{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 44,
  "input_formula": "Ba8K16P16Sn4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -156.84652498446616,
  "input_cartesian_polarization_e_A2": [
    0.001388147596486408,
    1.3207302319238163e-12,
    -0.0001630202184864349
  ],
  "input_reduced_polarization": [
    0.19593486614582845,
    1.0887052249621108e-10,
    -0.030616640463299177
  ],
  "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": "C2/c",
      "spacegroup_number": 15,
      "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": 7.475749875444855e-15,
      "parent_symmetrization_rmsd_A": 0.677122839129039,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -150.98371829422484,
      "reduced_polarization": [
        -6.1956552748393716e-15,
        4.1071193352179415e-15,
        7.951494713874782e-16
      ],
      "cartesian_polarization_e_A2": [
        -4.386864865167258e-17,
        4.9824291716152656e-17,
        4.2338231299526385e-18
      ],
      "ranking_score": 0.677122839129054
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.776612915260102e-07,
      "parent_symmetrization_rmsd_A": 0.02596700695669423,
      "parent_cell_rmsd_A": 0.021775571312999294,
      "energy_eV": -156.69822951272272,
      "reduced_polarization": [
        -6.349414121092905e-07,
        -1.1641750822379349e-15,
        2.3679997724104676e-07
      ],
      "cartesian_polarization_e_A2": [
        -4.507140608593471e-09,
        -1.4050878340539603e-17,
        1.2699687815877908e-09
      ],
      "ranking_score": 0.5314122551075271
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 1.140702876058722e-14,
      "parent_symmetrization_rmsd_A": 0.6771256037459801,
      "parent_cell_rmsd_A": 0.021775571312999294,
      "energy_eV": -150.88793477405008,
      "reduced_polarization": [
        -1.0964392792359899e-14,
        2.921600565194145e-15,
        -1.1690363455289082e-15
      ],
      "cartesian_polarization_e_A2": [
        -7.697401478543533e-17,
        3.530213208566847e-17,
        -6.019134717109333e-18
      ],
      "ranking_score": 0.6825694965742527
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.4453886505218697e-06,
      "parent_symmetrization_rmsd_A": 0.04019975953802334,
      "parent_cell_rmsd_A": 0.020243873228331967,
      "energy_eV": -156.77426656405444,
      "reduced_polarization": [
        0.4999975561190285,
        1.6759035242037586e-14,
        8.585714492053339e-08
      ],
      "cartesian_polarization_e_A2": [
        0.0035395713825506006,
        4.422492802332981e-14,
        9.11291097635536e-06
      ],
      "ranking_score": 0.5452656186224074
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.283352157577134e-07,
      "parent_symmetrization_rmsd_A": 0.042792379051772404,
      "parent_cell_rmsd_A": 0.07691837581441668,
      "energy_eV": -156.9538854553589,
      "reduced_polarization": [
        2.6169030172709466e-07,
        -1.8591424002745847e-14,
        -0.4999996608993615
      ],
      "cartesian_polarization_e_A2": [
        5.963948828933068e-05,
        -4.16166225319608e-14,
        -0.0026731074905522456
      ],
      "ranking_score": 0.5620228296758081
    },
    {
      "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": 0.0008946184383042656,
      "parent_symmetrization_rmsd_A": 0.10697048251456887,
      "parent_cell_rmsd_A": 0.11551976466024487,
      "energy_eV": -155.74503814410733,
      "reduced_polarization": [
        -0.00011079166100323563,
        0.4998167976770577,
        -0.0008686220506495681
      ],
      "cartesian_polarization_e_A2": [
        -2.3270710966542755e-05,
        0.006036821112615749,
        5.2494674468250574e-05
      ],
      "ranking_score": 0.6376396605562387
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.1724075622174866e-05,
      "parent_symmetrization_rmsd_A": 0.05768918896769962,
      "parent_cell_rmsd_A": 0.11134567551620461,
      "energy_eV": -156.8491677511333,
      "reduced_polarization": [
        0.5000248698510875,
        -3.196930192050081e-13,
        -0.5000196953669924
      ],
      "cartesian_polarization_e_A2": [
        0.0036464360768214965,
        -9.40205496312337e-14,
        -0.002642754975828475
      ],
      "ranking_score": 0.5855890559979952
    },
    {
      "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": 4.9052259459671715e-06,
      "parent_symmetrization_rmsd_A": 0.11204617842127018,
      "parent_cell_rmsd_A": 0.11231500681918431,
      "energy_eV": -155.74065867527992,
      "reduced_polarization": [
        0.5000016807612452,
        0.4999959800029423,
        -2.2529773354219337e-06
      ],
      "cartesian_polarization_e_A2": [
        0.003515422777201143,
        0.006074082903663773,
        6.546625413032716e-05
      ],
      "ranking_score": 0.6401347405779582
    },
    {
      "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": 5.010934086277358e-06,
      "parent_symmetrization_rmsd_A": 0.1105092258581315,
      "parent_cell_rmsd_A": 0.12878312991613103,
      "energy_eV": -155.85877962589763,
      "reduced_polarization": [
        1.7870050491023363e-07,
        0.4999952558458515,
        -0.4999983967133874
      ],
      "cartesian_polarization_e_A2": [
        3.8412278353034365e-05,
        0.006103198172184957,
        -0.0026163570085051316
      ],
      "ranking_score": 0.6427150302053368
    },
    {
      "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": 1.712315790585999e-05,
      "parent_symmetrization_rmsd_A": 0.11753588387235878,
      "parent_cell_rmsd_A": 0.1493559730113648,
      "energy_eV": -155.68421543721334,
      "reduced_polarization": [
        0.5000106382276598,
        0.49998799984389214,
        -0.4999939977585591
      ],
      "cartesian_polarization_e_A2": [
