{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Cu8K4Se16Ta4",
  "input_spacegroup": "Ama2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -158.7740580271584,
  "input_cartesian_polarization_e_A2": [
    5.485156801122819e-18,
    2.6796854334739308e-17,
    0.0009076729725000994
  ],
  "input_reduced_polarization": [
    6.030070512785107e-16,
    1.194682767743897e-15,
    0.13621370185703002
  ],
  "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": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.164586002254475e-16,
      "parent_symmetrization_rmsd_A": 0.8427738625981971,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -112.63561443673916,
      "reduced_polarization": [
        6.274413565423439e-16,
        4.0977041792181973e-16,
        -5.275432822277875e-16
      ],
      "cartesian_polarization_e_A2": [
        5.707419534890957e-18,
        9.191191583412999e-18,
        -3.51533489343636e-18
      ],
      "ranking_score": 0.842773862598199
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5425175597171872e-15,
      "parent_symmetrization_rmsd_A": 0.8489251705299302,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -106.17154517438946,
      "reduced_polarization": [
        1.9760338532096983e-16,
        4.039990035848927e-16,
        -1.4754992813444445e-15
      ],
      "cartesian_polarization_e_A2": [
        1.797467460156775e-18,
        9.061738180829718e-18,
        -9.832129957273843e-18
      ],
      "ranking_score": 0.8489251705299333
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.16102746236586e-16,
      "parent_symmetrization_rmsd_A": 0.9051281243203403,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -110.9129766623927,
      "reduced_polarization": [
        -1.908035773445683e-16,
        8.960120758079225e-16,
        7.723607367447477e-19
      ],
      "cartesian_polarization_e_A2": [
        -1.7356140989249154e-18,
        2.009764075105448e-17,
        5.1466993129611546e-21
      ],
      "ranking_score": 0.9051281243203422
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00032606070174159244,
      "parent_symmetrization_rmsd_A": 0.016782047564391302,
      "parent_cell_rmsd_A": 0.06857298073522305,
      "energy_eV": -158.70246573508848,
      "reduced_polarization": [
        -6.410217737722277e-15,
        3.699688011985291e-14,
        0.00032606070174159244
      ],
      "cartesian_polarization_e_A2": [
        -5.850947464774127e-17,
        8.268743487762888e-16,
        2.1725010256517823e-06
      ],
      "ranking_score": 0.5345774141516803
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.5773887218394e-15,
      "parent_symmetrization_rmsd_A": 0.8427945174625839,
      "parent_cell_rmsd_A": 0.06857298073522305,
      "energy_eV": -111.25365187224536,
      "reduced_polarization": [
        1.948042974354212e-15,
        9.063184629603355e-15,
        -2.406280879076093e-15
      ],
      "cartesian_polarization_e_A2": [
        1.7779668042774406e-17,
        2.0256059416684542e-16,
        -1.603274374948153e-17
      ],
      "ranking_score": 0.8599377626464089
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0352833861849084e-15,
      "parent_symmetrization_rmsd_A": 0.8489456757328916,
      "parent_cell_rmsd_A": 0.06857298073522305,
      "energy_eV": -105.21759325444847,
      "reduced_polarization": [
        -3.371901576636697e-16,
        -8.860493599548332e-16,
        -4.159699736866478e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.077513766111012e-18,
        -1.9803048503212362e-17,
        -2.7715550805345987e-18
      ],
      "ranking_score": 0.8660889209166994
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "pointgroup": "mm2",
      "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": 1.9434254579786536e-05,
      "parent_symmetrization_rmsd_A": 0.04517047950543517,
      "parent_cell_rmsd_A": 0.18680513374789834,
      "energy_eV": -157.99453373414198,
      "reduced_polarization": [
        1.001674481516356e-15,
        -4.876617881040024e-15,
        0.4999805657454202
      ],
      "cartesian_polarization_e_A2": [
        2.843854511503359e-17,
        -9.85585330423464e-17,
        0.003332640419484735
      ],
      "ranking_score": 0.5919106314515693
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0390239713670527,
      "parent_symmetrization_rmsd_A": 0.4436831456560029,
      "parent_cell_rmsd_A": 0.19326391871726142,
      "energy_eV": -141.25210530180343,
      "reduced_polarization": [
        -5.924637919059633e-14,
        0.46100055150023456,
        0.001383241833770115
      ],
      "cartesian_polarization_e_A2": [
        1.351291433909101e-15,
        0.010440035320568931,
        5.720309744068931e-05
      ],
      "ranking_score": 1.0700470680694236
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005038044126921267,
      "parent_symmetrization_rmsd_A": 0.143110571029403,
      "parent_cell_rmsd_A": 0.1464012372170245,
      "energy_eV": -153.1766806661865,
      "reduced_polarization": [
        0.49967894018479236,
        -1.726985912261404e-15,
        -0.00038825182717779625
      ],
      "cartesian_polarization_e_A2": [
        0.004557736286418858,
        -3.8016937757806285e-16,
        -0.00019184512301310925
      ],
      "ranking_score": 0.6807184891590434
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 0.10277180459685319,
      "parent_symmetrization_rmsd_A": 0.4216417164337423,
      "parent_cell_rmsd_A": 0.10207603740967315,
      "energy_eV": -145.8624787606367,
      "reduced_polarization": [
        1.5331051728277675e-14,
