{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 76,
  "input_formula": "Cl16O32Sr16Te12",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -394.6319867604234,
  "input_cartesian_polarization_e_A2": [
    2.181542330183194e-11,
    -0.0004943894075332423,
    -1.1088306677470631e-10
  ],
  "input_reduced_polarization": [
    -1.6217609144509014e-09,
    -0.13354644593113746,
    -1.0687811184732857e-08
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.291969500313151e-15,
      "parent_symmetrization_rmsd_A": 0.051443628269657427,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -394.61293074834686,
      "reduced_polarization": [
        -2.8098500003772152e-15,
        8.038977767822723e-16,
        1.515108752155007e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.533152711820834e-17,
        2.9760323669385815e-18,
        1.5718831670242007e-17
      ],
      "ranking_score": 0.05144362826966401
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.144229950125238e-05,
      "parent_symmetrization_rmsd_A": 0.008354283577986154,
      "parent_cell_rmsd_A": 0.005220593656907901,
      "energy_eV": -394.6088666431669,
      "reduced_polarization": [
        6.090866409573655e-12,
        -9.144229950125153e-05,
        1.0973954055303506e-11
      ],
      "cartesian_polarization_e_A2": [
        2.4550874212020953e-14,
        -3.3847498704712957e-07,
        1.137651289733042e-13
      ],
      "ranking_score": 0.5098423165912156
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.295365804858188e-15,
      "parent_symmetrization_rmsd_A": 0.05144375797272833,
      "parent_cell_rmsd_A": 0.005220593656907901,
      "energy_eV": -394.6125676742987,
      "reduced_polarization": [
        4.8641444009160375e-16,
        -2.9815248682585614e-15,
        -1.316566078954943e-15
      ],
      "cartesian_polarization_e_A2": [
        9.956436919676362e-18,
        -1.1036157190076822e-17,
        -1.3644190527647602e-17
      ],
      "ranking_score": 0.0527489063869619
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0007358423669240337,
      "parent_symmetrization_rmsd_A": 0.02298059410382739,
      "parent_cell_rmsd_A": 0.014319558918936881,
      "energy_eV": -394.4468148793035,
      "reduced_polarization": [
        -9.893725942133556e-12,
        -0.500735842366924,
        -2.255359966297929e-11
      ],
      "cartesian_polarization_e_A2": [
        -2.594393418485392e-14,
        -0.0018543980256793997,
        -3.2266278469613763e-13
      ],
      "ranking_score": 0.5280321685674096
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 5.765222824041726e-05,
      "parent_symmetrization_rmsd_A": 0.061863911574354856,
      "parent_cell_rmsd_A": 0.009241649233744688,
      "energy_eV": -393.27918986430956,
      "reduced_polarization": [
        1.6896058635996912e-05,
        -1.5912816095826912e-05,
        -0.4999472260963396
      ],
      "cartesian_polarization_e_A2": [
        0.0018230791797832838,
        -4.504683122998687e-06,
        -0.0051816444708623335
      ],
      "ranking_score": 0.5642896283392719
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.2954373326674652e-05,
      "parent_symmetrization_rmsd_A": 0.09172454550170701,
      "parent_cell_rmsd_A": 0.03770249229528954,
      "energy_eV": -391.6330028980726,
      "reduced_polarization": [
        -0.4999994429138558,
        -2.0278721631520358e-07,
        -1.2940800618960268e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.005299894745162263,
        3.0596575695389536e-05,
        -1.4223294705321513e-06
      ],
      "ranking_score": 0.6011760773221828
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 7.536024945093129e-05,
      "parent_symmetrization_rmsd_A": 0.06559134921988945,
      "parent_cell_rmsd_A": 0.01629639523207932,
      "energy_eV": -393.0985424526347,
      "reduced_polarization": [
        2.8746610171470525e-05,
        -0.5000167076755045,
        -0.499932371210419
      ],
      "cartesian_polarization_e_A2": [
        0.0018296864503514721,
        -0.0018562065913120232,
        -0.005203189841581673
      ],
      "ranking_score": 0.5698161685268112
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.058708499854546e-05,
      "parent_symmetrization_rmsd_A": 0.0941255386830384,
      "parent_cell_rmsd_A": 0.03941289185524196,
      "energy_eV": -391.30477722888475,
      "reduced_polarization": [
        -0.499998673809772,
        -0.4999912830972936,
        -1.8603357100911722e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.005299936035391687,
        -0.0018211303287360599,
        8.126729074768388e-06
      ],
      "ranking_score": 0.604019935816846
    },
    {
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 6.655700949173633e-05,
      "parent_symmetrization_rmsd_A": 0.07848057544663775,
      "parent_cell_rmsd_A": 0.03239649375163226,
      "energy_eV": -392.3761985584913,
      "reduced_polarization": [
        -0.49997969233335227,
        -2.151874878229154e-06,
        -0.49993665330614534
      ],
      "cartesian_polarization_e_A2": [
        -0.0034769676873604564,
        2.602339119289299e-05,
        -0.0051824811474234945
      ],
      "ranking_score": 0.5867128129035293
    },