        0.003622338329495865,
        0.006137070935971934,
        -0.002587423106528599
      ],
      "ranking_score": 0.6549091234410117
    }
  ],
  "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "target_residual": 0.1983125070308039,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.032846754517045156,
            "max_log_strain_component": 0.0027502507163309252,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.004625733842802,
              1.0005806000277266,
              0.9993472903359911
            ],
            "cell_volume_ratio": 1.0045529099303017,
            "cell_rmsd_from_input_A": 0.021721421829114615
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0009366395179066637,
              -7.1195709188212975e-12,
              -0.0007188621890175523
            ],
            "branch_aligned_reduced_polarization": [
              -0.0009366395179066637,
              -7.1195709188212975e-12,
              -0.0007188621890175523
            ],
            "target_residual": 0.0011807016698995281,
            "energy_eV": -156.6981380408468,
            "max_atomic_step_A": 0.00015564739870217771,
            "max_log_strain_component": 9.251126016040283e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0046337798354597,
              1.0005848977053853,
              0.999346140138893
            ],
            "cell_volume_ratio": 1.00456411391101,
            "cell_rmsd_from_input_A": 0.021775571312999294
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.349414121092905e-07,
              -1.1641750822379349e-15,
              2.3679997724104676e-07
            ],
            "branch_aligned_reduced_polarization": [
              -6.349414121092905e-07,
              -1.1641750822379349e-15,
              2.3679997724104676e-07
            ],
            "target_residual": 6.776612915260102e-07,
            "energy_eV": -156.69822951272272
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.776612915260102e-07,
        "parent_symmetrization_rmsd_A": 0.02596700695669423,
        "parent_cell_rmsd_A": 0.021775571312999294,
        "energy_eV": -156.69822951272272,
        "reduced_polarization": [
          -6.349414121092905e-07,
          -1.1641750822379349e-15,
          2.3679997724104676e-07
        ],
        "cartesian_polarization_e_A2": [
          -4.507140608593471e-09,
          -1.4050878340539603e-17,
          1.2699687815877908e-09
        ],
        "ranking_score": 0.5314122551075271
      },
      "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": [
          -156.84652498446616,
          -156.83449493457914,
          -156.82057201050577,
          -156.80477428417294,
          -156.78711884716662,
          -156.76762185725238,
          -156.74629856454752,
          -156.72316330823747,
          -156.69822951272272
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013881475964863995,
            1.3207254730291361e-12,
            -0.0001630202184864293
          ],
          [
            0.0012150729023583998,
            1.164149547295022e-12,
            -0.00014297271741197027
          ],
          [
            0.0010418636344349615,
            1.0062109975776395e-12,
            -0.00012282561350488732
          ],
          [
            0.0008685218370722158,
            8.466175761333406e-13,
            -0.00010258092162033735
          ],
          [
            0.0006950509027515224,
            6.846660540387458e-13,
            -8.224099397094854e-05
          ],
          [
            0.0005214557734080536,
            5.196719677728917e-13,
            -6.18088391638771e-05
          ],
          [
            0.00034774274213730257,
            3.5107514912536665e-13,
            -4.128808995313768e-05
          ],
          [
            0.00017391955069570987,
            1.7809740974495525e-13,
            -2.068304759933241e-05
          ],
          [
            -4.507140543330593e-09,
            2.4414100861624837e-17,
            1.269968794449103e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027792663e-07,
            2.0191823621667202e-15,
            2.3679997969185466e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027780054e-07,
            2.019182362165899e-15,
            2.3679997969167782e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.19593486614582734,
            1.0887013512927979e-10,
            -0.03061664046329815
          ],
          [
            0.17157150589782977,
            9.604972373011833e-11,
            -0.026785597383854165
          ],
          [
            0.14717040791023273,
            8.30929769435329e-11,
            -0.02295463246355056
          ],
          [
            0.12273182412590944,
            6.997569190758668e-11,
            -0.01912415338562984
          ],
          [
            0.09825619642060035,
            5.6639470891184374e-11,
            -0.015294630813861454
          ],
          [
            0.07374418416118456,
            4.302747047546518e-11,
            -0.011466657988933093
          ],
          [
            0.04919663651009176,
            2.9092950271092377e-11,
            -0.007640944412267425
          ],
          [
            0.02461460635171253,
            1.4770962231125395e-11,
            -0.0038183238790973073
          ],
          [
            -6.349414027884137e-07,
            1.9984014443252818e-15,
            2.3679997973591327e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -156.6982295127227,
          -156.70104417600857,
          -156.7019929272167,
          -156.70106684528102,
          -156.69825661738807,
          -156.69355255739032,
          -156.68694462590605,
          -156.67842245236193,
          -156.66797535914725