        0.43000213677714566,
        0.4247514587229204
      ],
      "cartesian_polarization_e_A2": [
        2.5970689932901176e-15,
        0.009961743383117345,
        0.002931242838292391
      ],
      "ranking_score": 1.152704334979867
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.7539303021005655e-07,
      "parent_symmetrization_rmsd_A": 0.18034661771367694,
      "parent_cell_rmsd_A": 0.33022563810651,
      "energy_eV": -147.6393589398295,
      "reduced_polarization": [
        0.5000004363919085,
        1.5646023497163987e-16,
        0.4999998114247223
      ],
      "cartesian_polarization_e_A2": [
        0.004334566148137951,
        -7.155363901017417e-16,
        0.003125098045204629
      ],
      "ranking_score": 0.7629039780263649
    },
    {
      "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": 0.016585017971284144,
      "parent_symmetrization_rmsd_A": 0.4589515169087621,
      "parent_cell_rmsd_A": 0.2152940029211576,
      "energy_eV": -137.19013639918631,
      "reduced_polarization": [
        0.4904815808979312,
        0.48652424920252757,
        0.0016931211857427616
      ],
      "cartesian_polarization_e_A2": [
        0.004534095569403353,
        0.011076941649673468,
        -7.098104690277274e-05
      ],
      "ranking_score": 1.0459450535816197
    },
    {
      "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": 0.10831960417168375,
      "parent_symmetrization_rmsd_A": 0.4341128038342434,
      "parent_cell_rmsd_A": 0.15878757410290253,
      "energy_eV": -140.7480865717775,
      "reduced_polarization": [
        0.450511730664008,
        0.44266583050867614,
        0.42256072795552174
      ],
      "cartesian_polarization_e_A2": [
        0.004031411072145762,
        0.010270790746535087,
        0.002797468587769014
      ],
      "ranking_score": 1.1904489057033365
    }
  ],
  "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": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "target_residual": 0.13621370185703002,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.02339871450265164,
            "max_log_strain_component": 0.003525967205455387,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0035321907403325,
              1.00005934621912,
              0.9965882641062471
            ],
            "cell_volume_ratio": 1.0001677565971316,
            "cell_rmsd_from_input_A": 0.06857298073522305
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.410217737722277e-15,
              3.699688011985291e-14,
              0.00032606070174159244
            ],
            "branch_aligned_reduced_polarization": [
              -6.410217737722277e-15,
              3.699688011985291e-14,
              0.00032606070174159244
            ],
            "target_residual": 0.00032606070174159244,
            "energy_eV": -158.70246573508848
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ama2",
        "spacegroup_number": 40,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00032606070174159244,
        "parent_symmetrization_rmsd_A": 0.016782047564391302,
        "parent_cell_rmsd_A": 0.06857298073522305,
        "energy_eV": -158.70246573508848,
        "reduced_polarization": [
          -6.410217737722277e-15,
          3.699688011985291e-14,
          0.00032606070174159244
        ],
        "cartesian_polarization_e_A2": [
          -5.850947464774127e-17,
          8.268743487762888e-16,
          2.1725010256517823e-06
        ],
        "ranking_score": 0.5345774141516803
      },
      "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": [
          -158.77405802715842,
          -158.77589453292126,
          -158.77466326489034,
          -158.7703580431886,
          -158.76297210982634,
          -158.75249812904462,
          -158.73892818782082,
          -158.7222537913766,
          -158.7024657350885
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.54978961251148e-18,
            2.705576113990587e-17,
            0.0009076729725000865
          ],
          [
            5.4330876575004927e-17,
            7.501667384471106e-17,
            0.0007942175705658991
          ],
          [
            -9.559527101591609e-18,
            1.595446279388178e-16,
            0.000680808460324544
          ],
          [
            6.555855548636656e-17,
            2.3986206636128317e-16,
            0.0005674609163677796
          ],
          [
            -6.153418137351948e-17,
            3.7790751193206054e-16,
            0.00045419009796832425
          ],
          [
            -8.433726094925546e-17,
            4.587994828194089e-16,
            0.00034101104086550846
          ],
          [
            2.0717032165871276e-17,
            5.676464786952913e-16,
            0.00022793864917299405
          ],
          [
            1.3440301075978325e-17,
            7.355757150437653e-16,
            0.0001149876786993276
          ],
          [
            -3.08220551621946e-17,
            8.79294183049498e-16,
            2.1725010256276435e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393628e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.3046136569532905e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.3766243727024908e-15,
            3.934230489620395e-14,
            0.0003260607017379696
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393624e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.304613656953291e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.376624372702491e-15,
            3.934230489620395e-14,
            0.00032606070173796936