    {
      "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": 7.945441915449897e-05,
      "parent_symmetrization_rmsd_A": 0.08154052122095946,
      "parent_cell_rmsd_A": 0.0346209834642697,
      "energy_eV": -392.1328244939237,
      "reduced_polarization": [
        -0.4999677619287245,
        -0.49999544400704304,
        -0.4999275227317582
      ],
      "cartesian_polarization_e_A2": [
        -0.0034703962659375664,
        -0.0018256558308137822,
        -0.00519433993774792
      ],
      "ranking_score": 0.5903546759253359
    }
  ],
  "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": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "target_residual": 0.1335464459311379,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.006982348349008109,
            "max_log_strain_component": 0.0006667541697960754,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.000666976499768,
              1.00035890473005,
              0.999773310159188
            ],
            "cell_volume_ratio": 1.0007991981589086,
            "cell_rmsd_from_input_A": 0.005220593656907901
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.090866409573655e-12,
              -9.144229950125153e-05,
              1.0973954055303506e-11
            ],
            "branch_aligned_reduced_polarization": [
              6.090866409573655e-12,
              -9.144229950125153e-05,
              1.0973954055303506e-11
            ],
            "target_residual": 9.144229950125238e-05,
            "energy_eV": -394.6088666431669
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.291969500313151e-15,
        "parent_symmetrization_rmsd_A": 0.051443628269657427,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -394.61293074834686,
        "reduced_polarization": [
          -2.8098500003772152e-15,
          8.038977767822723e-16,
          1.515108752155007e-15
        ],
        "cartesian_polarization_e_A2": [
          -3.533152711820834e-17,
          2.9760323669385815e-18,
          1.5718831670242007e-17
        ],
        "ranking_score": 0.05144362826966401
      },
      "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": [
          -394.6319867604234,
          -394.6288458346296,
          -394.6254968323425,
          -394.6221932056801,
          -394.61915225181343,
          -394.6165643165078,
          -394.6145897536163,
          -394.61335229830195,
          -394.6129307483467
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.1815423952839018e-11,
            -0.00049438940753325,
            -1.1088308395885749e-10
          ],
          [
            1.9082571662552272e-11,
            -0.00043231008689028136,
            -9.710161735219797e-11
          ],
          [
            1.6349083878639694e-11,
            -0.0003703175622019845,
            -8.329491801059265e-11
          ],
          [
            1.3617515538174158e-11,
            -0.00030841071627463803,
            -6.946371412531843e-11
          ],
          [
            1.0888942738144873e-11,
            -0.000246590912959733,
            -5.560840405568992e-11
          ],
          [
            8.163499510723837e-12,
            -0.00018485457053564033,
            -4.1730464938432997e-11
          ],
          [
            5.44080052172021e-12,
            -0.00012319077392012646,
            -2.783276207547816e-11
          ],
          [
            2.719961366943895e-12,
            -6.158094488084168e-05,
            -1.3920338078543195e-11
          ],
          [
            -2.7129723630752606e-17,
            -1.998636022618128e-17,
            3.658095142106927e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313816829e-15,
            -5.398795634848803e-15,
            3.525969411908963e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313934448e-15,
            -5.398459457239824e-15,
            3.5259694119270327e-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": [
          [
            -1.6217614473568176e-09,
            -0.1335464459311395,
            -1.0687812856957635e-08
          ],
          [
            -1.4222180655387717e-09,
            -0.1167773313195355,
            -9.359443053913452e-09
          ],
          [
            -1.2218975276034882e-09,
            -0.100031662378674,
            -8.028641196311526e-09
          ],
          [
            -1.0205830069942579e-09,
            -0.08330913732771456,
            -6.695477339224709e-09
          ],
          [
            -8.181862964917741e-10,
            -0.06661012457568183,
            -5.359989951880806e-09
          ],
          [
            -6.147437559000934e-10,
            -0.04993365661359084,
            -4.022321364871573e-09
          ],
          [
            -4.103867801141803e-10,
            -0.03327678501573267,
            -2.6827478016855366e-09
          ],
          [
            -2.0536605749299497e-10,
            -0.016634491355611625,
            -1.3417553179628783e-09
          ],
          [
            -1.3322676295501878e-15,
            -5.384581669432009e-15,
            3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -394.6129307483466,
          -394.6133522983022,
          -394.6145897536161,
          -394.6165643165077,