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.507140607618493e-09,
            1.704811915521314e-17,
            1.269968761388487e-09
          ],
          [
            -0.00016939892255434143,
            -1.7512459171655377e-13,
            4.8301274094479054e-06
          ],
          [
            -0.00033903185067286185,
            -3.5553947446842293e-13,
            9.465889011305659e-06
          ],
          [
            -0.0005088923740376327,
            -5.416948431954178e-13,
            1.390822025403823e-05
          ],
          [
            -0.0006789695983587696,
            -7.339202255150784e-13,
            1.815671574597667e-05
          ],
          [
            -0.0008492526869991304,
            -9.328123880513237e-13,
            2.2210898929439426e-05
          ],
          [
            -0.0010197308864213096,
            -1.1386660038915265e-12,
            2.6070224940806632e-05
          ],
          [
            -0.001190393541056403,
            -1.3520807394752662e-12,
            2.973408733281617e-05
          ],
          [
            -0.0013612300963921134,
            -1.5733081218703012e-12,
            3.320182868661484e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.349414120587448e-07,
            1.4095745270137338e-15,
            2.3679997344107685e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.349414120587448e-07,
            1.4095745270137338e-15,
            2.3679997344107685e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.1959361325850673,
          -1.0886610520110912e-10,
          0.03061711748606671
        ],
        "actual_opposite_endpoint_branch_residual": 0.024603174459125094
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027792663e-07,
            2.0191823621667202e-15,
            2.3679997969185466e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027780054e-07,
            2.019182362165899e-15,
            2.3679997969167782e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "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": [
          [
            0.19593486614582734,
            1.0887013512927979e-10,
            -0.03061664046329815
          ],
          [
            0.17157150589782977,
            9.604972373011833e-11,
            -0.026785597383854165
          ],
          [
            0.14717040791023273,
            8.30929769435329e-11,
            -0.02295463246355056
          ],
          [
            0.12273182412590944,
            6.997569190758668e-11,
            -0.01912415338562984
          ],
          [
            0.09825619642060035,
            5.6639470891184374e-11,
            -0.015294630813861454
          ],
          [
            0.07374418416118456,
            4.302747047546518e-11,
            -0.011466657988933093
          ],
          [
            0.04919663651009176,
            2.9092950271092377e-11,
            -0.007640944412267425
          ],
          [
            0.02461460635171253,
            1.4770962231125395e-11,
            -0.0038183238790973073
          ],
          [
            -6.349414027884137e-07,
            1.9984014443252818e-15,
            2.3679997973591327e-07
          ],
          [
            -0.024040829865080604,
            -1.4520995517131041e-11,
            0.0008381978474335527
          ],
          [
            -0.048095584151579995,
            -2.945499399942264e-11,
            0.0016594954637528803
          ],
          [
            -0.07216329970780594,
            -4.483863280668743e-11,
            0.0024641180040188004
          ],
          [
            -0.0962423846837917,
            -6.069839075806271e-11,
            0.003252037888087256
          ],
          [
            -0.12033125833620234,
            -7.708284011087585e-11,
            0.004023211565074347
          ],
          [
            -0.1444283545854919,
            -9.401546208209766e-11,
            0.004777580083953792
          ],
          [
            -0.16853212405038354,
            -1.1154493995135795e-10,
            0.005515070398560806
          ],
          [
            -0.19264103439500818,
            -1.2969103568849505e-10,
            0.006235597406629156
          ]
        ]
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "target_residual": 0.3056026575457324,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.049867286520589596,
            "max_log_strain_component": 0.0025634236394855405,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0006665258275254,
              0.9997362511849568,
              0.9955052800721337
            ],
            "cell_volume_ratio": 0.9959060717095056,
            "cell_rmsd_from_input_A": 0.020157192446462163
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49792289139187784,
              9.739726126859392e-12,
              -0.0005715236780594442
            ],
            "branch_aligned_reduced_polarization": [
              0.49792289139187784,
              9.739726126859392e-12,
              -0.0005715236780594442
            ],
            "target_residual": 0.002154302551759563,
            "energy_eV": -156.7759628807906,
            "max_atomic_step_A": 0.0003347795614967579,
            "max_log_strain_component": 1.1891005360056281e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0006698839858859,
              0.9997372650465585,
              0.9954855301622155
            ],
            "cell_volume_ratio": 0.9958906659252508,
            "cell_rmsd_from_input_A": 0.020243873228331967
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999975561190285,
              1.6759035242037586e-14,
              8.585714492053339e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.4999975561190285,
              1.6759035242037586e-14,
