{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "As4Cd2Hg8I8",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -40.760922396264775,
  "input_cartesian_polarization_e_A2": [
    -4.5730241535975905e-09,
    1.398035302384413e-08,
    6.37046556270437e-05
  ],
  "input_reduced_polarization": [
    2.590660580655231e-07,
    1.5495913000603066e-06,
    0.003861787482572304
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 1.0436443571845112e-14,
      "parent_symmetrization_rmsd_A": 0.7780081079089756,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -39.476440264886676,
      "reduced_polarization": [
        -9.777546370080349e-15,
        -3.4906448014154624e-15,
        -1.0650541204966726e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.194908674725238e-17,
        -3.149246294989863e-17,
        -1.756930081642164e-17
      ],
      "ranking_score": 0.7780081079089964
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 7.190824439170518e-15,
      "parent_symmetrization_rmsd_A": 0.7857229805229345,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -39.95199394500291,
      "reduced_polarization": [
        4.292249956932695e-15,
        5.746051884993658e-15,
        5.171403650307184e-16
      ],
      "cartesian_polarization_e_A2": [
        1.6471371988971597e-17,
        5.1840658786874976e-17,
        8.530829056181442e-18
      ],
      "ranking_score": 0.785722980522949
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.91829066883698e-15,
      "parent_symmetrization_rmsd_A": 0.8999627291909672,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -11.543948418149055,
      "reduced_polarization": [
        2.2231624312747964e-15,
        3.2158083634571162e-15,
        -2.62920404652329e-16
      ],
      "cartesian_polarization_e_A2": [
        7.422060924952409e-18,
        2.9012899192458854e-17,
        -4.33717647884214e-18
      ],
      "ranking_score": 0.8999627291909751
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0007077324999857e-06,
      "parent_symmetrization_rmsd_A": 0.0019170071184952996,
      "parent_cell_rmsd_A": 0.0036306773047364575,
      "energy_eV": -40.761825741862154,
      "reduced_polarization": [
        -6.598945133688728e-10,
        -1.2329770177159436e-09,
        1.0007067553445254e-06
      ],
      "cartesian_polarization_e_A2": [
        -9.159597012607863e-13,
        -1.1126935884935454e-11,
        1.6505681803544065e-08
      ],
      "ranking_score": 0.5028266778601445
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3629711447536135e-15,
      "parent_symmetrization_rmsd_A": 0.7857230373378479,
      "parent_cell_rmsd_A": 0.0036306773047364575,
      "energy_eV": -39.956452217392055,
      "reduced_polarization": [
        2.2409843945482225e-15,
        5.729879122043154e-16,
        4.830180398259254e-16
      ],
      "cartesian_polarization_e_A2": [
        1.9837542572305965e-17,
        5.174047568794104e-18,
        7.966911752733707e-18
      ],
      "ranking_score": 0.7866307066640368
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.08117664026015255,
      "parent_symmetrization_rmsd_A": 0.2545580015124082,
      "parent_cell_rmsd_A": 0.6470215038729111,
      "energy_eV": -35.19579297848885,
      "reduced_polarization": [
        1.4270502627036404e-07,
        2.2692092141176021e-07,
        0.41882335974029006
      ],
      "cartesian_polarization_e_A2": [
        -9.684081109547904e-10,
        4.528709256204561e-09,
        0.0071372081585656735
      ],
      "ranking_score": 1.078666658000941
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 5.629508722717851e-05,
      "parent_symmetrization_rmsd_A": 0.17981017075934003,
      "parent_cell_rmsd_A": 0.07153664749598686,
      "energy_eV": -39.00806078522305,
      "reduced_polarization": [
        -1.5513294499085205e-05,
        0.49995611439113935,
        -3.1662720581629457e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.0023140987142899784,
        0.004511189512290372,
        -3.550961347858779e-05
      ],
      "ranking_score": 0.6978069228077911
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00010357361026855378,
      "parent_symmetrization_rmsd_A": 0.17884006110811565,
      "parent_cell_rmsd_A": 0.13846795344147136,
      "energy_eV": -38.850280480093545,
      "reduced_polarization": [
        0.4999039794352619,
        -3.082225957710833e-05,
        -2.361211989627802e-05
      ],
      "cartesian_polarization_e_A2": [
        0.005018682125852494,
        1.974547615556734e-06,
        -6.822413832257373e-05
      ],
      "ranking_score": 0.7136641966890206
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.13469811631791748,
      "parent_symmetrization_rmsd_A": 0.31862601114545064,
      "parent_cell_rmsd_A": 0.6217954120793687,
      "energy_eV": -34.686445788385655,
      "reduced_polarization": [
        0.0011165700312133016,
        0.4328303762931493,
        0.38324993592275547
      ],
      "cartesian_polarization_e_A2": [
        -0.002080764571716618,
        0.0036993965387865425,
        0.00648706355147841
      ],
      "ranking_score": 1.2434710968011278
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.12915781338869733,
      "parent_symmetrization_rmsd_A": 0.3034191590479137,
      "parent_cell_rmsd_A": 0.6480805291096162,
      "energy_eV": -34.329438894776125,
      "reduced_polarization": [
        0.4334270612778986,
        -0.004780254105277359,
        0.3894245336435705
      ],
      "cartesian_polarization_e_A2": [
        0.004172188215837139,
        -0.00024756861869967595,
        0.006566195254414855
      ],
      "ranking_score": 1.2237549181027125
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00026989852104923416,
      "parent_symmetrization_rmsd_A": 0.16932408674879187,
      "parent_cell_rmsd_A": 0.1720189891565749,
      "energy_eV": -38.98122231624981,
      "reduced_polarization": [
        0.49980807205101807,
        0.49981213879131076,
        -2.6777608817260323e-05
      ],
      "cartesian_polarization_e_A2": [
        0.002699045054319652,
        0.004505077023872103,
        -0.00011674550568624399
      ],
      "ranking_score": 0.7128686310800341
    },
    {
      "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": 0.14220007139272675,
      "parent_symmetrization_rmsd_A": 0.2955205197495439,
      "parent_cell_rmsd_A": 0.6969931132096737,
      "energy_eV": -33.52731374928472,
      "reduced_polarization": [
        0.43892821582890723,
        0.43058674654019563,
        0.39195881467523136
      ],
      "cartesian_polarization_e_A2": [
        0.002108726674207484,
        0.0034686543196064804,
        0.0065526699607040325
      ],
      "ranking_score": 1.254168940837416
    }
  ],
  "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": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "target_residual": 0.0038617878021585486,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.0024770730063377253,
            "max_log_strain_component": 0.00029937878195461395,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0002307723521022,