          -394.61915225181355,
          -394.62219320568016,
          -394.6254968323425,
          -394.62884583462966,
          -394.6319867604234
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.929957027412645e-17,
            -6.589785955364002e-18,
            3.891870898907181e-17
          ],
          [
            -2.719897705537236e-12,
            6.158094488083584e-05,
            1.3920359366364004e-11
          ],
          [
            -5.4407743397211715e-12,
            0.0001231907739201332,
            2.7832755514478233e-11
          ],
          [
            -8.163477442912403e-12,
            0.00018485457053564897,
            4.173045740258318e-11
          ],
          [
            -1.088891323025252e-11,
            0.0002465909129597324,
            5.560845721407164e-11
          ],
          [
            -1.3617528527315427e-11,
            0.0003084107162746737,
            6.946374201676464e-11
          ],
          [
            -1.6349093094597067e-11,
            0.00037031756220199324,
            8.329497861071602e-11
          ],
          [
            -1.908255958127802e-11,
            0.0004323100868903086,
            9.710162807997535e-11
          ],
          [
            -2.1815369719963475e-11,
            0.0004943894075332641,
            1.108830661270207e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4143019210597126e-15,
            -1.7800593628750317e-15,
            3.751301486582342e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4143019210597126e-15,
            -1.7800593628750317e-15,
            3.751301486582342e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.621758734399958e-09,
          0.13354644593112874,
          1.0687819893019838e-08
        ],
        "actual_opposite_endpoint_branch_residual": 1.8494946721293275e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313816829e-15,
            -5.398795634848803e-15,
            3.525969411908963e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313934448e-15,
            -5.398459457239824e-15,
            3.5259694119270327e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.6217614473568176e-09,
            -0.1335464459311395,
            -1.0687812856957635e-08
          ],
          [
            -1.4222180655387717e-09,
            -0.1167773313195355,
            -9.359443053913452e-09
          ],
          [
            -1.2218975276034882e-09,
            -0.100031662378674,
            -8.028641196311526e-09
          ],
          [
            -1.0205830069942579e-09,
            -0.08330913732771456,
            -6.695477339224709e-09
          ],
          [
            -8.181862964917741e-10,
            -0.06661012457568183,
            -5.359989951880806e-09
          ],
          [
            -6.147437559000934e-10,
            -0.04993365661359084,
            -4.022321364871573e-09
          ],
          [
            -4.103867801141803e-10,
            -0.03327678501573267,
            -2.6827478016855366e-09
          ],
          [
            -2.0536605749299497e-10,
            -0.016634491355611625,
            -1.3417553179628783e-09
          ],
          [
            -1.3322676295501878e-15,
            -5.384581669432009e-15,
            3.552713678800501e-15
          ],
          [
            2.0537271883114272e-10,
            0.016634491355610015,
            1.3417573718754738e-09
          ],
          [
            4.1038905607138076e-10,
            0.0332767850157345,
            2.682747135551722e-09
          ],
          [
            6.147455877680841e-10,
            0.04993365661359317,
            4.022320698737758e-09
          ],
          [
            8.181908484061751e-10,
            0.06661012457568172,
            5.35999511441787e-09
          ],
          [
            1.0205827294385017e-09,
            0.08330913732772416,
            6.6954800592711194e-09
          ],
          [
            1.221898693337664e-09,
            0.10003166237867633,
            8.028646969471254e-09
          ],
          [
            1.422219564339855e-09,
            0.11677733131954282,
            9.359444108625325e-09
          ],
          [
            1.6217659437600673e-09,
            0.1335464459311433,
            1.0687811080600795e-08
          ]
        ]
      },
      "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,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "target_residual": 0.3664535540688627,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.019159674016742446,
            "max_log_strain_component": 0.0018295839586625637,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0006223045657563,
              0.999015821071436,
              0.9981720887098169
            ],
            "cell_volume_ratio": 0.9978102644817227,
            "cell_rmsd_from_input_A": 0.014319558918936881
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -9.893725942133556e-12,
              -0.500735842366924,
              -2.255359966297929e-11
            ],
            "branch_aligned_reduced_polarization": [
              -9.893725942133556e-12,
              -0.500735842366924,
              -2.255359966297929e-11
            ],
