{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 18,
  "input_formula": "K2Li2O8Zn6",
  "input_spacegroup": "Cm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -77.3424731191894,
  "input_cartesian_polarization_e_A2": [
    -0.002554825655802416,
    -2.385798353718526e-20,
    -0.0005770990741366578
  ],
  "input_reduced_polarization": [
    -0.07201415924076202,
    -1.6525305734054318e-18,
    -0.01604031537775283
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -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": "P2/c",
      "spacegroup_number": 13,
      "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": 1.9227305527307886e-15,
      "parent_symmetrization_rmsd_A": 0.6469984413705254,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -1.3727321200616758e-15,
        8.551467210124439e-16,
        -1.0398189219749204e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.84295629786705e-17,
        1.2345960020424624e-17,
        -3.7410644554644183e-17
      ],
      "ranking_score": 0.6469984413705293
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 3.1165267365469077e-15,
      "parent_symmetrization_rmsd_A": 0.6469984413705266,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -60.423342451861856,
      "reduced_polarization": [
        -1.9709776676036393e-15,
        -2.361464948786175e-15,
        -5.014670767595271e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.990079779680029e-17,
        -3.409304056364843e-17,
        -1.8041801479122942e-17
      ],
      "ranking_score": 0.6469984413705329
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 2.9886443944763403e-15,
      "parent_symmetrization_rmsd_A": 0.8214192297488169,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -69.4384338796498,
      "reduced_polarization": [
        -2.8662407737447472e-15,
        3.1499969795748233e-16,
        -7.85769898790135e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.0163051147248097e-16,
        4.547726819117766e-18,
        -2.8270459177204214e-17
      ],
      "ranking_score": 0.8214192297488229
    },
    {
      "candidate_id": "bec_projection_00",
      "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": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0005072542306746767,
      "parent_symmetrization_rmsd_A": 0.023725508816638062,
      "parent_cell_rmsd_A": 0.01621691113235258,
      "energy_eV": -77.30724843888245,
      "reduced_polarization": [
        -0.00020348040541342898,
        -3.906078845733642e-15,
        -0.00046465318157755533
      ],
      "cartesian_polarization_e_A2": [
        -7.089773485605492e-06,
        -5.636078001697625e-17,
        -1.6702551653099497e-05
      ],
      "ranking_score": 0.5287942450610755
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 0.00034921424822358544,
      "parent_symmetrization_rmsd_A": 0.6470015951512166,
      "parent_cell_rmsd_A": 0.01621691113235258,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        0.000348438575926078,
        2.0165812101854132e-05,
        -1.159698198858024e-05
      ],
      "cartesian_polarization_e_A2": [
        1.2403066107258358e-05,
        2.9071368570472767e-07,
        -4.0168819722456613e-07
      ],
      "ranking_score": 0.6517542514307519
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.7259756946737956e-15,
      "parent_symmetrization_rmsd_A": 0.6470015951512177,
      "parent_cell_rmsd_A": 0.01621691113235258,
      "energy_eV": -60.30636587498109,
      "reduced_polarization": [
        -1.451911747420507e-16,
        -2.6088422403658685e-16,
        1.6999561885620884e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.7196232182155945e-18,
        -3.760950163019369e-18,
        6.106889373615608e-17
      ],
      "ranking_score": 0.6510558229343093
    },
    {
      "candidate_id": "bec_projection_01",
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.6082767649215766e-06,
      "parent_symmetrization_rmsd_A": 0.1411224326430634,
      "parent_cell_rmsd_A": 0.10667365713260861,
      "energy_eV": -75.89640250580251,
      "reduced_polarization": [
        -0.5000010414601078,
        3.672335350762183e-15,
        2.391331956514828e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.017696081584672608,
        2.627570543269835e-16,
        0.00016173379920747717
      ],
      "ranking_score": 0.6677960634797454
    },
    {
      "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": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0009753630967429045,
      "parent_symmetrization_rmsd_A": 0.1282926021927975,
      "parent_cell_rmsd_A": 0.06904735063840886,
      "energy_eV": -75.67963773302084,
      "reduced_polarization": [
        0.00022169392596863596,
        -3.675859457125333e-15,
        -0.4990501658177995
      ],
      "cartesian_polarization_e_A2": [
        7.386686624475406e-05,
        5.77314907056036e-17,
        -0.01796068644265187
      ],
      "ranking_score": 0.6475051660458855
    },
    {
      "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": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 5.689750207739758e-06,
      "parent_symmetrization_rmsd_A": 0.0562363026155349,
      "parent_cell_rmsd_A": 0.017508619165499693,
      "energy_eV": -77.09788357012637,
      "reduced_polarization": [
        4.900622290176854e-06,
        0.4999979708642079,
        2.0590693365346265e-06
      ],
      "cartesian_polarization_e_A2": [
        -7.76264814962131e-06,
        0.007208099033493826,
        -1.1385328802117793e-05
      ],
      "ranking_score": 0.5606248369073253
    },
    {
      "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": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.210012715564537e-05,
      "parent_symmetrization_rmsd_A": 0.22155572140932375,
      "parent_cell_rmsd_A": 0.10929128435460045,
      "energy_eV": -73.36774945559479,
      "reduced_polarization": [
        -0.5000706450219509,
        -1.3990614014876278e-15,
        -0.5000144121202265
      ],
      "cartesian_polarization_e_A2": [
        -0.017441999179045403,
        5.365285137654387e-16,
        -0.01812051498393735
      ],
      "ranking_score": 0.7490227427522851
    },
    {
      "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": 2.5394016237461324e-05,
      "parent_symmetrization_rmsd_A": 0.1533223631904325,
      "parent_cell_rmsd_A": 0.10901905266292207,
      "energy_eV": -75.71555218885943,
      "reduced_polarization": [