              0.9998985837460039,
              0.9997006660257682
            ],
            "cell_volume_ratio": 0.9998299600061376,
            "cell_rmsd_from_input_A": 0.0036306773047364575
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.598945133688728e-10,
              -1.2329770177159436e-09,
              1.0007067553445254e-06
            ],
            "branch_aligned_reduced_polarization": [
              -6.598945133688728e-10,
              -1.2329770177159436e-09,
              1.0007067553445254e-06
            ],
            "target_residual": 1.0007077324999857e-06,
            "energy_eV": -40.761825741862154
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0007077324999857e-06,
        "parent_symmetrization_rmsd_A": 0.0019170071184952996,
        "parent_cell_rmsd_A": 0.0036306773047364575,
        "energy_eV": -40.761825741862154,
        "reduced_polarization": [
          -6.598945133688728e-10,
          -1.2329770177159436e-09,
          1.0007067553445254e-06
        ],
        "cartesian_polarization_e_A2": [
          -9.159597012607863e-13,
          -1.1126935884935454e-11,
          1.6505681803544065e-08
        ],
        "ranking_score": 0.5028266778601445
      },
      "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": [
          -40.760922396264775,
          -40.761063823956604,
          -40.76119711242222,
          -40.76132225851033,
          -40.761439259053475,
          -40.76154811086809,
          -40.76164881075441,
          -40.761741355496454,
          -40.761825741862154
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.573024155692e-09,
            1.3980353008394677e-08,
            6.370465562703373e-05
          ],
          [
            -4.000966351153901e-09,
            1.2233471624924503e-08,
            5.573925233491566e-05
          ],
          [
            -3.429064121213458e-09,
            1.0486001865186862e-08,
            4.777509048749002e-05
          ],
          [
            -2.85731740490344e-09,
            8.737944441059759e-09,
            3.981217576897522e-05
          ],
          [
            -2.285726168090543e-09,
            6.989300415492101e-09,
            3.185051382938623e-05
          ],
          [
            -1.7142904990893147e-09,
            5.240070359481106e-09,
            2.389011028498629e-05
          ],
          [
            -1.1430102495440664e-09,
            3.4902552867208842e-09,
            1.5930970718359225e-05
          ],
          [
            -5.718853676213375e-10,
            1.739855860250364e-09,
            7.973100678636072e-06
          ],
          [
            -9.15963114796619e-13,
            -1.1126912002905876e-11,
            1.6505681786039623e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094585e-10,
            -1.2329743713592442e-09,
            1.0007067542832658e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094589e-10,
            -1.2329743713592355e-09,
            1.0007067542832683e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.590660570511716e-07,
            1.5495912983887195e-06,
            0.0038617874825717102
          ],
          [
            2.2670845123418104e-07,
            1.3559025187070972e-06,
            0.0033789779498493155
          ],
          [
            1.9431984710216454e-07,
            1.1621666166083955e-06,
            0.0028962280652671257
          ],
          [
            1.6190029294982367e-07,
            9.683836769136533e-07,
            0.002413538176691543
          ],
          [
            1.2944985239293771e-07,
            7.745538233017157e-07,
            0.001930908629937833
          ],
          [
            9.696855185481468e-08,
            5.806771249394771e-07,
            0.0014483397687969912
          ],
          [
            6.445646383301806e-08,
            3.8675369995466724e-07,
            0.0009658319350406286
          ],
          [
            3.1913633180558065e-08,
            1.9278362761721013e-07,
            0.0004833854684341832
          ],
          [
            -6.598936397317345e-10,
            -1.2329743892536271e-09,
            1.0007067542394665e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -40.761825741862154,
          -40.76174999837161,
          -40.76166659545234,
          -40.76157553621839,
          -40.761476823769335,
          -40.761370461190424,
          -40.761256451552406,
          -40.761134797911694,
          -40.761005503310216
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.159753102364387e-13,
            -1.1126909373847222e-11,
            1.650568178468269e-08
          ],
          [
            6.128720515468366e-10,
            -1.701629956555833e-09,
            -6.6961776664785385e-06
          ],
          [
            1.2268059212605321e-09,
            -3.3920054234964147e-09,
            -1.3410814666446668e-05
          ],
          [
            1.8408858726035802e-09,
            -5.082252235735235e-09,
            -2.0127401472220657e-05
          ],
          [
            2.4551118314414874e-09,
            -6.7723695421340746e-09,
            -2.6845934194865184e-05
          ],
          [
            3.069483827609624e-09,
            -8.462356218200403e-09,
            -3.3566408902454584e-05
          ],
          [
            3.6840019816440817e-09,
            -1.015221117140451e-08,
            -4.0288821619341794e-05
          ],
          [
            4.298666264482142e-09,
            -1.1841933632042388e-08,
            -4.7013168326547035e-05
          ],
          [
            4.91347665204054e-09,
            -1.3531522372249406e-08,
            -5.373944496109217e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.598947139025517e-10,
            -1.2329740798357897e-09,
            1.0007067542009977e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.598947139025517e-10,
            -1.2329740798357897e-09,
            1.0007067542009977e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.6038649110156973e-07,
          -1.5520579264804928e-06,
          -0.003859786327877894
        ],
        "actual_opposite_endpoint_branch_residual": 0.000602091682094464
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094585e-10,
            -1.2329743713592442e-09,
            1.0007067542832658e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094589e-10,
            -1.2329743713592355e-09,
            1.0007067542832683e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "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": [
          [
            2.590660570511716e-07,
            1.5495912983887195e-06,
            0.0038617874825717102
          ],
          [
            2.2670845123418104e-07,
            1.3559025187070972e-06,
            0.0033789779498493155
          ],
          [
            1.9431984710216454e-07,
            1.1621666166083955e-06,
            0.0028962280652671257
          ],
          [
            1.6190029294982367e-07,
            9.683836769136533e-07,
            0.002413538176691543
          ],
          [
            1.2944985239293771e-07,
