization_rmsd_A": 0.02979787710717969,
      "parent_cell_rmsd_A": 0.008501720378179667,
      "energy_eV": -227.4672793804563,
      "reduced_polarization": [
        0.49999804603902614,
        0.5000000087286343,
        1.2486461743767307e-11
      ],
      "cartesian_polarization_e_A2": [
        0.006521966515227373,
        0.006435420002533251,
        -1.9988097246730109e-10
      ],
      "ranking_score": 0.5319272151626643
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.1425727373105291e-05,
      "parent_symmetrization_rmsd_A": 0.04472685693796888,
      "parent_cell_rmsd_A": 0.011849941277134238,
      "energy_eV": -227.0575440297267,
      "reduced_polarization": [
        0.9999927365843618,
        2.2604822315798296e-15,
        0.49999118013382915
      ],
      "cartesian_polarization_e_A2": [
        0.013092044031729406,
        8.197169255484085e-17,
        0.009245868004204415
      ],
      "ranking_score": 0.5477121937119986
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        1.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.5626132049539176e-05,
      "parent_symmetrization_rmsd_A": 0.03685080239224353,
      "parent_cell_rmsd_A": 0.014417823888991516,
      "energy_eV": -227.34046818427478,
      "reduced_polarization": [
        0.9999857012604266,
        0.4999936974569078,
        1.1649920248398785e-10
      ],
      "cartesian_polarization_e_A2": [
        0.013080222413046887,
        0.006442565892581718,
        -1.7629834651670586e-10
      ],
      "ranking_score": 0.5404865106285905
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 5.4979773758742e-06,
      "parent_symmetrization_rmsd_A": 0.04947570737597711,
      "parent_cell_rmsd_A": 0.008868644423840106,
      "energy_eV": -226.83614126665992,
      "reduced_polarization": [
        0.4999951562975808,
        0.4999983726318407,
        0.49999797072057767
      ],
      "cartesian_polarization_e_A2": [
        0.006524340344112676,
        0.0064353080213504586,
        0.009218900025939785
      ],
      "ranking_score": 0.5517038644366888
    },
    {
      "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": [
        1.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.6549889631409405e-05,
      "parent_symmetrization_rmsd_A": 0.05424033472228301,
      "parent_cell_rmsd_A": 0.014729358721390695,
      "energy_eV": -226.6727594152171,
      "reduced_polarization": [
        0.9999715176077745,
        0.49998313278471707,
        0.4999845033934754
      ],
      "cartesian_polarization_e_A2": [
        0.013082743596457305,
        0.0064424502192902775,
        0.009245990625874372
      ],
      "ranking_score": 0.5579957741818935
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "target_residual": 0.008284677427373181,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.0007260917593154032,
            "max_log_strain_component": 2.609705821366285e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0000260973991324,
              1.000018167405013,
              1.000015713145199
            ],
            "cell_volume_ratio": 1.0000599791190137,
            "cell_rmsd_from_input_A": 0.00019099028627861227
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4999989579118466,
              -3.9478412575791017e-16,
              -4.960425204445827e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.4999989579118466,
              -3.9478412575791017e-16,
              -4.960425204445827e-11
            ],
            "target_residual": 1.04208815456074e-06,
            "energy_eV": -227.78610106199912
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ima2",
        "spacegroup_number": 46,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.04208815456074e-06,
        "parent_symmetrization_rmsd_A": 0.0003482635349417854,
        "parent_cell_rmsd_A": 0.00019099028627861227,
        "energy_eV": -227.78610106199912,
        "reduced_polarization": [
          0.4999989579118466,
          -3.9478412575791017e-16,
          -4.960425204445827e-11
        ],
        "cartesian_polarization_e_A2": [
          0.006531088542241031,
          -5.380766326048256e-18,
          -1.4017302874547582e-11
        ],
        "ranking_score": 0.5003980952828205
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "target_residual": 0.4917153233975708,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.043088306523111256,
            "max_log_strain_component": 0.001548922667662011,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              0.9990678293771194,
              0.9989223120919537,
              0.9984522762939395
            ],
            "cell_volume_ratio": 0.9964465315028888,
            "cell_rmsd_from_input_A": 0.011322272954603196
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.9919301981780096,
              -6.730342533989737e-15,
              1.5215128139993058e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.9919301981780096,
              -6.730342533989737e-15,
              1.5215128139993058e-08
            ],
            "target_residual": 0.008069801822004695,
            "energy_eV": -227.67932865150607,
            "max_atomic_step_A": 0.0007313172345887998,
            "max_log_strain_component": 2.7687165637390303e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              0.9990511746306052,