        -0.5000176835577773,
        0.49998818932371014,
        -1.3880049372426277e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.01770374169146875,
        0.007292204121606349,
        0.0001516020197127856
      ],
      "ranking_score": 0.680627914388638
    },
    {
      "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": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.1204519020386235e-05,
      "parent_symmetrization_rmsd_A": 0.1407195564536842,
      "parent_cell_rmsd_A": 0.07029705128792,
      "energy_eV": -75.49689610633078,
      "reduced_polarization": [
        -8.233000819756323e-07,
        0.4999800679778474,
        -0.49999281193372536
      ],
      "cartesian_polarization_e_A2": [
        5.6365642201484414e-05,
        0.007301517834387215,
        -0.018008082921827765
      ],
      "ranking_score": 0.658336228313705
    },
    {
      "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": 1.1095498603796268e-05,
      "parent_symmetrization_rmsd_A": 0.23365947111578592,
      "parent_cell_rmsd_A": 0.11191853031992394,
      "energy_eV": -73.18423356077015,
      "reduced_polarization": [
        -0.4999968005756498,
        0.49998952535852026,
        -0.4999982235825476
      ],
      "cartesian_polarization_e_A2": [
        -0.01744701666853948,
        0.007407423416286933,
        -0.01813832882287358
      ],
      "ranking_score": 0.7616612946929745
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "target_residual": 0.07377893228132,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.02391563833278371,
            "max_log_strain_component": 0.0018003717684594047,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0023468769622814,
              0.9995945114582121,
              0.999117184964205
            ],
            "cell_volume_ratio": 1.0010559087062085,
            "cell_rmsd_from_input_A": 0.01621691113235258
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00020348040541342898,
              -3.906078845733642e-15,
              -0.00046465318157755533
            ],
            "branch_aligned_reduced_polarization": [
              -0.00020348040541342898,
              -3.906078845733642e-15,
              -0.00046465318157755533
            ],
            "target_residual": 0.0005072542306746767,
            "energy_eV": -77.30724843888245
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "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": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0005072542306746767,
        "parent_symmetrization_rmsd_A": 0.023725508816638062,
        "parent_cell_rmsd_A": 0.01621691113235258,
        "energy_eV": -77.30724843888245,
        "reduced_polarization": [
          -0.00020348040541342898,
          -3.906078845733642e-15,
          -0.00046465318157755533
        ],
        "cartesian_polarization_e_A2": [
          -7.089773485605492e-06,
          -5.636078001697625e-17,
          -1.6702551653099497e-05
        ],
        "ranking_score": 0.5287942450610755
      },
      "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": [
          -77.3424731191894,
          -77.34094818788772,
          -77.3385635487317,
          -77.33533854869714,
          -77.33129198713058,
          -77.32644215047945,
          -77.32080682615856,
          -77.31440331440564,
          -77.30724843888245
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.002554825655802454,
            1.4212032635460783e-17,
            -0.0005770990741367024
          ],
          [
            -0.00223634048320274,
            -6.404869261915035e-17,
            -0.0005057464574739926
          ],
          [
            -0.001917716218896982,
            -1.6650301039863252e-17,
            -0.00043471790597315163
          ],
          [
            -0.0015990219737325622,
            4.069964689707137e-18,
            -0.0003640375202547422
          ],
          [
            -0.0012803290796893185,
            1.4420347487409368e-17,
            -0.000293729322151123
          ],
          [
            -0.0009617114730414046,
            -8.034768857452874e-17,
            -0.00022381745401784653
          ],
          [
            -0.0006432457455470893,
            1.3702480573401277e-17,
            -0.00015432615607741682
          ],
          [
            -0.00032501117941963214,
            6.511796184400416e-17,
            -8.527973774463014e-05
          ],
          [
            -7.089773485540193e-06,
            -2.5781924217822234e-17,
            -1.670255165309543e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107755e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425327e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159296,
            -1.7849284126515566e-15,
            -0.00046465318157744447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107745e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425323e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159212,
            -1.784928412651557e-15,
            -0.00046465318157744447
          ]
        ],
        "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": [
          [
            -0.0720141592407631,
            9.992007221626409e-16,
            -0.016040315377754077
          ],
          [
            -0.06302895112082291,
            -4.385380947269368e-15,
            -0.014050153452692005
          ],
          [
            -0.05404221876998583,
            -1.0547118733938987e-15,
            -0.012070984899717196
          ],
          [
            -0.045055908098272146,
            3.3306690738754696e-16,
            -0.01010348554505286
          ],
          [
            -0.036072026293296755,
            1.1102230246251565e-15,
            -0.008148328296644747
          ],
          [
            -0.02709265261649968,
            -5.495603971894525e-15,
            -0.006206188632342846
          ],
          [
            -0.01811993979937021,
            9.992007221626409e-16,
            -0.0042777439165918585
          ],
          [
            -0.009156114982088903,
            4.551914400963142e-15,
            -0.002363672548153062
          ],
          [
            -0.0002034804054115713,
            -1.7763568394002505e-15,
            -0.00046465318157745683
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -77.30724843888245,
          -77.30013798282408,
          -77.29237737096597,
          -77.28397211176343,
          -77.27492722227149,