            7.745538233017157e-07,
            0.001930908629937833
          ],
          [
            9.696855185481468e-08,
            5.806771249394771e-07,
            0.0014483397687969912
          ],
          [
            6.445646383301806e-08,
            3.8675369995466724e-07,
            0.0009658319350406286
          ],
          [
            3.1913633180558065e-08,
            1.9278362761721013e-07,
            0.0004833854684341832
          ],
          [
            -6.598936397317345e-10,
            -1.2329743892536271e-09,
            1.0007067542394665e-06
          ],
          [
            -2.5878790110844818e-08,
            -1.8855165273556906e-07,
            -0.00040596940995618613
          ],
          [
            -5.1089781016866453e-08,
            -3.758727051272892e-07,
            -0.0008130448111886013
          ],
          [
            -7.629278864218492e-08,
            -5.631960128815727e-07,
            -0.0012202252583600748
          ],
          [
            -1.014877767935296e-07,
            -7.505214822400852e-07,
            -0.0016275105102939724
          ],
          [
            -1.2667468496374568e-07,
            -9.378489891909148e-07,
            -0.002034900323222899
          ],
          [
            -1.5185344515167287e-07,
            -1.125178413219352e-06,
            -0.002442394450744456
          ],
          [
            -1.7702402088648483e-07,
            -1.3125096695598693e-06,
            -0.0028499926438452228
          ],
          [
            -2.0218635155000442e-07,
            -1.499842622654235e-06,
            -0.0032576946508604543
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572321
            ],
            "target_residual": 0.49613821251991524,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.014503578271076048,
            "step_scale": 0.3770855054749454,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0146092654926238,
              1.0049255088511857,
              0.9888836382678449
            ],
            "cell_volume_ratio": 1.008272415148289,
            "cell_rmsd_from_input_A": 0.17835784409864203
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.541710280859114e-07,
              1.0792242941355155e-06,
              0.18692944181876325
            ],
            "branch_aligned_reduced_polarization": [
              1.541710280859114e-07,
              1.0792242941355155e-06,
              0.18692944181876325
            ],
            "target_residual": 0.3130705581831349,
            "energy_eV": -40.12026804792886,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.015692925638153304,
            "step_scale": 0.558719718684978,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0306570421954862,
              1.0102822578272799,
              0.9769948403412875
            ],
            "cell_volume_ratio": 1.0173002970732656,
            "cell_rmsd_from_input_A": 0.3769101273464801
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.015941079019783e-07,
              6.209989931817044e-07,
              0.3151551365715846
            ],
            "branch_aligned_reduced_polarization": [
              1.015941079019783e-07,
              6.209989931817044e-07,
              0.3151551365715846
            ],
            "target_residual": 0.18484486342948644,
            "energy_eV": -38.275577640509454,
            "max_atomic_step_A": 0.06831171680323263,
            "max_log_strain_component": 0.02,
            "step_scale": 0.495791505932071,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0514776955569078,
              1.017150623246176,
              0.9620499787117945
            ],
            "cell_volume_ratio": 1.02892322080898,
            "cell_rmsd_from_input_A": 0.638654906817167
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.435644288865728e-07,
              4.4336471308890835e-07,
              0.3590629873786331
            ],
            "branch_aligned_reduced_polarization": [
              1.435644288865728e-07,
              4.4336471308890835e-07,
              0.3590629873786331
            ],
            "target_residual": 0.14093701262213737,
            "energy_eV": -36.50402024750512,
            "max_atomic_step_A": 0.06113908009047308,
            "max_log_strain_component": 0.02,
            "step_scale": 0.48683161565142424,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.072718954016463,
              1.0240656829856842,
              0.9473337251361796
            ],
            "cell_volume_ratio": 1.0406789395086156,
            "cell_rmsd_from_input_A": 0.9105440286884589
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              2.4189743186549574e-07,
              3.8994834052770405e-07,
              0.37300189780052034
            ],
            "branch_aligned_reduced_polarization": [
              2.4189743186549574e-07,
              3.8994834052770405e-07,
              0.37300189780052034
            ],
            "target_residual": 0.12699810220030872,
            "energy_eV": -35.328085568418814,
            "max_atomic_step_A": 0.02382813581456312,
            "max_log_strain_component": 0.02,
            "step_scale": 0.38924109141277435,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6802370821627057,
            "cell_principal_stretches": [
              1.0514776955589284,
              1.0200306654469447,
              0.9490128798514647
            ],
            "cell_volume_ratio": 1.0178537934842768,
            "cell_rmsd_from_input_A": 0.6470215038729111
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.4270502627036404e-07,
              2.2692092141176021e-07,
              0.41882335974029006
            ],
            "branch_aligned_reduced_polarization": [
              1.4270502627036404e-07,
              2.2692092141176021e-07,
              0.41882335974029006
            ],
            "target_residual": 0.08117664026015255,
            "energy_eV": -35.19579297848885
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.08117664026015255,
        "parent_symmetrization_rmsd_A": 0.2545580015124082,
        "parent_cell_rmsd_A": 0.6470215038729111,
        "energy_eV": -35.19579297848885,
        "reduced_polarization": [
          1.4270502627036404e-07,
          2.2692092141176021e-07,
          0.41882335974029006
        ],
        "cartesian_polarization_e_A2": [
          -9.684081109547904e-10,
          4.528709256204561e-09,
          0.0071372081585656735
        ],
        "ranking_score": 1.078666658000941
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580655231e-07,
              1.549591300054054e-06,
              0.003861787482572304
            ],
            "target_residual": 0.5000133636351421,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005126584531375675,
            "step_scale": 0.6740424867671355,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0051293677934663,
              0.9999765798629952,
              0.9948063524936654
            ],
            "cell_volume_ratio": 0.999885662151232,
            "cell_rmsd_from_input_A": 0.044496272538073776