              8.585714492053339e-08
            ],
            "target_residual": 2.4453886505218697e-06,
            "energy_eV": -156.77426656405444
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.4453886505218697e-06,
        "parent_symmetrization_rmsd_A": 0.04019975953802334,
        "parent_cell_rmsd_A": 0.020243873228331967,
        "energy_eV": -156.77426656405444,
        "reduced_polarization": [
          0.4999975561190285,
          1.6759035242037586e-14,
          8.585714492053339e-08
        ],
        "cartesian_polarization_e_A2": [
          0.0035395713825506006,
          4.422492802332981e-14,
          9.11291097635536e-06
        ],
        "ranking_score": 0.5452656186224074
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.03061664046329915
            ],
            "target_residual": 0.5086366187972937,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.06003117311548142,
            "max_log_strain_component": 0.010119443919720791,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0022932401512445,
              0.9965101705692117,
              0.9869728513920918
            ],
            "cell_volume_ratio": 0.9857839514984355,
            "cell_rmsd_from_input_A": 0.07664885605942057
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0007273205557563607,
              1.4019595214503608e-11,
              -0.49836369614903014
            ],
            "branch_aligned_reduced_polarization": [
              0.0007273205557563607,
              1.4019595214503608e-11,
              -0.49836369614903014
            ],
            "target_residual": 0.0017906662122027437,
            "energy_eV": -156.95439210307705,
            "max_atomic_step_A": 0.00021741147551258743,
            "max_log_strain_component": 3.5811590804114324e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0023013831029526,
              0.9964977945178503,
              0.9869271647393004
            ],
            "cell_volume_ratio": 0.9857340859626851,
            "cell_rmsd_from_input_A": 0.07691837581441668
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.6169030172709466e-07,
              -1.8591424002745847e-14,
              -0.4999996608993615
            ],
            "branch_aligned_reduced_polarization": [
              2.6169030172709466e-07,
              -1.8591424002745847e-14,
              -0.4999996608993615
            ],
            "target_residual": 4.283352157577134e-07,
            "energy_eV": -156.9538854553589
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.283352157577134e-07,
        "parent_symmetrization_rmsd_A": 0.042792379051772404,
        "parent_cell_rmsd_A": 0.07691837581441668,
        "energy_eV": -156.9538854553589,
        "reduced_polarization": [
          2.6169030172709466e-07,
          -1.8591424002745847e-14,
          -0.4999996608993615
        ],
        "cartesian_polarization_e_A2": [
          5.963948828933068e-05,
          -4.16166225319608e-14,
          -0.0026731074905522456
        ],
        "ranking_score": 0.5620228296758081
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052370733841e-10,
              -0.030616640463299177
            ],
            "target_residual": 0.5378920433841461,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008570589724617182,
            "step_scale": 0.9020719601510994,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0116881198668513,
              0.9997399456658809,
              0.9927637862754816
            ],
            "cell_volume_ratio": 1.0041061383321375,
            "cell_rmsd_from_input_A": 0.10408438598597947
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.010757221491374046,
              0.45287092865267803,
              -0.019648878984380197
            ],
            "branch_aligned_reduced_polarization": [
              0.010757221491374046,
              0.45287092865267803,
              -0.019648878984380197
            ],
            "target_residual": 0.052181851496648356,
            "energy_eV": -155.94045630473045,
            "max_atomic_step_A": 0.013671800315695166,
            "max_log_strain_component": 0.0008711639771286873,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0133129192667287,
              0.9996208429804129,
              0.9923531092092237
            ],
            "cell_volume_ratio": 1.0051829593012662,
            "cell_rmsd_from_input_A": 0.11551976466024487
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00011079166100323563,
              0.4998167976770577,
              -0.0008686220506495681
            ],
            "branch_aligned_reduced_polarization": [
              -0.00011079166100323563,
              0.4998167976770577,
              -0.0008686220506495681
            ],
            "target_residual": 0.0008946184383042656,
            "energy_eV": -155.74503814410733
          }
        ],
        "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": 0.0008946184383042656,
        "parent_symmetrization_rmsd_A": 0.10697048251456887,
        "parent_cell_rmsd_A": 0.11551976466024487,
        "energy_eV": -155.74503814410733,
        "reduced_polarization": [
          -0.00011079166100323563,
          0.4998167976770577,
          -0.0008686220506495681
        ],
        "cartesian_polarization_e_A2": [
          -2.3270710966542755e-05,
          0.006036821112615749,
          5.2494674468250574e-05
        ],
        "ranking_score": 0.6376396605562387
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.03061664046329915
            ],
            "target_residual": 0.5592641091968222,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.08427303633314033,
            "max_log_strain_component": 0.015126712732668125,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0032937248196003,