          -77.26524728121487,
          -77.2549364956794,
          -77.24399870513602,
          -77.23243738488156
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.0897734856361155e-06,
            -3.221811876748882e-17,
            -1.670255165315127e-05
          ],
          [
            0.000299870783677393,
            3.475245678405e-17,
            5.4693399435634484e-05
          ],
          [
            0.0006069510201188584,
            -1.2790593535740207e-17,
            0.00012589889265176164
          ],
          [
            0.0009140825583361333,
            -1.0424893531703348e-16,
            0.000196896929367497
          ],
          [
            0.0012211961651288098,
            -2.508983466897549e-17,
            0.00026767053300126044
          ],
          [
            0.0015282216670575413,
            -2.7194075507933902e-17,
            0.0003382027742070659
          ],
          [
            0.001835087986474158,
            -3.41538844871362e-17,
            0.00040847676870517055
          ],
          [
            0.002141723177596794,
            -1.3936675018070558e-18,
            0.0004784756744314168
          ],
          [
            0.0024480544620079057,
            -3.558878432304152e-17,
            0.0005481826880043832
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0002034804054143027,
            -2.231385171730259e-15,
            -0.00046465318157899553
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0002034804054143027,
            -2.231385171730259e-15,
            -0.00046465318157899553
          ],
          [
            0.008441663356548605,
            2.3717489698609172e-15,
            0.0015132335398736268
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.07160577506154543,
          -4.555986648798944e-15,
          0.01511182941014215
        ],
        "actual_opposite_endpoint_branch_residual": 0.002605599890877764
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107755e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425327e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159296,
            -1.7849284126515566e-15,
            -0.00046465318157744447
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107745e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425323e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159212,
            -1.784928412651557e-15,
            -0.00046465318157744447
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.0034877025555624516
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "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": [
          [
            -0.0720141592407631,
            9.992007221626409e-16,
            -0.016040315377754077
          ],
          [
            -0.06302895112082291,
            -4.385380947269368e-15,
            -0.014050153452692005
          ],
          [
            -0.05404221876998583,
            -1.0547118733938987e-15,
            -0.012070984899717196
          ],
          [
            -0.045055908098272146,
            3.3306690738754696e-16,
            -0.01010348554505286
          ],
          [
            -0.036072026293296755,
            1.1102230246251565e-15,
            -0.008148328296644747
          ],
          [
            -0.02709265261649968,
            -5.495603971894525e-15,
            -0.006206188632342846
          ],
          [
            -0.01811993979937021,
            9.992007221626409e-16,
            -0.0042777439165918585
          ],
          [
            -0.009156114982088903,
            4.551914400963142e-15,
            -0.002363672548153062
          ],
          [
            -0.0002034804054115713,
            -1.7763568394002505e-15,
            -0.00046465318157745683
          ],
          [
            0.008441663356548612,
            2.3314683517128287e-15,
            0.0015132335398736485
          ],
          [
            0.01709235134039,
            -9.43689570931383e-16,
            0.003487702555562411
          ],
          [
            0.025746656270236645,
            -7.327471962526033e-15,
            0.005458286699320247
          ],
          [
            0.03440262580954401,
            -1.8318679906315083e-15,
            0.007424518612385356
          ],
          [
            0.04305828017974178,
            -1.9984014443252818e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4424906541753444e-15,
            0.011342058682160316
          ],
          [
            0.06036059309230091,
            -1.1102230246251565e-16,
            0.013292434229610683
          ],
          [
            0.06900316386126315,
            -2.4424906541753444e-15,
            0.015236592110928204
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076204,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "target_residual": 0.42828631965988545,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00838586274507613,
            "step_scale": 0.871592656041644,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0061231611173034,
              1.0014653527466788,
              0.9879960690070786
            ],
            "cell_volume_ratio": 0.9955023557588971,
            "cell_rmsd_from_input_A": 0.08693931710426953
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4320756033778894,
              -1.4186210407034167e-14,
              -0.0102492873134321
            ],
            "branch_aligned_reduced_polarization": [
              -0.4320756033778894,
              -1.4186210407034167e-14,
              -0.0102492873134321
            ],
            "target_residual": 0.06869331515446804,
            "energy_eV": -76.39369279251329,
            "max_atomic_step_A": 0.022935195569123247,
            "max_log_strain_component": 0.0017522736293702564,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0076740239748674,
              1.0017161398422,
              0.9853525841791899
            ],
            "cell_volume_ratio": 0.9946181831584495,
            "cell_rmsd_from_input_A": 0.10663269749329318
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5001898587209052,
              5.0408720112694545e-15,
              -0.0014738768518117273
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001898587209052,
              5.0408720112694545e-15,
              -0.0014738768518117273
            ],
            "target_residual": 0.0014860549479108066,
            "energy_eV": -75.89326742929026,