              0.9989030588697152,
              0.9984246323630773
            ],
            "cell_volume_ratio": 0.9963831278636563,
            "cell_rmsd_from_input_A": 0.011524419287186626
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.9999973871144704,
              2.6097638154130824e-15,
              5.936976201957929e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.9999973871144704,
              2.6097638154130824e-15,
              5.936976201957929e-11
            ],
            "target_residual": 2.6128855302815315e-06,
            "energy_eV": -227.67501166810112
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 8.310904796491584e-16,
        "parent_symmetrization_rmsd_A": 0.39959416637754125,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -227.64874936095634,
        "reduced_polarization": [
          -4.940250858165468e-16,
          6.486011590664666e-16,
          -1.6114321706189792e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.453275239372807e-18,
          8.360363940656917e-18,
          -2.970705916767843e-18
        ],
        "ranking_score": 0.3995941663775429
      },
      "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": [
          -227.78634921458814,
          -227.757574084206,
          -227.7301656022239,
          -227.70561623119818,
          -227.6850114569464,
          -227.66900179938054,
          -227.65774676190628,
          -227.65101985518777,
          -227.6487493609563
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00663954323845273,
            -6.213425392819963e-18,
            6.759032211139275e-08
          ],
          [
            0.005825597415213327,
            -8.181107106728001e-19,
            5.9311699323387937e-08
          ],
          [
            0.005008360395424046,
            1.2129649145086359e-17,
            5.0974903578346536e-08
          ],
          [
            0.0041874044793688845,
            -1.689867171556636e-17,
            4.258775973501793e-08
          ],
          [
            0.003361397872978601,
            8.647503773118372e-18,
            3.415163831813656e-08
          ],
          [
            0.002528930717052859,
            -2.2364489877142914e-17,
            2.566505830481075e-08
          ],
          [
            0.0016899425284669872,
            1.6904919602476864e-19,
            1.713371116555372e-08
          ],
          [
            0.00084617042672159,
            -7.286942477348082e-18,
            8.573177232687602e-09
          ],
          [
            6.584967781037137e-17,
            -1.8913386717759637e-18,
            -3.821574771940855e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.34694325454658e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.41024164787067e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955397e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309701e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.04106698142669e-15,
            -1.4673098724033913e-16,
            -2.0729781750431806e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.346943254546583e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.410241647870668e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955395e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309607e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.037636974236648e-15,
            -1.4673098724033913e-16,
            -2.0729781954684906e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.49171532338390156,
            -4.996003610813204e-16,
            3.6663750140331075e-06
          ],
          [
            0.445973735232023,
            -5.551115123125783e-17,
            3.2173087158859914e-06
          ],
          [
            0.3834108390501614,
            8.881784197001252e-16,
            2.7650868790196625e-06
          ],
          [
            0.32056324587665674,
            -1.3322676295501878e-15,
            2.3101339557962675e-06
          ],
          [
            0.25732900133099024,
            6.661338147750939e-16,
            1.8525242890810034e-06
          ],
          [
            0.19360017482185754,
            -1.7208456881689926e-15,
            1.3921775420255855e-06
          ],
          [
            0.12937213611426202,
            0.0,
            9.294024433392778e-07
          ],
          [
            0.06477786893794191,
            -5.551115123125783e-16,
            4.6504413375725306e-07
          ],
          [
            4.9960036108132044e-15,
            -1.6653345369377348e-16,
            -2.0539125955565396e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -227.6487493609563,
          -227.6510198551878,
          -227.6577467619063,
          -227.66900179938057,
          -227.6850114569464,
          -227.70561623119818,
          -227.73016560222396,
          -227.7575740842059,
          -227.78634921458814
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.517681156209158e-17,
            7.41322006516494e-18,
            -9.560049493466885e-18
          ],
          [
            -0.0008461704267215415,
            2.9805641754218464e-18,
            -8.573177270707746e-09
          ],
          [
            -0.00168994252846693,
            9.247910261805963e-18,
            -1.7133711215297763e-08
          ],
          [