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            1.2212453270876722e-15,
            0.13621370185702808
          ],
          [
            5.995204332975845e-15,
            3.3306690738754696e-15,
            0.11918916229976517
          ],
          [
            -9.992007221626409e-16,
            7.105427357601002e-15,
            0.10217110850033007
          ],
          [
            7.216449660063518e-15,
            1.0658141036401503e-14,
            0.08516183306976366
          ],
          [
            -6.716849298982197e-15,
            1.687538997430238e-14,
            0.06816361143659055
          ],
          [
            -9.2148511043888e-15,
            2.0539125955565396e-14,
            0.051178700612846795
          ],
          [
            2.3314683517128287e-15,
            2.5424107263916085e-14,
            0.03420933797832815
          ],
          [
            1.4432899320127035e-15,
            3.2862601528904634e-14,
            0.01725773877594816
          ],
          [
            -3.3861802251067274e-15,
            3.930189507173054e-14,
            0.00032606070173801793
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -158.70246573508854,
          -158.68649432507516,
          -158.66876716022142,
          -158.64927918212703,
          -158.62802516832576,
          -158.60499985946177,
          -158.58019796394643,
          -158.55361415723274,
          -158.52524308103474
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0985612164640513e-17,
            9.214241980024106e-16,
            2.172501025642237e-06
          ],
          [
            -4.349395938150567e-18,
            8.625508648691979e-16,
            -8.70569964064894e-05
          ],
          [
            5.199334548910661e-18,
            1.027342401414782e-15,
            -0.00017626738258150302
          ],
          [
            1.8598507997111226e-21,
            1.0663900519700099e-15,
            -0.0002654562644700695
          ],
          [
            -7.220062704778055e-17,
            1.1961785640569179e-15,
            -0.0003546214222289789
          ],
          [
            -1.2588580792758633e-16,
            1.0871460142122163e-15,
            -0.0004437605819502457
          ],
          [
            -1.0894197129832411e-16,
            1.3010168625550412e-15,
            -0.0005328714051367943
          ],
          [
            -6.249476404719055e-17,
            1.286351489206029e-15,
            -0.0006219514870560408
          ],
          [
            -1.2548540818057257e-16,
            1.3956371332503598e-15,
            -0.0007109983548671756
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.2988869465637802e-15,
            4.1227331475715714e-14,
            0.00032606070174015983
          ],
          [
            -4.913704791893165e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064747e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.166347011834207e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.2988869465637802e-15,
            4.1227331475715714e-14,
            0.00032606070174015983
          ],
          [
            -4.913704791893163e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064748e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.1663470118342026e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.166691701323177e-15,
          7.71968283698718e-14,
          -0.13556165113842214
        ],
        "actual_opposite_endpoint_branch_residual": 0.0288627398951377
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393628e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.3046136569532905e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.3766243727024908e-15,
            3.934230489620395e-14,
            0.0003260607017379696
          ],
          [
            -4.913704791893165e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064747e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.166347011834207e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393624e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.304613656953291e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.376624372702491e-15,
            3.934230489620395e-14,
            0.00032606070173796936
          ],
          [
            -4.913704791893163e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064748e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.1663470118342026e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            1.2212453270876722e-15,
            0.13621370185702808
          ],
          [
            5.995204332975845e-15,
            3.3306690738754696e-15,
            0.11918916229976517
          ],
          [
            -9.992007221626409e-16,
            7.105427357601002e-15,
            0.10217110850033007
          ],
          [
            7.216449660063518e-15,
            1.0658141036401503e-14,
            0.08516183306976366
          ],
          [
            -6.716849298982197e-15,
            1.687538997430238e-14,
            0.06816361143659055
          ],
          [
            -9.2148511043888e-15,
            2.0539125955565396e-14,
            0.051178700612846795
          ],
          [
            2.3314683517128287e-15,
            2.5424107263916085e-14,
            0.03420933797832815
          ],
          [
            1.4432899320127035e-15,
            3.2862601528904634e-14,
            0.01725773877594816
          ],
          [
            -3.3861802251067274e-15,
            3.930189507173054e-14,
            0.00032606070173801793