            "target_residual": 0.0007358423669240337,
            "energy_eV": -394.4468148793035
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0007358423669240337,
        "parent_symmetrization_rmsd_A": 0.02298059410382739,
        "parent_cell_rmsd_A": 0.014319558918936881,
        "energy_eV": -394.4468148793035,
        "reduced_polarization": [
          -9.893725942133556e-12,
          -0.500735842366924,
          -2.255359966297929e-11
        ],
        "cartesian_polarization_e_A2": [
          -2.594393418485392e-14,
          -0.0018543980256793997,
          -3.2266278469613763e-13
        ],
        "ranking_score": 0.5280321685674096
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811191623098e-08
            ],
            "target_residual": 0.5175274316720101,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.07973212344340233,
            "max_log_strain_component": 0.0011462672333452998,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0019351296473262,
              0.9999186893587498,
              0.9989474875019814
            ],
            "cell_volume_ratio": 1.0007991981593607,
            "cell_rmsd_from_input_A": 0.00933493008256719
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.006010350274778368,
              0.0004376516594677922,
              -0.4813296776860718
            ],
            "branch_aligned_reduced_polarization": [
              0.006010350274778368,
              0.0004376516594677922,
              -0.4813296776860718
            ],
            "target_residual": 0.019618786524821758,
            "energy_eV": -393.3534403428748,
            "max_atomic_step_A": 0.003112044057198516,
            "max_log_strain_component": 4.5572399048724874e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0019091097398483,
              0.9999347338348245,
              0.9989545415905203
            ],
            "cell_volume_ratio": 1.0007963330334146,
            "cell_rmsd_from_input_A": 0.009241649233744688
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.6896058635996912e-05,
              -1.5912816095826912e-05,
              -0.4999472260963396
            ],
            "branch_aligned_reduced_polarization": [
              1.6896058635996912e-05,
              -1.5912816095826912e-05,
              -0.4999472260963396
            ],
            "target_residual": 5.765222824041726e-05,
            "energy_eV": -393.27918986430956
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 5.765222824041726e-05,
        "parent_symmetrization_rmsd_A": 0.061863911574354856,
        "parent_cell_rmsd_A": 0.009241649233744688,
        "energy_eV": -393.27918986430956,
        "reduced_polarization": [
          1.6896058635996912e-05,
          -1.5912816095826912e-05,
          -0.4999472260963396
        ],
        "cartesian_polarization_e_A2": [
          0.0018230791797832838,
          -4.504683122998687e-06,
          -0.0051816444708623335
        ],
        "ranking_score": 0.5642896283392719
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217608922453053e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "target_residual": 0.5175274404310146,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.09276106472542142,
            "max_log_strain_component": 0.005764901151272354,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0069543263688945,
              0.9997735918553421,
              0.9941124562204844
            ],
            "cell_volume_ratio": 1.0007991982855333,
            "cell_rmsd_from_input_A": 0.03761611871799496
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4992924721357283,
              -0.0073382722676943336,
              0.0009755256838011665
            ],
            "branch_aligned_reduced_polarization": [
              -0.4992924721357283,
              -0.0073382722676943336,
              0.0009755256838011665
            ],
            "target_residual": 0.0074365641201625055,
            "energy_eV": -391.63790123515855,
            "max_atomic_step_A": 0.00044623376349326897,
            "max_log_strain_component": 3.6338950556624336e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0069894905458565,
              0.9997612487599679,
              0.9941332981796539
            ],
            "cell_volume_ratio": 1.000842773951425,
            "cell_rmsd_from_input_A": 0.03770249229528954
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999994429138558,
              -2.0278721631520358e-07,
              -1.2940800618960268e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999994429138558,
              -2.0278721631520358e-07,
              -1.2940800618960268e-05
            ],
            "target_residual": 1.2954373326674652e-05,
            "energy_eV": -391.6330028980726
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.2954373326674652e-05,
        "parent_symmetrization_rmsd_A": 0.09172454550170701,
        "parent_cell_rmsd_A": 0.03770249229528954,
        "energy_eV": -391.6330028980726,
        "reduced_polarization": [
          -0.4999994429138558,
          -2.0278721631520358e-07,
          -1.2940800618960268e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.005299894745162263,
          3.0596575695389536e-05,