              0.9956692565945601,
              0.9783271684586404
            ],
            "cell_volume_ratio": 0.9772986698721491,
            "cell_rmsd_from_input_A": 0.11212686129026238
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49749834406829185,
              1.1019868571299162e-11,
              -0.5050446276769903
            ],
            "branch_aligned_reduced_polarization": [
              0.49749834406829185,
              1.1019868571299162e-11,
              -0.5050446276769903
            ],
            "target_residual": 0.005630857021813582,
            "energy_eV": -156.84976301022024,
            "max_atomic_step_A": 0.0006589567007536402,
            "max_log_strain_component": 0.00010734148447863968,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0032706982255708,
              0.9957070261457367,
              0.9784596415956979
            ],
            "cell_volume_ratio": 0.9774456475771132,
            "cell_rmsd_from_input_A": 0.11134567551620461
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000248698510875,
              -3.196930192050081e-13,
              -0.5000196953669924
            ],
            "branch_aligned_reduced_polarization": [
              0.5000248698510875,
              -3.196930192050081e-13,
              -0.5000196953669924
            ],
            "target_residual": 3.1724075622174866e-05,
            "energy_eV": -156.8491677511333
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.1724075622174866e-05,
        "parent_symmetrization_rmsd_A": 0.05768918896769962,
        "parent_cell_rmsd_A": 0.11134567551620461,
        "energy_eV": -156.8491677511333,
        "reduced_polarization": [
          0.5000248698510875,
          -3.196930192050081e-13,
          -0.5000196953669924
        ],
        "cartesian_polarization_e_A2": [
          0.0036464360768214965,
          -9.40205496312337e-14,
          -0.002642754975828475
        ],
        "ranking_score": 0.5855890559979952
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052370733841e-10,
              -0.030616640463299177
            ],
            "target_residual": 0.5859974267777494,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008247726859938328,
            "step_scale": 0.8680899897701827,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0073376306555946,
              1.0000623318030646,
              0.9891251990119625
            ],
            "cell_volume_ratio": 0.9964451407455305,
            "cell_rmsd_from_input_A": 0.09882973870982707
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.448733495104547,
              0.43774111640901686,
              -0.01681558711739306
            ],
            "branch_aligned_reduced_polarization": [
              0.448733495104547,
              0.43774111640901686,
              -0.01681558711739306
            ],
            "target_residual": 0.08238438614381811,
            "energy_eV": -156.0254250986352,
            "max_atomic_step_A": 0.01886018931741857,
            "max_log_strain_component": 0.0011457247000123253,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0085737446695304,
              0.9999982514328363,
              0.9878668256465785
            ],
            "cell_volume_ratio": 0.9963348014158081,
            "cell_rmsd_from_input_A": 0.11235397621003154
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49946313987377744,
              0.5001629490932117,
              -0.0010120277962889677
            ],
            "branch_aligned_reduced_polarization": [
              0.49946313987377744,
              0.5001629490932117,
              -0.0010120277962889677
            ],
            "target_residual": 0.0011571393444904194,
            "energy_eV": -155.74079322680416,
            "max_atomic_step_A": 0.00014132212049724723,
            "max_log_strain_component": 1.9233435705639015e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0085849100071291,
              0.9999941732106027,
              0.9878863502901637
            ],
            "cell_volume_ratio": 0.9963614600824563,
            "cell_rmsd_from_input_A": 0.11231500681918431
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000016807612452,
              0.4999959800029423,
              -2.2529773354219337e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000016807612452,
              0.4999959800029423,
              -2.2529773354219337e-06
            ],
            "target_residual": 4.9052259459671715e-06,
            "energy_eV": -155.74065867527992
          }
        ],
        "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": 4.9052259459671715e-06,
        "parent_symmetrization_rmsd_A": 0.11204617842127018,
        "parent_cell_rmsd_A": 0.11231500681918431,
        "energy_eV": -155.74065867527992,
        "reduced_polarization": [
          0.5000016807612452,
          0.4999959800029423,
          -2.2529773354219337e-06
        ],
        "cartesian_polarization_e_A2": [
          0.003515422777201143,
          0.006074082903663773,
          6.546625413032716e-05
        ],
        "ranking_score": 0.6401347405779582
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052370733841e-10,
              -0.03061664046329915
            ],
            "target_residual": 0.7132399385008337,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008697729870067068,
            "step_scale": 0.8595067006613215,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0029197919892545,
              1.0016046858813774,
              0.9833153468606131
            ],
            "cell_volume_ratio": 0.9877689425628959,
            "cell_rmsd_from_input_A": 0.11531791810232825
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.020597223963153458,
              0.43925073939407844,