            -0.0025289307170527895,
            -1.1498591653075718e-17,
            -2.566505835719542e-08
          ],
          [
            -0.0033613978729785153,
            2.2786623167062087e-18,
            -3.41516383510466e-08
          ],
          [
            -0.00418740447936887,
            -2.268030063840665e-17,
            -4.2587759808967727e-08
          ],
          [
            -0.005008360395424029,
            -4.2445280738146804e-18,
            -5.09749035890802e-08
          ],
          [
            -0.005825597415213236,
            2.0598321081141295e-18,
            -5.9311699366738236e-08
          ],
          [
            -0.0066395432384527015,
            -1.3426025802394006e-17,
            -6.759032213655206e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.22401463689855e-15,
            5.751212699363612e-16,
            -5.185761141662722e-16
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.767797466985148e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.292925819865733e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698047e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.22401463689855e-15,
            5.751212699363612e-16,
            -5.185761141662722e-16
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.7677974669851489e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.2929258198657323e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698052e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.5082846766160886,
          1.885786328615163e-16,
          -3.666375018179678e-06
        ],
        "actual_opposite_endpoint_branch_residual": 8.345396419008671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.34694325454658e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.41024164787067e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955397e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309701e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.04106698142669e-15,
            -1.4673098724033913e-16,
            -2.0729781750431806e-15
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.767797466985148e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.292925819865733e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698047e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.346943254546583e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.410241647870668e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955395e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309607e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.037636974236648e-15,
            -1.4673098724033913e-16,
            -2.0729781954684906e-15
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.7677974669851489e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.2929258198657323e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698052e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.49171532338390156,
            -4.996003610813204e-16,
            3.6663750140331075e-06
          ],
          [
            0.445973735232023,
            -5.551115123125783e-17,
            3.2173087158859914e-06
          ],
          [
            0.3834108390501614,
            8.881784197001252e-16,
            2.7650868790196625e-06
          ],
          [
            0.32056324587665674,
            -1.3322676295501878e-15,
            2.3101339557962675e-06
          ],
          [
            0.25732900133099024,
            6.661338147750939e-16,
            1.8525242890810034e-06
          ],
          [
            0.19360017482185754,
            -1.7208456881689926e-15,
            1.3921775420255855e-06
          ],
          [
            0.12937213611426202,
            0.0,
            9.294024433392778e-07
          ],
          [
            0.06477786893794191,
            -5.551115123125783e-16,
            4.6504413375725306e-07
          ],
          [
            4.9960036108132044e-15,
            -1.6653345369377348e-16,
            -2.0539125955565396e-15
          ],
          [
            -0.06477786893793824,
            2.220446049250313e-16,
            -4.6504413581116566e-07
          ],
          [
            -0.12937213611425763,
            6.661338147750939e-16,
            -9.294024460038131e-07
          ],
          [
            -0.1936001748218522,
            -8.881784197001252e-16,
            -1.3921775448566542e-06
          ],
          [
            -0.2573290013309837,
            2.220446049250313e-16,
            -1.8525242908573603e-06
          ],
          [
            -0.3205632458766556,
            -1.7763568394002505e-15,
            -2.3101339598485815e-06
          ],
          [
            -0.3834108390501601,
            -3.3306690738754696e-16,
            -2.765086879630285e-06
          ],
          [
            -0.445973735232016,
            1.1102230246251565e-16,
            -3.217308718272971e-06
          ],
          [
            0.49171532338390367,
            -1.0547118733938987e-15,
            -3.6663750154208863e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148102636e-06
            ],
            "target_residual": 0.5000649652845726,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.06337836937988127,
            "max_log_strain_component": 0.0002673722493710166,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0002883794709663,