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0006846420281425141,
              0.32987892210583064,
              0.001106129238987716
            ],
            "branch_aligned_reduced_polarization": [
              -0.0006846420281425141,
              0.32987892210583064,
              0.001106129238987716
            ],
            "target_residual": 0.17012605150438917,
            "energy_eV": -40.03528683265243,
            "max_atomic_step_A": 0.06512143668219696,
            "max_log_strain_component": 0.0029645862047599884,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0081506536549953,
              0.9999796896079509,
              0.9918442430074258
            ],
            "cell_volume_ratio": 0.9999081129736105,
            "cell_rmsd_from_input_A": 0.06987059419999446
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0010047518844663037,
              0.49162270081835274,
              -0.0002448963434234015
            ],
            "branch_aligned_reduced_polarization": [
              -0.0010047518844663037,
              0.49162270081835274,
              -0.0002448963434234015
            ],
            "target_residual": 0.008440891075424948,
            "energy_eV": -39.06715272241735,
            "max_atomic_step_A": 0.0032331283296559367,
            "max_log_strain_component": 0.00020632356477265557,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0083707591103144,
              0.9999827419617237,
              0.9916405363224948
            ],
            "cell_volume_ratio": 0.9999240633504922,
            "cell_rmsd_from_input_A": 0.07153664749598686
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.5513294499085205e-05,
              0.49995611439113935,
              -3.1662720581629457e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.5513294499085205e-05,
              0.49995611439113935,
              -3.1662720581629457e-05
            ],
            "target_residual": 5.629508722717851e-05,
            "energy_eV": -39.00806078522305
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 5.629508722717851e-05,
        "parent_symmetrization_rmsd_A": 0.17981017075934003,
        "parent_cell_rmsd_A": 0.07153664749598686,
        "energy_eV": -39.00806078522305,
        "reduced_polarization": [
          -1.5513294499085205e-05,
          0.49995611439113935,
          -3.1662720581629457e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.0023140987142899784,
          0.004511189512290372,
          -3.550961347858779e-05
        ],
        "ranking_score": 0.6978069228077911
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580503723e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "target_residual": 0.5000146541242275,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00872653277283558,
            "step_scale": 0.6942413186647043,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.010468520221979,
              0.9999663648539161,
              0.9895562662366605
            ],
            "cell_volume_ratio": 0.9998818237181105,
            "cell_rmsd_from_input_A": 0.08927813016644333
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.33947575414903314,
              0.0003576959997092947,
              0.0036456112041913877
            ],
            "branch_aligned_reduced_polarization": [
              0.33947575414903314,
              0.0003576959997092947,
              0.0036456112041913877
            ],
            "target_residual": 0.16056603605215514,
            "energy_eV": -39.92104671069579,
            "max_atomic_step_A": 0.05880397179399032,
            "max_log_strain_component": 0.004515906028338882,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0158569342509742,
              0.9998813154942618,
              0.9840971726150696
            ],
            "cell_volume_ratio": 0.9995832876475444,
            "cell_rmsd_from_input_A": 0.13557836766387402
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49200313555338737,
              -0.0002372161363021998,
              0.00012264911309234003
            ],
            "branch_aligned_reduced_polarization": [
              0.49200313555338737,
              -0.0002372161363021998,
              0.00012264911309234003
            ],
            "target_residual": 0.008001322095614048,
            "energy_eV": -38.91449098407233,
            "max_atomic_step_A": 0.003041257875304275,
            "max_log_strain_component": 0.00028108966889005624,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0161971416735969,
              0.9998760558011136,
              0.9837554122438027
            ],
            "cell_volume_ratio": 0.9995655323215514,
            "cell_rmsd_from_input_A": 0.13846795344147136
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999039794352619,
              -3.082225957710833e-05,
              -2.361211989627802e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999039794352619,
              -3.082225957710833e-05,
              -2.361211989627802e-05
            ],
            "target_residual": 0.00010357361026855378,
            "energy_eV": -38.850280480093545
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00010357361026855378,
        "parent_symmetrization_rmsd_A": 0.17884006110811565,
        "parent_cell_rmsd_A": 0.13846795344147136,
        "energy_eV": -38.850280480093545,
        "reduced_polarization": [
          0.4999039794352619,
          -3.082225957710833e-05,
          -2.361211989627802e-05
        ],
        "cartesian_polarization_e_A2": [
          0.005018682125852494,
          1.974547615556734e-06,
          -6.822413832257373e-05
        ],
        "ranking_score": 0.7136641966890206
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580655231e-07,
              1.549591300054054e-06,
              0.003861787482572321
            ],
            "target_residual": 0.7043802782099713,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013116533540266147,
            "step_scale": 0.3410223064923565,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0135895312909435,
              1.0043044318349026,
              0.9897107205031387
            ],
            "cell_volume_ratio": 1.0074784609786107,
            "cell_rmsd_from_input_A": 0.1627577341475028
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00299457653162711,
              0.16248195544809152,
              0.16976588781734328
            ],
            "branch_aligned_reduced_polarization": [
              -0.00299457653162711,
              0.16248195544809152,
              0.16976588781734325
            ],
            "target_residual": 0.4722096639585168,
            "energy_eV": -40.042119872359365,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014205523944389776,
            "step_scale": 0.48658347503773824,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.028650745416506,
              1.0090323601487659,
              0.9785142380415746
            ],
            "cell_volume_ratio": 1.0156409170537253,
            "cell_rmsd_from_input_A": 0.3443975812713113
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.004082321014532107,