          -1.4223294705321513e-06
        ],
        "ranking_score": 0.6011760773221828
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811191623098e-08
            ],
            "target_residual": 0.6199098294122216,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.08129190083470926,
            "max_log_strain_component": 0.0018295838897423116,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0008691547091277,
              0.9997911018876587,
              0.9971520692981144
            ],
            "cell_volume_ratio": 0.9978102644821734,
            "cell_rmsd_from_input_A": 0.016254608466868763
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0071366518268754335,
              -0.49727985378629813,
              -0.4795308318647862
            ],
            "branch_aligned_reduced_polarization": [
              0.0071366518268754335,
              -0.49727985378629813,
              -0.4795308318647862
            ],
            "target_residual": 0.02184760487718537,
            "energy_eV": -393.18026333500904,
            "max_atomic_step_A": 0.0034270264119562487,
            "max_log_strain_component": 5.677304825562519e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0008830134385203,
              0.9997357517076957,
              0.997175014515101
            ],
            "cell_volume_ratio": 0.9977917989831342,
            "cell_rmsd_from_input_A": 0.01629639523207932
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.8746610171470525e-05,
              -0.5000167076755045,
              -0.499932371210419
            ],
            "branch_aligned_reduced_polarization": [
              2.8746610171470525e-05,
              -0.5000167076755045,
              -0.499932371210419
            ],
            "target_residual": 7.536024945093129e-05,
            "energy_eV": -393.0985424526347
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 7.536024945093129e-05,
        "parent_symmetrization_rmsd_A": 0.06559134921988945,
        "parent_cell_rmsd_A": 0.01629639523207932,
        "energy_eV": -393.0985424526347,
        "reduced_polarization": [
          2.8746610171470525e-05,
          -0.5000167076755045,
          -0.499932371210419
        ],
        "cartesian_polarization_e_A2": [
          0.0018296864503514721,
          -0.0018562065913120232,
          -0.005203189841581673
        ],
        "ranking_score": 0.5698161685268112
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217608922453053e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "target_residual": 0.619909836724616,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.09408436865955216,
            "max_log_strain_component": 0.0057649011481352526,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.005035699493685,
              1.000621459246201,
              0.9921941596920284
            ],
            "cell_volume_ratio": 0.9978102646079692,
            "cell_rmsd_from_input_A": 0.039619573375387115
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5010317908867649,
              -0.5101932577517622,
              0.0008723104074334373
            ],
            "branch_aligned_reduced_polarization": [
              -0.5010317908867649,
              -0.5101932577517622,
              0.0008723104074334373
            ],
            "target_residual": 0.010282413212606617,
            "energy_eV": -391.2761153337914,
            "max_atomic_step_A": 0.0006518360032477906,
            "max_log_strain_component": 4.967038992441007e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0050592196008648,
              1.0006046003161835,
              0.9922467074361084
            ],
            "cell_volume_ratio": 0.9978696491902646,
            "cell_rmsd_from_input_A": 0.03941289185524196
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.499998673809772,
              -0.4999912830972936,
              -1.8603357100911722e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.499998673809772,
              -0.4999912830972936,
              -1.8603357100911722e-05
            ],
            "target_residual": 2.058708499854546e-05,
            "energy_eV": -391.30477722888475
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.058708499854546e-05,
        "parent_symmetrization_rmsd_A": 0.0941255386830384,
        "parent_cell_rmsd_A": 0.03941289185524196,
        "energy_eV": -391.30477722888475,
        "reduced_polarization": [
          -0.499998673809772,
          -0.4999912830972936,
          -1.8603357100911722e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.005299936035391687,
          -0.0018211303287360599,
          8.126729074768388e-06
        ],
        "ranking_score": 0.604019935816846
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217608922453053e-09,
              -0.13354644593113746,
              -1.0687811191623098e-08
            ],
            "target_residual": 0.7196072824195613,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.09973569291883107,
            "max_log_strain_component": 0.00487034255461928,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0056769671887764,
              0.9997795381017712,
              0.9953692067028345
            ],
            "cell_volume_ratio": 1.0007991982859854,