            "max_atomic_step_A": 0.0004725712531204191,
            "max_log_strain_component": 1.9813064977727607e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0076975393675767,
              1.0017047428939236,
              0.9853587862706119
            ],
            "cell_volume_ratio": 0.9946363379067427,
            "cell_rmsd_from_input_A": 0.10667365713260861
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000010414601078,
              3.672335350762183e-15,
              2.391331956514828e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000010414601078,
              3.672335350762183e-15,
              2.391331956514828e-06
            ],
            "target_residual": 2.6082767649215766e-06,
            "energy_eV": -75.89640250580251
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.6082767649215766e-06,
        "parent_symmetrization_rmsd_A": 0.1411224326430634,
        "parent_cell_rmsd_A": 0.10667365713260861,
        "energy_eV": -75.89640250580251,
        "reduced_polarization": [
          -0.5000010414601078,
          3.672335350762183e-15,
          2.391331956514828e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.017696081584672608,
          2.627570543269835e-16,
          0.00016173379920747717
        ],
        "ranking_score": 0.6677960634797454
      },
      "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": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.016040315377752856
            ],
            "target_residual": 0.48928827440560924,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005797658672377284,
            "step_scale": 0.8723596967604506,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.002861883572812,
              1.0025097097561557,
              0.9912857556225366
            ],
            "cell_volume_ratio": 0.9966176594816282,
            "cell_rmsd_from_input_A": 0.060294358478356756
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0016687006448920273,
              -4.635222952955929e-15,
              -0.43436205491254015
            ],
            "branch_aligned_reduced_polarization": [
              -0.0016687006448920273,
              -4.635222952955929e-15,
              -0.43436205491254015
            ],
            "target_residual": 0.0656591531863354,
            "energy_eV": -76.12187408017044,
            "max_atomic_step_A": 0.019531180509136624,
            "max_log_strain_component": 0.0007735266072054557,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0030419779706794,
              1.0029806211690424,
              0.9899406391432045
            ],
            "cell_volume_ratio": 0.9959116305607556,
            "cell_rmsd_from_input_A": 0.06904735063840886
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00022169392596863596,
              -3.675859457125333e-15,
              -0.4990501658177995
            ],
            "branch_aligned_reduced_polarization": [
              0.00022169392596863596,
              -3.675859457125333e-15,
              -0.4990501658177995
            ],
            "target_residual": 0.0009753630967429045,
            "energy_eV": -75.67963773302084
          }
        ],
        "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": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0009753630967429045,
        "parent_symmetrization_rmsd_A": 0.1282926021927975,
        "parent_cell_rmsd_A": 0.06904735063840886,
        "energy_eV": -75.67963773302084,
        "reduced_polarization": [
          0.00022169392596863596,
          -3.675859457125333e-15,
          -0.4990501658177995
        ],
        "cartesian_polarization_e_A2": [
          7.386686624475406e-05,
          5.77314907056036e-17,
          -0.01796068644265187
        ],
        "ranking_score": 0.6475051660458855
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076202,
              0.0,
              -0.01604031537775283
            ],
            "target_residual": 0.5054140192441952,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.05700763136250067,
            "max_log_strain_component": 0.0018003717684595155,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.003170577609936,
              0.999851532229956,
              0.9980401914291324
            ],
            "cell_volume_ratio": 1.0010559087062083,
            "cell_rmsd_from_input_A": 0.017751106990758558
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0010472912045397084,
              0.4995947562041517,
              -0.0007913886679203695
            ],
            "branch_aligned_reduced_polarization": [
              0.0010472912045397084,
              0.4995947562041517,
              -0.0007913886679203695
            ],
            "target_residual": 0.0013738039979897165,
            "energy_eV": -77.09745206126792,
            "max_atomic_step_A": 0.0003629822589354623,
            "max_log_strain_component": 2.8857947331413264e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0031440553989943,
              0.9998679596469021,
              0.9980448980441854
            ],
            "cell_volume_ratio": 1.001050609963035,
            "cell_rmsd_from_input_A": 0.017508619165499693
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.900622290176854e-06,
              0.4999979708642079,
              2.0590693365346265e-06
            ],
            "branch_aligned_reduced_polarization": [
              4.900622290176854e-06,
              0.4999979708642079,
              2.0590693365346265e-06
            ],
            "target_residual": 5.689750207739758e-06,
            "energy_eV": -77.09788357012637
          }
        ],
        "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": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 5.689750207739758e-06,
        "parent_symmetrization_rmsd_A": 0.0562363026155349,
        "parent_cell_rmsd_A": 0.017508619165499693,
        "energy_eV": -77.09788357012637,
        "reduced_polarization": [
          4.900622290176854e-06,
          0.4999979708642079,
          2.0590693365346265e-06
        ],
        "cartesian_polarization_e_A2": [
          -7.76264814962131e-06,
          0.007208099033493826,
          -1.1385328802117793e-05
        ],
        "ranking_score": 0.5606248369073253
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076204,
              -1.6525305734054318e-18,
              -0.016040315377752856
            ],
            "target_residual": 0.6460563878099626,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00867252295009653,