              0.3056108369986119,
              0.29272191114263707
            ],
            "branch_aligned_reduced_polarization": [
              -0.004082321014532107,
              0.3056108369986119,
              0.29272191114263707
            ],
            "target_residual": 0.2841971466387493,
            "energy_eV": -37.90669302334583,
            "max_atomic_step_A": 0.0767251003090179,
            "max_log_strain_component": 0.02,
            "step_scale": 0.44043004019318355,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0497971869737155,
              1.015849609737178,
              0.9632504449670046
            ],
            "cell_volume_ratio": 1.0272450119154233,
            "cell_rmsd_from_input_A": 0.606800026988525
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0015109709019410934,
              0.37298774698523507,
              0.3331272817749575
            ],
            "branch_aligned_reduced_polarization": [
              -0.0015109709019410934,
              0.37298774698523507,
              0.3331272817749575
            ],
            "target_residual": 0.20971623574908932,
            "energy_eV": -35.63579701939294,
            "max_atomic_step_A": 0.062057448445787776,
            "max_log_strain_component": 0.02,
            "step_scale": 0.35379524810786345,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0712382567900949,
              1.0227126387895455,
              0.9483489951015251
            ],
            "cell_volume_ratio": 1.0389816695276668,
            "cell_rmsd_from_input_A": 0.8788690102780123
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.0006566483914612967,
              0.40725367925265676,
              0.34290611445333014
            ],
            "branch_aligned_reduced_polarization": [
              0.0006566483914612967,
              0.40725367925265676,
              0.34290611445333014
            ],
            "target_residual": 0.18243026085446812,
            "energy_eV": -34.70175452517253,
            "max_atomic_step_A": 0.026318471592343465,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2889487216649955,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6406684018998223,
            "cell_principal_stretches": [
              1.0515060389684554,
              1.0151796279529566,
              0.9495073344816553
            ],
            "cell_volume_ratio": 1.01356822952492,
            "cell_rmsd_from_input_A": 0.6217954120793687
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0011165700312133016,
              0.4328303762931493,
              0.38324993592275547
            ],
            "branch_aligned_reduced_polarization": [
              0.0011165700312133016,
              0.4328303762931493,
              0.38324993592275547
            ],
            "target_residual": 0.13469811631791748,
            "energy_eV": -34.686445788385655
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.13469811631791748,
        "parent_symmetrization_rmsd_A": 0.31862601114545064,
        "parent_cell_rmsd_A": 0.6217954120793687,
        "energy_eV": -34.686445788385655,
        "reduced_polarization": [
          0.0011165700312133016,
          0.4328303762931493,
          0.38324993592275547
        ],
        "cartesian_polarization_e_A2": [
          -0.002080764571716618,
          0.0036993965387865425,
          0.00648706355147841
        ],
        "ranking_score": 1.2434710968011278
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580503723e-07,
              1.5495913000603066e-06,
              0.003861787482572321
            ],
            "target_residual": 0.7043811942807662,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013052036770275374,
            "step_scale": 0.3393463112962269,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0144741752168007,
              1.004034124433573,
              0.9890774726162275
            ],
            "cell_volume_ratio": 1.0074413677075522,
            "cell_rmsd_from_input_A": 0.1665039493855166
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.16404624921423752,
              -0.004212790623830492,
              0.16961214041367598
            ],
            "branch_aligned_reduced_polarization": [
              0.1640462492142375,
              -0.004212790623830492,
              0.169612140413676
            ],
            "target_residual": 0.47120994050836296,
            "energy_eV": -40.033490195848266,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013979504882074641,
            "step_scale": 0.4842478462146573,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0302405826778762,
              1.0084188431639818,
              0.9774369542003493
            ],
            "cell_volume_ratio": 1.015472952026964,
            "cell_rmsd_from_input_A": 0.3501220614377499
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.30885340378731474,
              -0.005403073200615948,
              0.29356345676016043
            ],
            "branch_aligned_reduced_polarization": [
              0.30885340378731474,
              -0.005403073200615948,
              0.29356345676016043
            ],
            "target_residual": 0.28139342712387705,
            "energy_eV": -37.873818896526316,
            "max_atomic_step_A": 0.07762046086875121,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4610711632573357,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0517044525156272,
              1.0150760303499853,
              0.9620770454451771
            ],
            "cell_volume_ratio": 1.0270749521260216,
            "cell_rmsd_from_input_A": 0.6143971397457204
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.37608868735209533,
              -0.006250327641073195,
              0.33705150932782807
            ],
            "branch_aligned_reduced_polarization": [
              0.37608868735209533,
              -0.006250327641073195,
              0.33705150932782807
            ],
            "target_residual": 0.2048054945798243,
            "energy_eV": -35.408207208155275,
            "max_atomic_step_A": 0.0749541184815191,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3616734268898933,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0733257399710363,
              1.0218116084555795,
              0.9471822194766233
            ],
            "cell_volume_ratio": 1.0388095024040866,
            "cell_rmsd_from_input_A": 0.8878123791599778
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.40637633596142064,
              -0.00698908885816026,
              0.3474237001460396
            ],
            "branch_aligned_reduced_polarization": [
              0.40637633596142064,
              -0.00698908885816026,
              0.3474237001460396
            ],
            "target_residual": 0.17914732794044588,
            "energy_eV": -34.38603899333389,
            "max_atomic_step_A": 0.03182379834826457,
            "max_log_strain_component": 0.02,
            "step_scale": 0.30566562614307746,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.047110130128586,