            "cell_rmsd_from_input_A": 0.031624056025903985
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4879511504599462,
              -0.007433418765458197,
              -0.47437277107311304
            ],
            "branch_aligned_reduced_polarization": [
              -0.4879511504599462,
              -0.007433418765458197,
              -0.47437277107311304
            ],
            "target_residual": 0.029277727921623163,
            "energy_eV": -392.5006951078316,
            "max_atomic_step_A": 0.00459451217931408,
            "max_log_strain_component": 0.00011329200881757243,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0058179064755846,
              0.9997673205058555,
              0.9952885171989374
            ],
            "cell_volume_ratio": 1.0008460821499479,
            "cell_rmsd_from_input_A": 0.03239649375163226
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49997969233335227,
              -2.151874878229154e-06,
              -0.49993665330614534
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997969233335227,
              -2.151874878229154e-06,
              -0.49993665330614534
            ],
            "target_residual": 6.655700949173633e-05,
            "energy_eV": -392.3761985584913
          }
        ],
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 6.655700949173633e-05,
        "parent_symmetrization_rmsd_A": 0.07848057544663775,
        "parent_cell_rmsd_A": 0.03239649375163226,
        "energy_eV": -392.3761985584913,
        "reduced_polarization": [
          -0.49997969233335227,
          -2.151874878229154e-06,
          -0.49993665330614534
        ],
        "cartesian_polarization_e_A2": [
          -0.0034769676873604564,
          2.602339119289299e-05,
          -0.0051824811474234945
        ],
        "ranking_score": 0.5867128129035293
      },
      "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": [
              -1.6217609144509014e-09,
              -0.13354644593113746,
              -1.0687811184732857e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.6217608922453053e-09,
              -0.13354644593113746,
              -1.0687811191623098e-08
            ],
            "target_residual": 0.7964221211016986,
            "energy_eV": -394.6319867604234,
            "max_atomic_step_A": 0.10097771645927126,
            "max_log_strain_component": 0.004870342551482178,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.003779423256991,
              1.0006026729918776,
              0.9934545881368553
            ],
            "cell_volume_ratio": 0.9978102646084195,
            "cell_rmsd_from_input_A": 0.03409965895614931
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4882940702313217,
              -0.5068338382602365,
              -0.4728771121334521
            ],
            "branch_aligned_reduced_polarization": [
              -0.4882940702313217,
              -0.5068338382602365,
              -0.4728771121334521
            ],
            "target_residual": 0.0303212991696865,
            "energy_eV": -392.2485456017725,
            "max_atomic_step_A": 0.004844755265031339,
            "max_log_strain_component": 0.00010845263756263062,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3039728602376526,
            "cell_principal_stretches": [
              1.0039107737214756,
              1.0005891763720671,
              0.993379491165869
            ],
            "cell_volume_ratio": 0.9978519381809887,
            "cell_rmsd_from_input_A": 0.0346209834642697
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999677619287245,
              -0.49999544400704304,
              -0.4999275227317582
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999677619287245,
              -0.49999544400704304,
              -0.4999275227317582
            ],
            "target_residual": 7.945441915449897e-05,
            "energy_eV": -392.1328244939237
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 7.945441915449897e-05,
        "parent_symmetrization_rmsd_A": 0.08154052122095946,
        "parent_cell_rmsd_A": 0.0346209834642697,
        "energy_eV": -392.1328244939237,
        "reduced_polarization": [
          -0.4999677619287245,
          -0.49999544400704304,
          -0.4999275227317582
        ],
        "cartesian_polarization_e_A2": [
          -0.0034703962659375664,
          -0.0018256558308137822,
          -0.00519433993774792
        ],
        "ranking_score": 0.5903546759253359
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75
        ],
        "endpoint_rmsd_A": 0.051443628269657427,
        "minimum_distance_A_by_image": [
          1.8798462514067804,
          1.8798640437287477,
          1.87988183997544,
          1.8798996401467372,
          1.8799174442425304,
          1.8799352522627133,
          1.8799530642071676,
          1.8799708800757817,
          1.8799886998684499
        ],
        "minimum_distance_A": 1.8798462514067804,
        "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": [
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474,
          1566.8299697366474
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.3443881313816829e-15,