            "step_scale": 0.5996328981877703,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0029779404534436,
              0.9999975730066587,
              0.9910066753189998
            ],
            "cell_volume_ratio": 0.9939554218580193,
            "cell_rmsd_from_input_A": 0.05772746848335662
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.31327436270692227,
              -1.9358286896956043e-14,
              -0.30312752149028743
            ],
            "branch_aligned_reduced_polarization": [
              -0.31327436270692227,
              -1.9358286896956043e-14,
              -0.30312752149028743
            ],
            "target_residual": 0.2713397066723985,
            "energy_eV": -76.37168919393073,
            "max_atomic_step_A": 0.09497522694044311,
            "max_log_strain_component": 0.007437398762623916,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0054192826816308,
              1.00041303284687,
              0.9831772978561704
            ],
            "cell_volume_ratio": 0.9889136987645243,
            "cell_rmsd_from_input_A": 0.10756424102809146
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49606950461217053,
              -1.5319070419324358e-14,
              -0.48985968459157014
            ],
            "branch_aligned_reduced_polarization": [
              -0.49606950461217053,
              -1.5319070419324358e-14,
              -0.48985968459157014
            ],
            "target_residual": 0.010875421397637367,
            "energy_eV": -73.53202298404489,
            "max_atomic_step_A": 0.004194278465308932,
            "max_log_strain_component": 0.0002994725227093507,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0055435695383645,
              1.0003381032385963,
              0.982903851376672
            ],
            "cell_volume_ratio": 0.9886868124572072,
            "cell_rmsd_from_input_A": 0.10929128435460045
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000706450219509,
              -1.3990614014876278e-15,
              -0.5000144121202265
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000706450219509,
              -1.3990614014876278e-15,
              -0.5000144121202265
            ],
            "target_residual": 7.210012715564537e-05,
            "energy_eV": -73.36774945559479
          }
        ],
        "iterations": 3
      },
      "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": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.210012715564537e-05,
        "parent_symmetrization_rmsd_A": 0.22155572140932375,
        "parent_cell_rmsd_A": 0.10929128435460045,
        "energy_eV": -73.36774945559479,
        "reduced_polarization": [
          -0.5000706450219509,
          -1.3990614014876278e-15,
          -0.5000144121202265
        ],
        "cartesian_polarization_e_A2": [
          -0.017441999179045403,
          5.365285137654387e-16,
          -0.01812051498393735
        ],
        "ranking_score": 0.7490227427522851
      },
      "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": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076204,
              0.0,
              -0.01604031537775283
            ],
            "target_residual": 0.6583533789750073,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.007848653233802398,
            "step_scale": 0.8157572722516158,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0058604352710905,
              1.00139110384629,
              0.988612849034841
            ],
            "cell_volume_ratio": 0.9957898734221557,
            "cell_rmsd_from_input_A": 0.08161087234179809
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.40796803115125996,
              0.39189392819030294,
              -0.00998653228874917
            ],
            "branch_aligned_reduced_polarization": [
              -0.40796803115125996,
              0.39189392819030294,
              -0.00998653228874917
            ],
            "target_residual": 0.14232546110746688,
            "energy_eV": -76.43620053950448,
            "max_atomic_step_A": 0.03282376716479097,
            "max_log_strain_component": 0.002462875547999095,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0079529030193246,
              1.0017869540883029,
              0.9849154599380185
            ],
            "cell_volume_ratio": 0.9945223928799448,
            "cell_rmsd_from_input_A": 0.10857249381210665
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49919968675451226,
              0.49498605434182524,
              -0.002130912677108087
            ],
            "branch_aligned_reduced_polarization": [
              -0.49919968675451226,
              0.49498605434182524,
              -0.002130912677108087
            ],
            "target_residual": 0.0055064454225473404,
            "energy_eV": -75.72467123711633,
            "max_atomic_step_A": 0.0009119072367284566,
            "max_log_strain_component": 5.356782630444347e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.008016629803829,
              1.0017794396718398,
              0.9848678063422723
            ],
            "cell_volume_ratio": 0.9945296890442645,
            "cell_rmsd_from_input_A": 0.10901905266292207
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000176835577773,
              0.49998818932371014,
              -1.3880049372426277e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000176835577773,
              0.49998818932371014,
              -1.3880049372426277e-05
            ],
            "target_residual": 2.5394016237461324e-05,
            "energy_eV": -75.71555218885943
          }
        ],
        "iterations": 3
      },
      "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": 2.5394016237461324e-05,
        "parent_symmetrization_rmsd_A": 0.1533223631904325,
        "parent_cell_rmsd_A": 0.10901905266292207,
        "energy_eV": -75.71555218885943,
        "reduced_polarization": [
          -0.5000176835577773,
          0.49998818932371014,
          -1.3880049372426277e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.01770374169146875,
          0.007292204121606349,
          0.0001516020197127856
        ],
        "ranking_score": 0.680627914388638
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076202,
              0.0,
              -0.016040315377752856
            ],