            "cell_principal_stretches": [
              1.0558726517043313,
              1.0144784872884944,
              0.9447260906735244
            ],
            "cell_volume_ratio": 1.0119528847555064,
            "cell_rmsd_from_input_A": 0.6480805291096162
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4334270612778986,
              -0.004780254105277359,
              0.3894245336435705
            ],
            "branch_aligned_reduced_polarization": [
              0.4334270612778986,
              -0.004780254105277359,
              0.3894245336435705
            ],
            "target_residual": 0.12915781338869733,
            "energy_eV": -34.329438894776125
          }
        ],
        "iterations": 5
      },
      "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.12915781338869733,
        "parent_symmetrization_rmsd_A": 0.3034191590479137,
        "parent_cell_rmsd_A": 0.6480805291096162,
        "energy_eV": -34.329438894776125,
        "reduced_polarization": [
          0.4334270612778986,
          -0.004780254105277359,
          0.3894245336435705
        ],
        "cartesian_polarization_e_A2": [
          0.004172188215837139,
          -0.00024756861869967595,
          0.006566195254414855
        ],
        "ranking_score": 1.2237549181027125
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580503723e-07,
              1.549591300054054e-06,
              0.003861787482572304
            ],
            "target_residual": 0.7071160475817748,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011884255890100042,
            "step_scale": 0.7474848731027244,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0156472470207132,
              0.999928100008161,
              0.9845396321511289
            ],
            "cell_volume_ratio": 0.9998730709421146,
            "cell_rmsd_from_input_A": 0.11887452923074283
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3642455510246165,
              0.3639195964165964,
              -0.006898846839978312
            ],
            "branch_aligned_reduced_polarization": [
              0.3642455510246165,
              0.3639195964165964,
              -0.006898846839978312
            ],
            "target_residual": 0.19234016934523454,
            "energy_eV": -39.87027083606598,
            "max_atomic_step_A": 0.04533309520770522,
            "max_log_strain_component": 0.004964588498541948,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0223856042001767,
              1.0002628623209195,
              0.9783014780231866
            ],
            "cell_volume_ratio": 1.000464262946304,
            "cell_rmsd_from_input_A": 0.16908771454698956
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4934680324987369,
              0.4927959220024643,
              -0.0004949724334130594
            ],
            "branch_aligned_reduced_polarization": [
              0.4934680324987369,
              0.4927959220024643,
              -0.0004949724334130594
            ],
            "target_residual": 0.009737059974241418,
            "energy_eV": -39.03381401988587,
            "max_atomic_step_A": 0.0024660766128713984,
            "max_log_strain_component": 0.00029222065915603,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0227784503228017,
              1.0002835192921449,
              0.9779410089390801
            ],
            "cell_volume_ratio": 1.00050057044272,
            "cell_rmsd_from_input_A": 0.1720189891565749
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49980807205101807,
              0.49981213879131076,
              -2.6777608817260323e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49980807205101807,
              0.49981213879131076,
              -2.6777608817260323e-05
            ],
            "target_residual": 0.00026989852104923416,
            "energy_eV": -38.98122231624981
          }
        ],
        "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": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00026989852104923416,
        "parent_symmetrization_rmsd_A": 0.16932408674879187,
        "parent_cell_rmsd_A": 0.1720189891565749,
        "energy_eV": -38.98122231624981,
        "reduced_polarization": [
          0.49980807205101807,
          0.49981213879131076,
          -2.6777608817260323e-05
        ],
        "cartesian_polarization_e_A2": [
          0.002699045054319652,
          0.004505077023872103,
          -0.00011674550568624399
        ],
        "ranking_score": 0.7128686310800341
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.590660580655231e-07,
              1.5495913000603066e-06,
              0.003861787482572304
            ],
            "branch_aligned_reduced_polarization": [
              2.590660580503723e-07,
              1.549591300054054e-06,
              0.003861787482572321
            ],
            "target_residual": 0.8638005077939572,
            "energy_eV": -40.760922396264775,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014039806100784619,
            "step_scale": 0.3650270017306958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0163506238280513,
              1.0046979524480986,
              0.9871529178229859
            ],
            "cell_volume_ratio": 1.0080069089216541,
            "cell_rmsd_from_input_A": 0.1827699285568358
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1725983757327893,
              0.1683697973307998,
              0.17851756259142937
            ],
            "branch_aligned_reduced_polarization": [
              0.1725983757327893,
              0.16836979733079982,
              0.17851756259142937
            ],
            "target_residual": 0.5661460698948445,
            "energy_eV": -39.91664982798119,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0152272731166197,
            "step_scale": 0.5078779810794054,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0347348167314732,
              1.0098253702016813,
              0.9730712077618667
            ],
            "cell_volume_ratio": 1.0167635347885398,
            "cell_rmsd_from_input_A": 0.38933410895566845
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.31702547448124396,
              0.3111372581322489,
              0.2989069969315322
            ],
            "branch_aligned_reduced_polarization": [
              0.31702547448124396,
              0.3111372581322489,
              0.2989069969315322
            ],
            "target_residual": 0.331039586964631,
            "energy_eV": -37.42125600808589,
            "max_atomic_step_A": 0.07888915440324626,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4388763684547728,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0570320629371803,
              1.0166573616014831,
              0.9569539165340876
            ],
            "cell_volume_ratio": 1.02838040971037,
            "cell_rmsd_from_input_A": 0.6592587358734132
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3786409109309245,
              0.37039097628179846,
              0.3421102680319637
            ],
            "branch_aligned_reduced_polarization": [