        -5.398795634848803e-15,
        3.525969411908963e-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": [
          -394.6319867604234,
          -394.6288458346296,
          -394.6254968323425,
          -394.6221932056801,
          -394.61915225181343,
          -394.6165643165078,
          -394.6145897536163,
          -394.61335229830195,
          -394.6129307483467
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.1815423952839018e-11,
            -0.00049438940753325,
            -1.1088308395885749e-10
          ],
          [
            1.9082571662552272e-11,
            -0.00043231008689028136,
            -9.710161735219797e-11
          ],
          [
            1.6349083878639694e-11,
            -0.0003703175622019845,
            -8.329491801059265e-11
          ],
          [
            1.3617515538174158e-11,
            -0.00030841071627463803,
            -6.946371412531843e-11
          ],
          [
            1.0888942738144873e-11,
            -0.000246590912959733,
            -5.560840405568992e-11
          ],
          [
            8.163499510723837e-12,
            -0.00018485457053564033,
            -4.1730464938432997e-11
          ],
          [
            5.44080052172021e-12,
            -0.00012319077392012646,
            -2.783276207547816e-11
          ],
          [
            2.719961366943895e-12,
            -6.158094488084168e-05,
            -1.3920338078543195e-11
          ],
          [
            -2.7129723630752606e-17,
            -1.998636022618128e-17,
            3.658095142106927e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313816829e-15,
            -5.398795634848803e-15,
            3.525969411908963e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313934448e-15,
            -5.398459457239824e-15,
            3.5259694119270327e-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": [
          [
            -1.6217614473568176e-09,
            -0.1335464459311395,
            -1.0687812856957635e-08
          ],
          [
            -1.4222180655387717e-09,
            -0.1167773313195355,
            -9.359443053913452e-09
          ],
          [
            -1.2218975276034882e-09,
            -0.100031662378674,
            -8.028641196311526e-09
          ],
          [
            -1.0205830069942579e-09,
            -0.08330913732771456,
            -6.695477339224709e-09
          ],
          [
            -8.181862964917741e-10,
            -0.06661012457568183,
            -5.359989951880806e-09
          ],
          [
            -6.147437559000934e-10,
            -0.04993365661359084,
            -4.022321364871573e-09
          ],
          [
            -4.103867801141803e-10,
            -0.03327678501573267,
            -2.6827478016855366e-09
          ],
          [
            -2.0536605749299497e-10,
            -0.016634491355611625,
            -1.3417553179628783e-09
          ],
          [
            -1.3322676295501878e-15,
            -5.384581669432009e-15,
            3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -394.6129307483466,
          -394.6133522983022,
          -394.6145897536161,
          -394.6165643165077,
          -394.61915225181355,
          -394.62219320568016,
          -394.6254968323425,
          -394.62884583462966,
          -394.6319867604234
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.929957027412645e-17,
            -6.589785955364002e-18,
            3.891870898907181e-17
          ],
          [
            -2.719897705537236e-12,
            6.158094488083584e-05,
            1.3920359366364004e-11
          ],
          [
            -5.4407743397211715e-12,
            0.0001231907739201332,
            2.7832755514478233e-11
          ],
          [
            -8.163477442912403e-12,
            0.00018485457053564897,
            4.173045740258318e-11
          ],
          [
            -1.088891323025252e-11,
            0.0002465909129597324,
            5.560845721407164e-11
          ],
          [
            -1.3617528527315427e-11,
            0.0003084107162746737,
            6.946374201676464e-11
          ],
          [
            -1.6349093094597067e-11,
            0.00037031756220199324,
            8.329497861071602e-11
          ],
          [
            -1.908255958127802e-11,
            0.0004323100868903086,
            9.710162807997535e-11
          ],
          [
            -2.1815369719963475e-11,
            0.0004943894075332641,
            1.108830661270207e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4143019210597126e-15,
            -1.7800593628750317e-15,
            3.751301486582342e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4143019210597126e-15,
            -1.7800593628750317e-15,
            3.751301486582342e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.621758734399958e-09,
          0.13354644593112874,
          1.0687819893019838e-08
        ],
        "actual_opposite_endpoint_branch_residual": 1.8494946721293275e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313816829e-15,
            -5.398795634848803e-15,
            3.525969411908963e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6217614231762208e-09,