              1.000018151899325,
              0.9997535235206543
            ],
            "cell_volume_ratio": 1.000059984571518,
            "cell_rmsd_from_input_A": 0.0023023304701828046
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5011073469232828,
              -9.900750184339885e-16,
              0.49635890199520466
            ],
            "branch_aligned_reduced_polarization": [
              0.5011073469232828,
              -9.900750184339885e-16,
              0.49635890199520466
            ],
            "target_residual": 0.003805760356226939,
            "energy_eV": -227.21207760293,
            "max_atomic_step_A": 0.0004945875490371258,
            "max_log_strain_component": 3.5577742232683665e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0002932778819975,
              1.0000206285631925,
              0.9997543264497903
            ],
            "cell_volume_ratio": 1.0000681618248852,
            "cell_rmsd_from_input_A": 0.002322024773789459
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000004052302824,
              5.731841911770361e-15,
              0.49999989959997904
            ],
            "branch_aligned_reduced_polarization": [
              0.5000004052302824,
              5.731841911770361e-15,
              0.49999989959997904
            ],
            "target_residual": 4.1748262959867453e-07,
            "energy_eV": -227.2033164176995
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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": 4.1748262959867453e-07,
        "parent_symmetrization_rmsd_A": 0.03918006504995782,
        "parent_cell_rmsd_A": 0.002322024773789459,
        "energy_eV": -227.2033164176995,
        "reduced_polarization": [
          0.5000004052302824,
          5.731841911770361e-15,
          0.49999989959997904
        ],
        "cartesian_polarization_e_A2": [
          0.00653356061455948,
          9.549949674374643e-17,
          0.009218889822620813
        ],
        "ranking_score": 0.5397614062086644
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.996003610813204e-16,
              3.6663750148076065e-06
            ],
            "target_residual": 0.5000686311698377,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.04803582611858556,
            "max_log_strain_component": 0.001411148776360619,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.001434314141814,
              1.000015713145672,
              0.9986119420471289
            ],
            "cell_volume_ratio": 1.0000599791190106,
            "cell_rmsd_from_input_A": 0.008469059604490773
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49953204062967393,
              0.49809989238496544,
              1.8957151163791083e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49953204062967393,
              0.49809989238496544,
              1.8957151163791083e-08
            ],
            "target_residual": 0.0019568839825977614,
            "energy_eV": -227.46972672997052,
            "max_atomic_step_A": 0.00018787463277650693,
            "max_log_strain_component": 5.491613789794254e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0014384969051806,
              1.0000147801049721,
              0.9986051463743596
            ],
            "cell_volume_ratio": 1.0000564175072846,
            "cell_rmsd_from_input_A": 0.008501720378179667
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999804603902614,
              0.5000000087286343,
              1.2486461743767307e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.49999804603902614,
              0.5000000087286343,
              1.2486461743767307e-11
            ],
            "target_residual": 1.9539804698513355e-06,
            "energy_eV": -227.4672793804563
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.9539804698513355e-06,
        "parent_symmetrization_rmsd_A": 0.02979787710717969,
        "parent_cell_rmsd_A": 0.008501720378179667,
        "energy_eV": -227.4672793804563,
        "reduced_polarization": [
          0.49999804603902614,
          0.5000000087286343,
          1.2486461743767307e-11
        ],
        "cartesian_polarization_e_A2": [
          0.006521966515227373,
          0.006435420002533251,
          -1.9988097246730109e-10
        ],
        "ranking_score": 0.5319272151626643
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        1.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148102636e-06
            ],
            "target_residual": 0.7012704848266201,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.0851755405860627,
            "max_log_strain_component": 0.001548926479643477,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              0.9991675881536971,
              0.9989222966032573,
              0.998352609858505
            ],
            "cell_volume_ratio": 0.996446536935692,
            "cell_rmsd_from_input_A": 0.011550543151070248
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.9884450539597768,
              -7.962324978553898e-15,
              0.49441626538233596
            ],
            "branch_aligned_reduced_polarization": [
              0.9884450539597768,
              -7.962324978553898e-15,
              0.49441626538233596
            ],
            "target_residual": 0.012833349924044389,