              -0.4504229361073316
            ],
            "branch_aligned_reduced_polarization": [
              0.020597223963153458,
              0.43925073939407844,
              -0.4504229361073316
            ],
            "target_residual": 0.08107159529312473,
            "energy_eV": -156.12657313470876,
            "max_atomic_step_A": 0.016502839285013567,
            "max_log_strain_component": 0.0010541437470890493,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0033900199313888,
              1.0018151234655448,
              0.9814246498835738
            ],
            "cell_volume_ratio": 0.9865391449244394,
            "cell_rmsd_from_input_A": 0.12895050989485657
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00013605978750655344,
              0.5005593379695275,
              -0.5009103463342552
            ],
            "branch_aligned_reduced_polarization": [
              -0.00013605978750655344,
              0.5005593379695275,
              -0.5009103463342552
            ],
            "target_residual": 0.0010770801633227564,
            "energy_eV": -155.85596363448144,
            "max_atomic_step_A": 0.0001907445760165375,
            "max_log_strain_component": 1.9767628690021984e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0033903741052599,
              1.0018136682182794,
              0.981453863203304
            ],
            "cell_volume_ratio": 0.9865674256193273,
            "cell_rmsd_from_input_A": 0.12878312991613103
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.7870050491023363e-07,
              0.4999952558458515,
              -0.4999983967133874
            ],
            "branch_aligned_reduced_polarization": [
              1.7870050491023363e-07,
              0.4999952558458515,
              -0.4999983967133874
            ],
            "target_residual": 5.010934086277358e-06,
            "energy_eV": -155.85877962589763
          }
        ],
        "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": 5.010934086277358e-06,
        "parent_symmetrization_rmsd_A": 0.1105092258581315,
        "parent_cell_rmsd_A": 0.12878312991613103,
        "energy_eV": -155.85877962589763,
        "reduced_polarization": [
          1.7870050491023363e-07,
          0.4999952558458515,
          -0.4999983967133874
        ],
        "cartesian_polarization_e_A2": [
          3.8412278353034365e-05,
          0.006103198172184957,
          -0.0026163570085051316
        ],
        "ranking_score": 0.6427150302053368
      },
      "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": [
              0.19593486614582845,
              1.0887052249621108e-10,
              -0.030616640463299177
            ],
            "branch_aligned_reduced_polarization": [
              0.19593486614582845,
              1.0887052370733841e-10,
              -0.03061664046329915
            ],
            "target_residual": 0.750184206529866,
            "energy_eV": -156.84652498446616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011818083820669468,
            "step_scale": 0.781272442777977,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0030998801513218,
              0.9996743937042317,
              0.9795032105568617
            ],
            "cell_volume_ratio": 0.982219632053087,
            "cell_rmsd_from_input_A": 0.12246798043529893
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4259488705149347,
              0.3997350919759673,
              -0.41378684279477557
            ],
            "branch_aligned_reduced_polarization": [
              0.4259488705149347,
              0.3997350919759673,
              -0.41378684279477557
            ],
            "target_residual": 0.1515563592673511,
            "energy_eV": -156.2124867620582,
            "max_atomic_step_A": 0.02892966291577752,
            "max_log_strain_component": 0.0026160378268192874,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0038394863719482,
              0.999650826251352,
              0.9748654763080584
            ],
            "cell_volume_ratio": 0.9782667546347324,
            "cell_rmsd_from_input_A": 0.14980269990362646
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4996624151116244,
              0.5017149975649574,
              -0.5021048938923474
            ],
            "branch_aligned_reduced_polarization": [
              0.4996624151116244,
              0.5017149975649574,
              -0.5021048938923474
            ],
            "target_residual": 0.0027360114222551458,
            "energy_eV": -155.6751703181829,
            "max_atomic_step_A": 0.0005197786833890923,
            "max_log_strain_component": 4.332894004619699e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1612644684861553,
            "cell_principal_stretches": [
              1.0038291056599906,
              0.9996503397764279,
              0.9749370245182641
            ],
            "cell_volume_ratio": 0.9783279593695439,
            "cell_rmsd_from_input_A": 0.1493559730113648
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000106382276598,
              0.49998799984389214,
              -0.4999939977585591
            ],
            "branch_aligned_reduced_polarization": [
              0.5000106382276598,
              0.49998799984389214,
              -0.4999939977585591
            ],
            "target_residual": 1.712315790585999e-05,
            "energy_eV": -155.68421543721334
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.712315790585999e-05,
        "parent_symmetrization_rmsd_A": 0.11753588387235878,
        "parent_cell_rmsd_A": 0.1493559730113648,
        "energy_eV": -155.68421543721334,
        "reduced_polarization": [
          0.5000106382276598,
          0.49998799984389214,