            "target_residual": 0.6995734525200472,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00560640946236373,
            "step_scale": 0.8435828900732787,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.004209462846777,
              1.0009976427006089,
              0.9915617205056582
            ],
            "cell_volume_ratio": 0.99672905114407,
            "cell_rmsd_from_input_A": 0.05864110744965236
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0035794030992813966,
              0.40704318960165153,
              -0.41884777798132855
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035794030992813966,
              0.40704318960165153,
              -0.41884777798132855
            ],
            "target_residual": 0.1234482234159301,
            "energy_eV": -76.10544944180711,
            "max_atomic_step_A": 0.026524174058635833,
            "max_log_strain_component": 0.0010063667416068667,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.005066811332963,
              1.000999564075493,
              0.9898339682908205
            ],
            "cell_volume_ratio": 0.9958436858501896,
            "cell_rmsd_from_input_A": 0.07004907382469569
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0003549981467652832,
              0.4967789490679799,
              -0.4980694489841977
            ],
            "branch_aligned_reduced_polarization": [
              0.0003549981467652832,
              0.4967789490679799,
              -0.4980694489841977
            ],
            "target_residual": 0.0037720312850624,
            "energy_eV": -75.51301834650695,
            "max_atomic_step_A": 0.0007620076498745208,
            "max_log_strain_component": 3.429994366116417e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0050890479811945,
              1.0009886861608543,
              0.9897932354247164
            ],
            "cell_volume_ratio": 0.9958139156814941,
            "cell_rmsd_from_input_A": 0.07029705128792
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -8.233000819756323e-07,
              0.4999800679778474,
              -0.49999281193372536
            ],
            "branch_aligned_reduced_polarization": [
              -8.233000819756323e-07,
              0.4999800679778474,
              -0.49999281193372536
            ],
            "target_residual": 2.1204519020386235e-05,
            "energy_eV": -75.49689610633078
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.1204519020386235e-05,
        "parent_symmetrization_rmsd_A": 0.1407195564536842,
        "parent_cell_rmsd_A": 0.07029705128792,
        "energy_eV": -75.49689610633078,
        "reduced_polarization": [
          -8.233000819756323e-07,
          0.4999800679778474,
          -0.49999281193372536
        ],
        "cartesian_polarization_e_A2": [
          5.6365642201484414e-05,
          0.007301517834387215,
          -0.018008082921827765
        ],
        "ranking_score": 0.658336228313705
      },
      "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": [
              -0.07201415924076202,
              -1.6525305734054318e-18,
              -0.01604031537775283
            ],
            "branch_aligned_reduced_polarization": [
              -0.07201415924076204,
              0.0,
              -0.016040315377752856
            ],
            "target_residual": 0.8169387102041724,
            "energy_eV": -77.3424731191894,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008452902490726319,
            "step_scale": 0.584447968345413,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0031521891194475,
              0.9998053553780306,
              0.9911771986334732
            ],
            "cell_volume_ratio": 0.9941080411599459,
            "cell_rmsd_from_input_A": 0.0564300113881072
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.30685406235913426,
              0.27816793525231226,
              -0.2952611441088062
            ],
            "branch_aligned_reduced_polarization": [
              -0.30685406235913426,
              0.27816793525231226,
              -0.2952611441088062
            ],
            "target_residual": 0.3583752464791989,
            "energy_eV": -76.38750559241468,
            "max_atomic_step_A": 0.10279880734270902,
            "max_log_strain_component": 0.0078033171600113815,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0060065724513199,
              1.0000021032204536,
              0.9829069839414364
            ],
            "cell_volume_ratio": 0.9888129656406691,
            "cell_rmsd_from_input_A": 0.10882149067941208
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49396455031118475,
              0.45914547616312007,
              -0.4868965737438453
            ],
            "branch_aligned_reduced_polarization": [
              -0.49396455031118475,
              0.45914547616312007,
              -0.4868965737438453
            ],
            "target_residual": 0.04332688023080931,
            "energy_eV": -73.43359263524798,
            "max_atomic_step_A": 0.008818118384131048,
            "max_log_strain_component": 0.0005057926622196165,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.006305604927368,
              0.9998401459116365,
              0.982403609422848
            ],
            "cell_volume_ratio": 0.9884402269897248,
            "cell_rmsd_from_input_A": 0.11191585413001359
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000763697760636,
              0.49900584306190493,
              -0.49989601290716146
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000763697760636,
              0.49900584306190493,
              -0.49989601290716146
            ],
            "target_residual": 0.0010024937285268093,
            "energy_eV": -73.18473661491757,
            "max_atomic_step_A": 0.00014012543328224475,
            "max_log_strain_component": 4.747257022048406e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.11727785776527,
            "cell_principal_stretches": [
              1.0063093093035094,
              0.9998356183527652,
              0.9824028139567642
            ],
            "cell_volume_ratio": 0.9884385892938446,
            "cell_rmsd_from_input_A": 0.11191853031992394
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999968005756498,
              0.49998952535852026,
              -0.4999982235825476
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999968005756498,
              0.49998952535852026,
              -0.4999982235825476