            "energy_eV": -227.0791812305707,
            "max_atomic_step_A": 0.0014425499187603833,
            "max_log_strain_component": 4.107383207587587e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              0.9991430012487267,
              0.9988937344812322,
              0.9983114822289556
            ],
            "cell_volume_ratio": 0.9963524794328618,
            "cell_rmsd_from_input_A": 0.011849941277134238
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.9999927365843618,
              2.2604822315798296e-15,
              0.49999118013382915
            ],
            "branch_aligned_reduced_polarization": [
              0.9999927365843618,
              2.2604822315798296e-15,
              0.49999118013382915
            ],
            "target_residual": 1.1425727373105291e-05,
            "energy_eV": -227.0575440297267
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          1.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.1425727373105291e-05,
        "parent_symmetrization_rmsd_A": 0.04472685693796888,
        "parent_cell_rmsd_A": 0.011849941277134238,
        "energy_eV": -227.0575440297267,
        "reduced_polarization": [
          0.9999927365843618,
          2.2604822315798296e-15,
          0.49999118013382915
        ],
        "cartesian_polarization_e_A2": [
          0.013092044031729406,
          8.197169255484085e-17,
          0.009245868004204415
        ],
        "ranking_score": 0.5477121937119986
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        1.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.996003610813204e-16,
              3.6663750148076065e-06
            ],
            "target_residual": 0.7012730989165186,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.06452528474715911,
            "max_log_strain_component": 0.0015489226676626423,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0001170470759768,
              0.9990678293768144,
              0.9972595300373371
            ],
            "cell_volume_ratio": 0.9964465315028861,
            "cell_rmsd_from_input_A": 0.01411767217554908
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.9885612189851151,
              0.4941669645284104,
              2.914588401304232e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.9885612189851151,
              0.4941669645284104,
              2.914588401304232e-08
            ],
            "target_residual": 0.012840171880475895,
            "energy_eV": -227.35494284373712,
            "max_atomic_step_A": 0.0011884652538507665,
            "max_log_strain_component": 4.040553086270075e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0001014211849557,
              0.9990435242057191,
              0.9972067671244413
            ],
            "cell_volume_ratio": 0.9963540041458154,
            "cell_rmsd_from_input_A": 0.014417823888991516
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.9999857012604266,
              0.4999936974569078,
              1.1649920248398785e-10
            ],
            "branch_aligned_reduced_polarization": [
              0.9999857012604266,
              0.4999936974569078,
              1.1649920248398785e-10
            ],
            "target_residual": 1.5626132049539176e-05,
            "energy_eV": -227.34046818427478
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          1.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.5626132049539176e-05,
        "parent_symmetrization_rmsd_A": 0.03685080239224353,
        "parent_cell_rmsd_A": 0.014417823888991516,
        "energy_eV": -227.34046818427478,
        "reduced_polarization": [
          0.9999857012604266,
          0.4999936974569078,
          1.1649920248398785e-10
        ],
        "cartesian_polarization_e_A2": [
          0.013080222413046887,
          0.006442565892581718,
          -1.7629834651670586e-10
        ],
        "ranking_score": 0.5404865106285905
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.996003610813204e-16,
              3.6663750148102636e-06
            ],
            "target_residual": 0.7071527200718811,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.0832978550978015,
            "max_log_strain_component": 0.001411148776362083,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0014594106331092,
              1.000015810994372,
              0.9985868246487515
            ],
            "cell_volume_ratio": 1.000059984571515,
            "cell_rmsd_from_input_A": 0.008774352112439323
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5003750185208461,
              0.49504489626903087,
              0.49428402098453955
            ],
            "branch_aligned_reduced_polarization": [
              0.5003750185208461,
              0.49504489626903087,
              0.49428402098453955
            ],
            "target_residual": 0.007574041720298749,
            "energy_eV": -226.85827844177476,
            "max_atomic_step_A": 0.0009533982282973419,
            "max_log_strain_component": 1.4987074574146287e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0014756591264844,
              1.0000164490317718,
              0.9985724031826319
            ],
            "cell_volume_ratio": 1.0000624054505416,
            "cell_rmsd_from_input_A": 0.008868644423840106