              0.3786409109309245,
              0.37039097628179846,
              0.3421102680319637
            ],
            "target_residual": 0.23760407191333963,
            "energy_eV": -35.02956208842306,
            "max_atomic_step_A": 0.06441231434376683,
            "max_log_strain_component": 0.02,
            "step_scale": 0.37846421947363984,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7607166416252535,
            "cell_principal_stretches": [
              1.0794733677763555,
              1.0235548553645328,
              0.9413791424928377
            ],
            "cell_volume_ratio": 1.040130009240318,
            "cell_rmsd_from_input_A": 0.9387539653183282
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.41413585893471966,
              0.40250568387833635,
              0.35340534249388345
            ],
            "branch_aligned_reduced_polarization": [
              0.41413585893471966,
              0.40250568387833635,
              0.35340534249388345
            ],
            "target_residual": 0.19587696650255962,
            "energy_eV": -33.700375692756744,
            "max_atomic_step_A": 0.027253575198448246,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.29479377074209306,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.058278246403683,
            "cell_principal_stretches": [
              1.061252122790829,
              1.018926527133055,
              0.9378453022463722
            ],
            "cell_volume_ratio": 1.0141277070645822,
            "cell_rmsd_from_input_A": 0.6969931132096737
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.43892821582890723,
              0.43058674654019563,
              0.39195881467523136
            ],
            "branch_aligned_reduced_polarization": [
              0.43892821582890723,
              0.43058674654019563,
              0.39195881467523136
            ],
            "target_residual": 0.14220007139272675,
            "energy_eV": -33.52731374928472
          }
        ],
        "iterations": 5
      },
      "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": 0.14220007139272675,
        "parent_symmetrization_rmsd_A": 0.2955205197495439,
        "parent_cell_rmsd_A": 0.6969931132096737,
        "energy_eV": -33.52731374928472,
        "reduced_polarization": [
          0.43892821582890723,
          0.43058674654019563,
          0.39195881467523136
        ],
        "cartesian_polarization_e_A2": [
          0.002108726674207484,
          0.0034686543196064804,
          0.0065526699607040325
        ],
        "ranking_score": 1.254168940837416
      },
      "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
        ],
        "endpoint_rmsd_A": 0.0019170071184952996,
        "minimum_distance_A_by_image": [
          2.5689491195676317,
          2.56875776709981,
          2.5685664453604167,
          2.5683751543488604,
          2.568183894064554,
          2.5679926645069013,
          2.5678014656753083,
          2.567610297569186,
          2.5674191601879395
        ],
        "minimum_distance_A": 2.5674191601879395,
        "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": [
          818.3244352818833,
          818.3070405025572,
          818.2896460929848,
          818.2722520531564,
          818.2548583830674,
          818.2374650827082,
          818.2200721520705,
          818.202679591147,
          818.1852873999306
        ],
        "cell_deformation_log_strain_norm": 0.0003913534808022488
      },
      "parent_reduced_polarization": [
        -6.598936331094585e-10,
        -1.2329743713592442e-09,
        1.0007067542832658e-06
      ],
      "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": [
          -40.760922396264775,
          -40.761063823956604,
          -40.76119711242222,
          -40.76132225851033,
          -40.761439259053475,
          -40.76154811086809,
          -40.76164881075441,
          -40.761741355496454,
          -40.761825741862154
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.573024155692e-09,
            1.3980353008394677e-08,
            6.370465562703373e-05
          ],
          [
            -4.000966351153901e-09,
            1.2233471624924503e-08,
            5.573925233491566e-05
          ],
          [
            -3.429064121213458e-09,
            1.0486001865186862e-08,
            4.777509048749002e-05
          ],
          [
            -2.85731740490344e-09,
            8.737944441059759e-09,
            3.981217576897522e-05
          ],
          [
            -2.285726168090543e-09,
            6.989300415492101e-09,
            3.185051382938623e-05
          ],
          [
            -1.7142904990893147e-09,
            5.240070359481106e-09,
            2.389011028498629e-05
          ],
          [
            -1.1430102495440664e-09,
            3.4902552867208842e-09,
            1.5930970718359225e-05
          ],
          [
            -5.718853676213375e-10,
            1.739855860250364e-09,
            7.973100678636072e-06
          ],
          [
            -9.15963114796619e-13,
            -1.1126912002905876e-11,
            1.6505681786039623e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094585e-10,
            -1.2329743713592442e-09,
            1.0007067542832658e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094589e-10,
            -1.2329743713592355e-09,
            1.0007067542832683e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.590660570511716e-07,
            1.5495912983887195e-06,
            0.0038617874825717102
          ],
          [
            2.2670845123418104e-07,
            1.3559025187070972e-06,
            0.0033789779498493155
          ],
          [
            1.9431984710216454e-07,
            1.1621666166083955e-06,
            0.0028962280652671257
          ],
          [
            1.6190029294982367e-07,
            9.683836769136533e-07,
            0.002413538176691543
          ],
          [
            1.2944985239293771e-07,
            7.745538233017157e-07,
            0.001930908629937833
          ],
          [
            9.696855185481468e-08,
            5.806771249394771e-07,
            0.0014483397687969912
          ],
          [
            6.445646383301806e-08,
            3.8675369995466724e-07,
            0.0009658319350406286
          ],
          [
            3.1913633180558065e-08,
            1.9278362761721013e-07,
            0.0004833854684341832
          ],
          [
            -6.598936397317345e-10,
            -1.2329743892536271e-09,
            1.0007067542394665e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -40.761825741862154,
          -40.76174999837161,
          -40.76166659545234,
          -40.76157553621839,
          -40.761476823769335,
          -40.761370461190424,
          -40.761256451552406,
          -40.761134797911694,
          -40.761005503310216
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.159753102364387e-13,
            -1.1126909373847222e-11,
            1.650568178468269e-08
          ],
          [
            6.128720515468366e-10,