            ],
            "target_residual": 1.1095498603796268e-05,
            "energy_eV": -73.18423356077015
          }
        ],
        "iterations": 4
      },
      "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": 1.1095498603796268e-05,
        "parent_symmetrization_rmsd_A": 0.23365947111578592,
        "parent_cell_rmsd_A": 0.11191853031992394,
        "energy_eV": -73.18423356077015,
        "reduced_polarization": [
          -0.4999968005756498,
          0.49998952535852026,
          -0.4999982235825476
        ],
        "cartesian_polarization_e_A2": [
          -0.01744701666853948,
          0.007407423416286933,
          -0.01813832882287358
        ],
        "ranking_score": 0.7616612946929745
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_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
        ],
        "endpoint_rmsd_A": 0.023725508816638062,
        "minimum_distance_A_by_image": [
          1.9208774279917722,
          1.9206559153174445,
          1.9204429679898443,
          1.9202386069028199,
          1.920042850561709,
          1.919855717383014,
          1.9196772256935422,
          1.9195073937295621,
          1.9193462396359486
        ],
        "minimum_distance_A": 1.9193462396359486,
        "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": [
          232.68357191057783,
          232.71426930858382,
          232.74497075642535,
          232.7756762546369,
          232.80638580375302,
          232.83709940430754,
          232.86781705683578,
          232.89853876187166,
          232.92926451995007
        ],
        "cell_deformation_log_strain_norm": 0.0025376114069921296
      },
      "parent_reduced_polarization": [
        -0.00020348040541159296,
        -1.7849284126515566e-15,
        -0.00046465318157744447
      ],
      "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": [
          -77.3424731191894,
          -77.34094818788772,
          -77.3385635487317,
          -77.33533854869714,
          -77.33129198713058,
          -77.32644215047945,
          -77.32080682615856,
          -77.31440331440564,
          -77.30724843888245
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.002554825655802454,
            1.4212032635460783e-17,
            -0.0005770990741367024
          ],
          [
            -0.00223634048320274,
            -6.404869261915035e-17,
            -0.0005057464574739926
          ],
          [
            -0.001917716218896982,
            -1.6650301039863252e-17,
            -0.00043471790597315163
          ],
          [
            -0.0015990219737325622,
            4.069964689707137e-18,
            -0.0003640375202547422
          ],
          [
            -0.0012803290796893185,
            1.4420347487409368e-17,
            -0.000293729322151123
          ],
          [
            -0.0009617114730414046,
            -8.034768857452874e-17,
            -0.00022381745401784653
          ],
          [
            -0.0006432457455470893,
            1.3702480573401277e-17,
            -0.00015432615607741682
          ],
          [
            -0.00032501117941963214,
            6.511796184400416e-17,
            -8.527973774463014e-05
          ],
          [
            -7.089773485540193e-06,
            -2.5781924217822234e-17,
            -1.670255165309543e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107755e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425327e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159296,
            -1.7849284126515566e-15,
            -0.00046465318157744447
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107745e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425323e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159212,
            -1.784928412651557e-15,
            -0.00046465318157744447
          ]
        ],
        "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": [
          [
            -0.0720141592407631,
            9.992007221626409e-16,
            -0.016040315377754077
          ],
          [
            -0.06302895112082291,
            -4.385380947269368e-15,
            -0.014050153452692005
          ],
          [
            -0.05404221876998583,
            -1.0547118733938987e-15,
            -0.012070984899717196
          ],
          [
            -0.045055908098272146,
            3.3306690738754696e-16,
            -0.01010348554505286
          ],
          [
            -0.036072026293296755,
            1.1102230246251565e-15,
            -0.008148328296644747
          ],
          [
            -0.02709265261649968,
            -5.495603971894525e-15,
            -0.006206188632342846
          ],
          [
            -0.01811993979937021,
            9.992007221626409e-16,
            -0.0042777439165918585
          ],
          [
            -0.009156114982088903,
            4.551914400963142e-15,
            -0.002363672548153062
          ],
          [
            -0.0002034804054115713,
            -1.7763568394002505e-15,
            -0.00046465318157745683
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -77.30724843888245,
          -77.30013798282408,
          -77.29237737096597,
          -77.28397211176343,
          -77.27492722227149,
          -77.26524728121487,
          -77.2549364956794,
          -77.24399870513602,
          -77.23243738488156
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.0897734856361155e-06,
            -3.221811876748882e-17,
            -1.670255165315127e-05
          ],
          [
            0.000299870783677393,
            3.475245678405e-17,
            5.4693399435634484e-05
          ],
          [
            0.0006069510201188584,
            -1.2790593535740207e-17,
            0.00012589889265176164
          ],
          [
            0.0009140825583361333,
            -1.0424893531703348e-16,
            0.000196896929367497
          ],
          [
            0.0012211961651288098,
            -2.508983466897549e-17,
            0.00026767053300126044
          ],
          [
            0.0015282216670575413,
            -2.7194075507933902e-17,
            0.0003382027742070659
          ],
          [
            0.001835087986474158,
            -3.41538844871362e-17,
            0.00040847676870517055
          ],
          [
            0.002141723177596794,
            -1.3936675018070558e-18,
            0.0004784756744314168
          ],
          [