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999951562975808,
              0.4999983726318407,
              0.49999797072057767
            ],
            "branch_aligned_reduced_polarization": [
              0.4999951562975808,
              0.4999983726318407,
              0.49999797072057767
            ],
            "target_residual": 5.4979773758742e-06,
            "energy_eV": -226.83614126665992
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 5.4979773758742e-06,
        "parent_symmetrization_rmsd_A": 0.04947570737597711,
        "parent_cell_rmsd_A": 0.008868644423840106,
        "energy_eV": -226.83614126665992,
        "reduced_polarization": [
          0.4999951562975808,
          0.4999983726318407,
          0.49999797072057767
        ],
        "cartesian_polarization_e_A2": [
          0.006524340344112676,
          0.0064353080213504586,
          0.009218900025939785
        ],
        "ranking_score": 0.5517038644366888
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        1.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.508284676616098,
              4.966597898483803e-16,
              3.6663750148076065e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.508284676616098,
              4.996003610813204e-16,
              3.6663750148102636e-06
            ],
            "target_residual": 0.8612666793095866,
            "energy_eV": -227.78634921458817,
            "max_atomic_step_A": 0.09778438520729232,
            "max_log_strain_component": 0.0015489264796441082,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0001451345127652,
              0.9990625793447727,
              0.9972367694850525
            ],
            "cell_volume_ratio": 0.9964465369356893,
            "cell_rmsd_from_input_A": 0.014301394540056536
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.9848202110463173,
              0.49107859290578876,
              0.49242074768216815
            ],
            "branch_aligned_reduced_polarization": [
              0.9848202110463173,
              0.49107859290578876,
              0.49242074768216815
            ],
            "target_residual": 0.019169313052802603,
            "energy_eV": -226.71768791305985,
            "max_atomic_step_A": 0.002117841671932852,
            "max_log_strain_component": 5.580043054470737e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9319596102033616,
            "cell_principal_stretches": [
              1.0001275414054476,
              0.9990288505029052,
              0.9971600940886368
            ],
            "cell_volume_ratio": 0.9963187582545802,
            "cell_rmsd_from_input_A": 0.014729358721390695
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.9999715176077745,
              0.49998313278471707,
              0.4999845033934754
            ],
            "branch_aligned_reduced_polarization": [
              0.9999715176077745,
              0.49998313278471707,
              0.4999845033934754
            ],
            "target_residual": 3.6549889631409405e-05,
            "energy_eV": -226.6727594152171
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          1.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.6549889631409405e-05,
        "parent_symmetrization_rmsd_A": 0.05424033472228301,
        "parent_cell_rmsd_A": 0.014729358721390695,
        "energy_eV": -226.6727594152171,
        "reduced_polarization": [
          0.9999715176077745,
          0.49998313278471707,
          0.4999845033934754
        ],
        "cartesian_polarization_e_A2": [
          0.013082743596457305,
          0.0064424502192902775,
          0.009245990625874372
        ],
        "ranking_score": 0.5579957741818935
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35
        ],
        "endpoint_rmsd_A": 0.39959416637754125,
        "minimum_distance_A_by_image": [
          1.9219632458895,
          1.925457826199226,
          1.92667098636651,
          1.92770843706877,
          1.9287602150933993,
          1.9298262970147209,
          1.9309066591405613,
          1.9320012775147355,
          1.933110127919559
        ],
        "minimum_distance_A": 1.9219632458895,
        "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": [
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648,
          567.5927762260648
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.04106698142669e-15,
        -1.4673098724033913e-16,
        -2.0729781750431806e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -227.78634921458814,
          -227.757574084206,
          -227.7301656022239,
          -227.70561623119818,
          -227.6850114569464,
          -227.66900179938054,
          -227.65774676190628,
          -227.65101985518777,
          -227.6487493609563
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00663954323845273,
            -6.213425392819963e-18,
            6.759032211139275e-08
          ],
          [
            0.005825597415213327,
            -8.181107106728001e-19,
            5.9311699323387937e-08
          ],
          [
            0.005008360395424046,
            1.2129649145086359e-17,
            5.0974903578346536e-08
          ],
          [
            0.0041874044793688845,
            -1.689867171556636e-17,
            4.258775973501793e-08
          ],
          [
            0.003361397872978601,