          -0.4999939977585591
        ],
        "cartesian_polarization_e_A2": [
          0.003622338329495865,
          0.006137070935971934,
          -0.002587423106528599
        ],
        "ranking_score": 0.6549091234410117
      },
      "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,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43
        ],
        "endpoint_rmsd_A": 0.02596700695669423,
        "minimum_distance_A_by_image": [
          2.5631251115819356,
          2.563675377426853,
          2.5642422451852123,
          2.5648257220326562,
          2.565425814865942,
          2.566042530302904,
          2.561922293388915,
          2.5571728865455756,
          2.5524304533491127
        ],
        "minimum_distance_A": 2.5524304533491127,
        "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": [
          1480.6897889614077,
          1481.53286155951,
          1482.376414184835,
          1483.2204471106982,
          1484.0649606105737,
          1484.909954958088,
          1485.755430427029,
          1486.601387291333,
          1487.4478258250972
        ],
        "cell_deformation_log_strain_norm": 0.00470558796036204
      },
      "parent_reduced_polarization": [
        -6.349414027792663e-07,
        2.0191823621667202e-15,
        2.3679997969185466e-07
      ],
      "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": [
          -156.84652498446616,
          -156.83449493457914,
          -156.82057201050577,
          -156.80477428417294,
          -156.78711884716662,
          -156.76762185725238,
          -156.74629856454752,
          -156.72316330823747,
          -156.69822951272272
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013881475964863995,
            1.3207254730291361e-12,
            -0.0001630202184864293
          ],
          [
            0.0012150729023583998,
            1.164149547295022e-12,
            -0.00014297271741197027
          ],
          [
            0.0010418636344349615,
            1.0062109975776395e-12,
            -0.00012282561350488732
          ],
          [
            0.0008685218370722158,
            8.466175761333406e-13,
            -0.00010258092162033735
          ],
          [
            0.0006950509027515224,
            6.846660540387458e-13,
            -8.224099397094854e-05
          ],
          [
            0.0005214557734080536,
            5.196719677728917e-13,
            -6.18088391638771e-05
          ],
          [
            0.00034774274213730257,
            3.5107514912536665e-13,
            -4.128808995313768e-05
          ],
          [
            0.00017391955069570987,
            1.7809740974495525e-13,
            -2.068304759933241e-05
          ],
          [
            -4.507140543330593e-09,
            2.4414100861624837e-17,
            1.269968794449103e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027792663e-07,
            2.0191823621667202e-15,
            2.3679997969185466e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027780054e-07,
            2.019182362165899e-15,
            2.3679997969167782e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.19593486614582734,
            1.0887013512927979e-10,
            -0.03061664046329815
          ],
          [
            0.17157150589782977,
            9.604972373011833e-11,
            -0.026785597383854165
          ],
          [
            0.14717040791023273,
            8.30929769435329e-11,
            -0.02295463246355056
          ],
          [
            0.12273182412590944,
            6.997569190758668e-11,
            -0.01912415338562984
          ],
          [
            0.09825619642060035,
            5.6639470891184374e-11,
            -0.015294630813861454
          ],
          [
            0.07374418416118456,
            4.302747047546518e-11,
            -0.011466657988933093
          ],
          [
            0.04919663651009176,
            2.9092950271092377e-11,
            -0.007640944412267425
          ],
          [
            0.02461460635171253,
            1.4770962231125395e-11,
            -0.0038183238790973073
          ],
          [
            -6.349414027884137e-07,
            1.9984014443252818e-15,
            2.3679997973591327e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -156.6982295127227,
          -156.70104417600857,
          -156.7019929272167,
          -156.70106684528102,
          -156.69825661738807,
          -156.69355255739032,
          -156.68694462590605,
          -156.67842245236193,
          -156.66797535914725
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.507140607618493e-09,
            1.704811915521314e-17,
            1.269968761388487e-09
          ],
          [
            -0.00016939892255434143,
            -1.7512459171655377e-13,
            4.8301274094479054e-06
          ],
          [
            -0.00033903185067286185,
            -3.5553947446842293e-13,
            9.465889011305659e-06
          ],
          [
            -0.0005088923740376327,
            -5.416948431954178e-13,
            1.390822025403823e-05
          ],
          [
            -0.0006789695983587696,
            -7.339202255150784e-13,
            1.815671574597667e-05
          ],
          [
            -0.0008492526869991304,
            -9.328123880513237e-13,
            2.2210898929439426e-05
          ],
          [
            -0.0010197308864213096,
            -1.1386660038915265e-12,
            2.6070224940806632e-05
          ],
          [
            -0.001190393541056403,
            -1.3520807394752662e-12,
            2.973408733281617e-05
          ],
          [
            -0.0013612300963921134,
            -1.5733081218703012e-12,