            -0.13354644593113954,
            -1.0687812841081015e-08
          ],
          [
            -1.4222180774034042e-09,
            -0.11677733131953551,
            -9.359443079808525e-09
          ],
          [
            -1.2218975208773822e-09,
            -0.10003166237867399,
            -8.028641182461347e-09
          ],
          [
            -1.0205830120961278e-09,
            -0.08330913732771456,
            -6.695477338033163e-09
          ],
          [
            -8.181863039990927e-10,
            -0.06661012457568184,
            -5.359989943632409e-09
          ],
          [
            -6.147437649609683e-10,
            -0.04993365661359081,
            -4.022321377702243e-09
          ],
          [
            -4.103867877055338e-10,
            -0.03327678501573266,
            -2.682747821330647e-09
          ],
          [
            -2.053660565430153e-10,
            -0.01663449135561164,
            -1.341755322419118e-09
          ],
          [
            -1.3443881313934448e-15,
            -5.398459457239824e-15,
            3.5259694119270327e-15
          ],
          [
            2.0537276531032433e-10,
            0.01663449135561006,
            1.3417573743123057e-09
          ],
          [
            4.1038903868715666e-10,
            0.03327678501573449,
            2.682747188928149e-09
          ],
          [
            6.147455956815694e-10,
            0.04993365661359314,
            4.02232065133579e-09
          ],
          [
            8.181908498445837e-10,
            0.06661012457568168,
            5.3599950674692875e-09
          ],
          [
            1.020582712710914e-09,
            0.0833091373277242,
            6.695480026437438e-09
          ],
          [
            1.2218986624134154e-09,
            0.10003166237867633,
            8.028647023593769e-09
          ],
          [
            1.4222195724327394e-09,
            0.11677733131954285,
            9.359444113838901e-09
          ],
          [
            1.6217659450971882e-09,
            0.13354644593114334,
            1.0687811122303655e-08
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.6217614473568176e-09,
            -0.1335464459311395,
            -1.0687812856957635e-08
          ],
          [
            -1.4222180655387717e-09,
            -0.1167773313195355,
            -9.359443053913452e-09
          ],
          [
            -1.2218975276034882e-09,
            -0.100031662378674,
            -8.028641196311526e-09
          ],
          [
            -1.0205830069942579e-09,
            -0.08330913732771456,
            -6.695477339224709e-09
          ],
          [
            -8.181862964917741e-10,
            -0.06661012457568183,
            -5.359989951880806e-09
          ],
          [
            -6.147437559000934e-10,
            -0.04993365661359084,
            -4.022321364871573e-09
          ],
          [
            -4.103867801141803e-10,
            -0.03327678501573267,
            -2.6827478016855366e-09
          ],
          [
            -2.0536605749299497e-10,
            -0.016634491355611625,
            -1.3417553179628783e-09
          ],
          [
            -1.3322676295501878e-15,
            -5.384581669432009e-15,
            3.552713678800501e-15
          ],
          [
            2.0537271883114272e-10,
            0.016634491355610015,
            1.3417573718754738e-09
          ],
          [
            4.1038905607138076e-10,
            0.0332767850157345,
            2.682747135551722e-09
          ],
          [
            6.147455877680841e-10,
            0.04993365661359317,
            4.022320698737758e-09
          ],
          [
            8.181908484061751e-10,
            0.06661012457568172,
            5.35999511441787e-09
          ],
          [
            1.0205827294385017e-09,
            0.08330913732772416,
            6.6954800592711194e-09
          ],
          [
            1.221898693337664e-09,
            0.10003166237867633,
            8.028646969471254e-09
          ],
          [
            1.422219564339855e-09,
            0.11677733131954282,
            9.359444108625325e-09
          ],
          [
            1.6217659437600673e-09,
            0.1335464459311433,
            1.0687811080600795e-08
          ]
        ]
      },
      "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": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.291969500313151e-15,
        "parent_symmetrization_rmsd_A": 0.051443628269657427,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -394.61293074834686,
        "reduced_polarization": [
          -2.8098500003772152e-15,
          8.038977767822723e-16,
          1.515108752155007e-15
        ],
        "cartesian_polarization_e_A2": [
          -3.533152711820834e-17,
          2.9760323669385815e-18,
          1.5718831670242007e-17
        ],
        "ranking_score": 0.05144362826966401
      }
    }
  ],
  "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": 47,
      "full_response": 15,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 72,
      "full_response": 40,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1186.78751800803
  }
}