            8.647503773118372e-18,
            3.415163831813656e-08
          ],
          [
            0.002528930717052859,
            -2.2364489877142914e-17,
            2.566505830481075e-08
          ],
          [
            0.0016899425284669872,
            1.6904919602476864e-19,
            1.713371116555372e-08
          ],
          [
            0.00084617042672159,
            -7.286942477348082e-18,
            8.573177232687602e-09
          ],
          [
            6.584967781037137e-17,
            -1.8913386717759637e-18,
            -3.821574771940855e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.34694325454658e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.41024164787067e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955397e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309701e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.04106698142669e-15,
            -1.4673098724033913e-16,
            -2.0729781750431806e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.346943254546583e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.410241647870668e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955395e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309607e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.037636974236648e-15,
            -1.4673098724033913e-16,
            -2.0729781954684906e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.49171532338390156,
            -4.996003610813204e-16,
            3.6663750140331075e-06
          ],
          [
            0.445973735232023,
            -5.551115123125783e-17,
            3.2173087158859914e-06
          ],
          [
            0.3834108390501614,
            8.881784197001252e-16,
            2.7650868790196625e-06
          ],
          [
            0.32056324587665674,
            -1.3322676295501878e-15,
            2.3101339557962675e-06
          ],
          [
            0.25732900133099024,
            6.661338147750939e-16,
            1.8525242890810034e-06
          ],
          [
            0.19360017482185754,
            -1.7208456881689926e-15,
            1.3921775420255855e-06
          ],
          [
            0.12937213611426202,
            0.0,
            9.294024433392778e-07
          ],
          [
            0.06477786893794191,
            -5.551115123125783e-16,
            4.6504413375725306e-07
          ],
          [
            4.9960036108132044e-15,
            -1.6653345369377348e-16,
            -2.0539125955565396e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -227.6487493609563,
          -227.6510198551878,
          -227.6577467619063,
          -227.66900179938057,
          -227.6850114569464,
          -227.70561623119818,
          -227.73016560222396,
          -227.7575740842059,
          -227.78634921458814
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.517681156209158e-17,
            7.41322006516494e-18,
            -9.560049493466885e-18
          ],
          [
            -0.0008461704267215415,
            2.9805641754218464e-18,
            -8.573177270707746e-09
          ],
          [
            -0.00168994252846693,
            9.247910261805963e-18,
            -1.7133711215297763e-08
          ],
          [
            -0.0025289307170527895,
            -1.1498591653075718e-17,
            -2.566505835719542e-08
          ],
          [
            -0.0033613978729785153,
            2.2786623167062087e-18,
            -3.41516383510466e-08
          ],
          [
            -0.00418740447936887,
            -2.268030063840665e-17,
            -4.2587759808967727e-08
          ],
          [
            -0.005008360395424029,
            -4.2445280738146804e-18,
            -5.09749035890802e-08
          ],
          [
            -0.005825597415213236,
            2.0598321081141295e-18,
            -5.9311699366738236e-08
          ],
          [
            -0.0066395432384527015,
            -1.3426025802394006e-17,
            -6.759032213655206e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.22401463689855e-15,
            5.751212699363612e-16,
            -5.185761141662722e-16
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.767797466985148e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.292925819865733e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698047e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.22401463689855e-15,
            5.751212699363612e-16,
            -5.185761141662722e-16
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.7677974669851489e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.2929258198657323e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698052e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.5082846766160886,
          1.885786328615163e-16,
          -3.666375018179678e-06
        ],
        "actual_opposite_endpoint_branch_residual": 8.345396419008671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.34694325454658e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.41024164787067e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955397e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309701e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.04106698142669e-15,
            -1.4673098724033913e-16,
            -2.0729781750431806e-15