            0.0024480544620079057,
            -3.558878432304152e-17,
            0.0005481826880043832
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.0002034804054143027,
            -2.231385171730259e-15,
            -0.00046465318157899553
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0002034804054143027,
            -2.231385171730259e-15,
            -0.00046465318157899553
          ],
          [
            0.008441663356548605,
            2.3717489698609172e-15,
            0.0015132335398736268
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.07160577506154543,
          -4.555986648798944e-15,
          0.01511182941014215
        ],
        "actual_opposite_endpoint_branch_residual": 0.002605599890877764
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107755e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425327e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159296,
            -1.7849284126515566e-15,
            -0.00046465318157744447
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.003487702555562451
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.0720141592407631,
            9.84400815086888e-16,
            -0.016040315377754064
          ],
          [
            -0.06302895112082291,
            -4.394194673249422e-15,
            -0.014050153452692019
          ],
          [
            -0.054042218769985835,
            -1.079977006332605e-15,
            -0.012070984899717193
          ],
          [
            -0.045055908098272146,
            3.7437414997107745e-16,
            -0.010103485545052852
          ],
          [
            -0.03607202629329678,
            1.0982917885372574e-15,
            -0.00814832829664477
          ],
          [
            -0.02709265261649967,
            -5.477368242029309e-15,
            -0.0062061886323428635
          ],
          [
            -0.01811993979937021,
            1.0253696873425323e-15,
            -0.0042777439165918385
          ],
          [
            -0.009156114982088901,
            4.561560472398556e-15,
            -0.0023636725481530397
          ],
          [
            -0.00020348040541159212,
            -1.784928412651557e-15,
            -0.00046465318157744447
          ],
          [
            0.008441663356548605,
            2.371748969860917e-15,
            0.0015132335398736266
          ],
          [
            0.017092351340389996,
            -9.555016069503236e-16,
            0.0034877025555624516
          ],
          [
            0.02574665627023663,
            -7.314246036588333e-15,
            0.00545828669932024
          ],
          [
            0.03440262580954405,
            -1.8322869828670812e-15,
            0.007424518612385307
          ],
          [
            0.04305828017974178,
            -1.9722740436304523e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4367955462589168e-15,
            0.011342058682160332
          ],
          [
            0.06036059309230092,
            -1.3758178446228424e-16,
            0.01329243422961064
          ],
          [
            0.06900316386126315,
            -2.465068100683943e-15,
            0.015236592110928234
          ]
        ],
        "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": [
          [
            -0.0720141592407631,
            9.992007221626409e-16,
            -0.016040315377754077
          ],
          [
            -0.06302895112082291,
            -4.385380947269368e-15,
            -0.014050153452692005
          ],
          [
            -0.05404221876998583,
            -1.0547118733938987e-15,
            -0.012070984899717196
          ],
          [
            -0.045055908098272146,
            3.3306690738754696e-16,
            -0.01010348554505286
          ],
          [
            -0.036072026293296755,
            1.1102230246251565e-15,
            -0.008148328296644747
          ],
          [
            -0.02709265261649968,
            -5.495603971894525e-15,
            -0.006206188632342846
          ],
          [
            -0.01811993979937021,
            9.992007221626409e-16,
            -0.0042777439165918585
          ],
          [
            -0.009156114982088903,
            4.551914400963142e-15,
            -0.002363672548153062
          ],
          [
            -0.0002034804054115713,
            -1.7763568394002505e-15,
            -0.00046465318157745683
          ],
          [
            0.008441663356548612,
            2.3314683517128287e-15,
            0.0015132335398736485
          ],
          [
            0.01709235134039,
            -9.43689570931383e-16,
            0.003487702555562411
          ],
          [
            0.025746656270236645,
            -7.327471962526033e-15,
            0.005458286699320247
          ],
          [
            0.03440262580954401,
            -1.8318679906315083e-15,
            0.007424518612385356
          ],
          [
            0.04305828017974178,
            -1.9984014443252818e-15,
            0.00938593142645272
          ],
          [
            0.051711613160620895,
            -2.4424906541753444e-15,
            0.011342058682160316
          ],
          [
            0.06036059309230091,
            -1.1102230246251565e-16,
            0.013292434229610683
          ],
          [
            0.06900316386126315,
            -2.4424906541753444e-15,
            0.015236592110928204
          ]
        ]
      },
      "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": "bec_projection_00",
        "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": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0005072542306746767,
        "parent_symmetrization_rmsd_A": 0.023725508816638062,
        "parent_cell_rmsd_A": 0.01621691113235258,
        "energy_eV": -77.30724843888245,
        "reduced_polarization": [
          -0.00020348040541342898,
          -3.906078845733642e-15,
          -0.00046465318157755533
        ],
        "cartesian_polarization_e_A2": [
          -7.089773485605492e-06,
          -5.636078001697625e-17,
          -1.6702551653099497e-05
        ],
        "ranking_score": 0.5287942450610755
      }
    }
  ],
  "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": 57,
      "full_response": 22,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 82,
      "full_response": 47,
      "energy_polarization": 35
    },
    "elapsed_seconds": 400.59104181604926
  }
}