            3.320182868661484e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.349414120587448e-07,
            1.4095745270137338e-15,
            2.3679997344107685e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.349414120587448e-07,
            1.4095745270137338e-15,
            2.3679997344107685e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.1959361325850673,
          -1.0886610520110912e-10,
          0.03061711748606671
        ],
        "actual_opposite_endpoint_branch_residual": 0.024603174459125094
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027792663e-07,
            2.0191823621667202e-15,
            2.3679997969185466e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.19593486614582728,
            1.0887013021068768e-10,
            -0.030616640463298123
          ],
          [
            0.1715715058978298,
            9.604968108049793e-11,
            -0.02678559738385415
          ],
          [
            0.14717040791023267,
            8.309297587131486e-11,
            -0.022954632463550548
          ],
          [
            0.12273182412590944,
            6.997568184647205e-11,
            -0.01912415338562983
          ],
          [
            0.09825619642060031,
            5.6639473512812014e-11,
            -0.015294630813861457
          ],
          [
            0.07374418416118451,
            4.302746153586799e-11,
            -0.011466657988933074
          ],
          [
            0.049196636510091755,
            2.9092921704546204e-11,
            -0.007640944412267413
          ],
          [
            0.02461460635171258,
            1.4771004666517728e-11,
            -0.0038183238790973194
          ],
          [
            -6.349414027780054e-07,
            2.019182362165899e-15,
            2.3679997969167782e-07
          ],
          [
            -0.02404082986508061,
            -1.4520968628266916e-11,
            0.00083819784743356
          ],
          [
            -0.048095584151580016,
            -2.945498376393915e-11,
            0.001659495463752897
          ],
          [
            -0.07216329970780595,
            -4.4838612824692955e-11,
            0.002464118004018768
          ],
          [
            -0.0962423846837917,
            -6.06983833998261e-11,
            0.0032520378880872315
          ],
          [
            -0.12033125833620233,
            -7.708283294037603e-11,
            0.00402321156507433
          ],
          [
            -0.1444283545854919,
            -9.401547626479944e-11,
            0.004777580083953797
          ],
          [
            -0.16853212405038356,
            -1.1154493575623329e-10,
            0.005515070398560795
          ],
          [
            -0.19264103439500818,
            -1.2969103995298913e-10,
            0.006235597406629201
          ]
        ],
        "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": [
          [
            0.19593486614582734,
            1.0887013512927979e-10,
            -0.03061664046329815
          ],
          [
            0.17157150589782977,
            9.604972373011833e-11,
            -0.026785597383854165
          ],
          [
            0.14717040791023273,
            8.30929769435329e-11,
            -0.02295463246355056
          ],
          [
            0.12273182412590944,
            6.997569190758668e-11,
            -0.01912415338562984
          ],
          [
            0.09825619642060035,
            5.6639470891184374e-11,
            -0.015294630813861454
          ],
          [
            0.07374418416118456,
            4.302747047546518e-11,
            -0.011466657988933093
          ],
          [
            0.04919663651009176,
            2.9092950271092377e-11,
            -0.007640944412267425
          ],
          [
            0.02461460635171253,
            1.4770962231125395e-11,
            -0.0038183238790973073
          ],
          [
            -6.349414027884137e-07,
            1.9984014443252818e-15,
            2.3679997973591327e-07
          ],
          [
            -0.024040829865080604,
            -1.4520995517131041e-11,
            0.0008381978474335527
          ],
          [
            -0.048095584151579995,
            -2.945499399942264e-11,
            0.0016594954637528803
          ],
          [
            -0.07216329970780594,
            -4.483863280668743e-11,
            0.0024641180040188004
          ],
          [
            -0.0962423846837917,
            -6.069839075806271e-11,
            0.003252037888087256
          ],
          [
            -0.12033125833620234,
            -7.708284011087585e-11,
            0.004023211565074347
          ],
          [
            -0.1444283545854919,
            -9.401546208209766e-11,
            0.004777580083953792
          ],
          [
            -0.16853212405038354,
            -1.1154493995135795e-10,
            0.005515070398560806
          ],
          [
            -0.19264103439500818,
            -1.2969103568849505e-10,
            0.006235597406629156
          ]
        ]
      },
      "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": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.776612915260102e-07,
        "parent_symmetrization_rmsd_A": 0.02596700695669423,
        "parent_cell_rmsd_A": 0.021775571312999294,
        "energy_eV": -156.69822951272272,
        "reduced_polarization": [
          -6.349414121092905e-07,
          -1.1641750822379349e-15,
          2.3679997724104676e-07
        ],
        "cartesian_polarization_e_A2": [
          -4.507140608593471e-09,
          -1.4050878340539603e-17,
          1.2699687815877908e-09
        ],
        "ranking_score": 0.5314122551075271
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 300.0747054500389
  }
}