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.767797466985148e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.292925819865733e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698047e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.5082846766160986,
            -4.820406073421946e-16,
            3.6663750140337216e-06
          ],
          [
            0.44597373523202294,
            -6.346943254546583e-17,
            3.2173087158952347e-06
          ],
          [
            0.3834108390501613,
            9.410241647870668e-16,
            2.7650868790714925e-06
          ],
          [
            0.32056324587665674,
            -1.3110072885820845e-15,
            2.310133955846651e-06
          ],
          [
            0.25732900133099024,
            6.70877608928052e-16,
            1.8525242890775801e-06
          ],
          [
            0.19360017482185757,
            -1.7350481580955395e-15,
            1.3921775420362446e-06
          ],
          [
            0.12937213611426202,
            1.3114920027309607e-17,
            9.294024433191494e-07
          ],
          [
            0.06477786893794193,
            -5.653245923750137e-16,
            4.650441337593575e-07
          ],
          [
            5.037636974236648e-15,
            -1.4673098724033913e-16,
            -2.0729781954684906e-15
          ],
          [
            -0.06477786893793823,
            2.312336391779968e-16,
            -4.650441358217253e-07
          ],
          [
            -0.12937213611425763,
            7.174574405284452e-16,
            -9.294024460174693e-07
          ],
          [
            -0.19360017482185224,
            -8.920664132273283e-16,
            -1.392177544877803e-06
          ],
          [
            -0.2573290013309837,
            1.7677974669851489e-16,
            -1.8525242908627554e-06
          ],
          [
            -0.3205632458766556,
            -1.759548912758288e-15,
            -2.31013395985799e-06
          ],
          [
            -0.3834108390501601,
            -3.2929258198657323e-16,
            -2.7650868796537302e-06
          ],
          [
            -0.445973735232016,
            1.5980279115698052e-16,
            -3.217308718246732e-06
          ],
          [
            -0.5082846766160963,
            -1.0415977054229527e-15,
            -3.6663750153984653e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.49171532338390156,
            -4.996003610813204e-16,
            3.6663750140331075e-06
          ],
          [
            0.445973735232023,
            -5.551115123125783e-17,
            3.2173087158859914e-06
          ],
          [
            0.3834108390501614,
            8.881784197001252e-16,
            2.7650868790196625e-06
          ],
          [
            0.32056324587665674,
            -1.3322676295501878e-15,
            2.3101339557962675e-06
          ],
          [
            0.25732900133099024,
            6.661338147750939e-16,
            1.8525242890810034e-06
          ],
          [
            0.19360017482185754,
            -1.7208456881689926e-15,
            1.3921775420255855e-06
          ],
          [
            0.12937213611426202,
            0.0,
            9.294024433392778e-07
          ],
          [
            0.06477786893794191,
            -5.551115123125783e-16,
            4.6504413375725306e-07
          ],
          [
            4.9960036108132044e-15,
            -1.6653345369377348e-16,
            -2.0539125955565396e-15
          ],
          [
            -0.06477786893793824,
            2.220446049250313e-16,
            -4.6504413581116566e-07
          ],
          [
            -0.12937213611425763,
            6.661338147750939e-16,
            -9.294024460038131e-07
          ],
          [
            -0.1936001748218522,
            -8.881784197001252e-16,
            -1.3921775448566542e-06
          ],
          [
            -0.2573290013309837,
            2.220446049250313e-16,
            -1.8525242908573603e-06
          ],
          [
            -0.3205632458766556,
            -1.7763568394002505e-15,
            -2.3101339598485815e-06
          ],
          [
            -0.3834108390501601,
            -3.3306690738754696e-16,
            -2.765086879630285e-06
          ],
          [
            -0.445973735232016,
            1.1102230246251565e-16,
            -3.217308718272971e-06
          ],
          [
            0.49171532338390367,
            -1.0547118733938987e-15,
            -3.6663750154208863e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 8.310904796491584e-16,
        "parent_symmetrization_rmsd_A": 0.39959416637754125,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -227.64874936095634,
        "reduced_polarization": [
          -4.940250858165468e-16,
          6.486011590664666e-16,
          -1.6114321706189792e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.453275239372807e-18,
          8.360363940656917e-18,
          -2.970705916767843e-18
        ],
        "ranking_score": 0.3995941663775429
      }
    }
  ],
  "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": 48,
      "full_response": 16,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 41,
      "energy_polarization": 32
    },
    "elapsed_seconds": 567.8472533830209
  }
}