            -1.701629956555833e-09,
            -6.6961776664785385e-06
          ],
          [
            1.2268059212605321e-09,
            -3.3920054234964147e-09,
            -1.3410814666446668e-05
          ],
          [
            1.8408858726035802e-09,
            -5.082252235735235e-09,
            -2.0127401472220657e-05
          ],
          [
            2.4551118314414874e-09,
            -6.7723695421340746e-09,
            -2.6845934194865184e-05
          ],
          [
            3.069483827609624e-09,
            -8.462356218200403e-09,
            -3.3566408902454584e-05
          ],
          [
            3.6840019816440817e-09,
            -1.015221117140451e-08,
            -4.0288821619341794e-05
          ],
          [
            4.298666264482142e-09,
            -1.1841933632042388e-08,
            -4.7013168326547035e-05
          ],
          [
            4.91347665204054e-09,
            -1.3531522372249406e-08,
            -5.373944496109217e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.598947139025517e-10,
            -1.2329740798357897e-09,
            1.0007067542009977e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.598947139025517e-10,
            -1.2329740798357897e-09,
            1.0007067542009977e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.6038649110156973e-07,
          -1.5520579264804928e-06,
          -0.003859786327877894
        ],
        "actual_opposite_endpoint_branch_residual": 0.000602091682094464
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094585e-10,
            -1.2329743713592442e-09,
            1.0007067542832658e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.590660570668428e-07,
            1.5495912983478793e-06,
            0.003861787482571699
          ],
          [
            2.267084512811661e-07,
            1.3559025187194813e-06,
            0.0033789779498492717
          ],
          [
            1.9431984708404487e-07,
            1.1621666166464948e-06,
            0.0028962280652671205
          ],
          [
            1.6190029289505465e-07,
            9.683836769429169e-07,
            0.0024135381766915644
          ],
          [
            1.2944985238595538e-07,
            7.745538233086115e-07,
            0.0019309086299377804
          ],
          [
            9.696855185830404e-08,
            5.806771248997871e-07,
            0.0014483397687969852
          ],
          [
            6.44564638070655e-08,
            3.8675369990968905e-07,
            0.0009658319350406786
          ],
          [
            3.191363316509017e-08,
            1.9278362764941477e-07,
            0.00048338546843421657
          ],
          [
            -6.598936331094589e-10,
            -1.2329743713592355e-09,
            1.0007067542832683e-06
          ],
          [
            -2.5878790125794215e-08,
            -1.8855165272211e-07,
            -0.00040596940995620966
          ],
          [
            -5.1089781015752056e-08,
            -3.7587270513604287e-07,
            -0.0008130448111885898
          ],
          [
            -7.629278863003865e-08,
            -5.631960128832356e-07,
            -0.0012202252583600629
          ],
          [
            -1.0148777678777402e-07,
            -7.505214822464206e-07,
            -0.0016275105102939711
          ],
          [
            -1.2667468495659457e-07,
            -9.378489891942799e-07,
            -0.002034900323222874
          ],
          [
            -1.518534451769535e-07,
            -1.125178413213481e-06,
            -0.0024423944507444397
          ],
          [
            -1.770240208805388e-07,
            -1.3125096695460065e-06,
            -0.0028499926438452093
          ],
          [
            -2.0218635156035008e-07,
            -1.4998426226323927e-06,
            -0.003257694650860476
          ]
        ],
        "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": [
          [
            2.590660570511716e-07,
            1.5495912983887195e-06,
            0.0038617874825717102
          ],
          [
            2.2670845123418104e-07,
            1.3559025187070972e-06,
            0.0033789779498493155
          ],
          [
            1.9431984710216454e-07,
            1.1621666166083955e-06,
            0.0028962280652671257
          ],
          [
            1.6190029294982367e-07,
            9.683836769136533e-07,
            0.002413538176691543
          ],
          [
            1.2944985239293771e-07,
            7.745538233017157e-07,
            0.001930908629937833
          ],
          [
            9.696855185481468e-08,
            5.806771249394771e-07,
            0.0014483397687969912
          ],
          [
            6.445646383301806e-08,
            3.8675369995466724e-07,
            0.0009658319350406286
          ],
          [
            3.1913633180558065e-08,
            1.9278362761721013e-07,
            0.0004833854684341832
          ],
          [
            -6.598936397317345e-10,
            -1.2329743892536271e-09,
            1.0007067542394665e-06
          ],
          [
            -2.5878790110844818e-08,
            -1.8855165273556906e-07,
            -0.00040596940995618613
          ],
          [
            -5.1089781016866453e-08,
            -3.758727051272892e-07,
            -0.0008130448111886013
          ],
          [
            -7.629278864218492e-08,
            -5.631960128815727e-07,
            -0.0012202252583600748
          ],
          [
            -1.014877767935296e-07,
            -7.505214822400852e-07,
            -0.0016275105102939724
          ],
          [
            -1.2667468496374568e-07,
            -9.378489891909148e-07,
            -0.002034900323222899
          ],
          [
            -1.5185344515167287e-07,
            -1.125178413219352e-06,
            -0.002442394450744456
          ],
          [
            -1.7702402088648483e-07,
            -1.3125096695598693e-06,
            -0.0028499926438452228
          ],
          [
            -2.0218635155000442e-07,
            -1.499842622654235e-06,
            -0.0032576946508604543
          ]
        ]
      },
      "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": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0007077324999857e-06,
        "parent_symmetrization_rmsd_A": 0.0019170071184952996,
        "parent_cell_rmsd_A": 0.0036306773047364575,
        "energy_eV": -40.761825741862154,
        "reduced_polarization": [
          -6.598945133688728e-10,
          -1.2329770177159436e-09,
          1.0007067553445254e-06
        ],
        "cartesian_polarization_e_A2": [
          -9.159597012607863e-13,
          -1.1126935884935454e-11,
          1.6505681803544065e-08
        ],
        "ranking_score": 0.5028266778601445
      }
    }
  ],
  "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": 113,
      "full_response": 31,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 138,
      "full_response": 56,
      "energy_polarization": 82
    },
    "elapsed_seconds": 265.3771740650409
  }
}