          ],
          [
            -4.996003610813204e-16,
            3.852473895449293e-14,
            -0.013065807742152769
          ],
          [
            5.551115123125783e-16,
            4.596323321948148e-14,
            -0.026454445032309704
          ],
          [
            -5.551115123125783e-17,
            4.7628567756419216e-14,
            -0.03983949214851501
          ],
          [
            -7.93809462606987e-15,
            5.340172748447003e-14,
            -0.05322061608131545
          ],
          [
            -1.3877787807814457e-14,
            4.851674617611934e-14,
            -0.06659747572552616
          ],
          [
            -1.199040866595169e-14,
            5.806466418789569e-14,
            -0.07996972030136212
          ],
          [
            -6.8833827526759706e-15,
            5.739853037312059e-14,
            -0.09333698910801408
          ],
          [
            -1.3822276656583199e-14,
            6.217248937900877e-14,
            -0.10669891124328446
          ]
        ]
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "target_residual": 0.36378629814297,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.06249100945188645,
            "max_log_strain_component": 0.009416810053312033,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0091690919618042,
              0.9998415211557335,
              0.9906273892548435
            ],
            "cell_volume_ratio": 0.9995521099153657,
            "cell_rmsd_from_input_A": 0.18532140703683936
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1299114530605444e-14,
              -1.087369763223982e-13,
              0.49720631603849763
            ],
            "branch_aligned_reduced_polarization": [
              1.1299114530605444e-14,
              -1.087369763223982e-13,
              0.49720631603849763
            ],
            "target_residual": 0.002793683961502369,
            "energy_eV": -158.00599601396937,
            "max_atomic_step_A": 0.00048742318011931883,
            "max_log_strain_component": 7.474117368926391e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0092422022718284,
              0.9998402634104169,
              0.9905533513679557
            ],
            "cell_volume_ratio": 0.9995485558165731,
            "cell_rmsd_from_input_A": 0.18680513374789834
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.001674481516356e-15,
              -4.876617881040024e-15,
              0.4999805657454202
            ],
            "branch_aligned_reduced_polarization": [
              1.001674481516356e-15,
              -4.876617881040024e-15,
              0.4999805657454202
            ],
            "target_residual": 1.9434254579786536e-05,
            "energy_eV": -157.99453373414198
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ama2",
        "spacegroup_number": 40,
        "pointgroup": "mm2",
        "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": 1.9434254579786536e-05,
        "parent_symmetrization_rmsd_A": 0.04517047950543517,
        "parent_cell_rmsd_A": 0.18680513374789834,
        "energy_eV": -157.99453373414198,
        "reduced_polarization": [
          1.001674481516356e-15,
          -4.876617881040024e-15,
          0.4999805657454202
        ],
        "cartesian_polarization_e_A2": [
          2.843854511503359e-17,
          -9.85585330423464e-17,
          0.003332640419484735
        ],
        "ranking_score": 0.5919106314515693
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.030070512785107e-16,
              1.2212453270876722e-15,
              0.13621370185703002
            ],
            "target_residual": 0.518222126673104,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006665031857332091,
            "step_scale": 0.2670021948597062,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0062523133690058,
              1.0009418842774211,
              0.9928958525012003
            ],
            "cell_volume_ratio": 1.0000447886260617,
            "cell_rmsd_from_input_A": 0.05821298331965531
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.676635283798748e-14,
              0.1297324834107079,
              0.10154597780320701
            ],
            "branch_aligned_reduced_polarization": [
              3.676635283798748e-14,
              0.12973248341070787,
              0.10154597780320701
            ],
            "target_residual": 0.3839396039082334,
            "energy_eV": -156.98476274938383,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00536963717300917,
            "step_scale": 0.2881522668777091,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0104117081822093,
              1.0038377090570092,
              0.9860916082091395
            ],
            "cell_volume_ratio": 1.0001822403382976,
            "cell_rmsd_from_input_A": 0.12301298557292031
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.6740626179700814e-14,
              0.23230804418879558,
              0.065141120689043
            ],
            "branch_aligned_reduced_polarization": [
              3.6740626179700814e-14,
              0.23230804418879558,
              0.065141120689043
            ],
            "target_residual": 0.2755038090674107,
            "energy_eV": -153.40023674502768,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005309972528297034,
            "step_scale": 0.3606714634291421,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0150079136863723,
              1.0056152750461982,
              0.9799736588337145
            ],
            "cell_volume_ratio": 1.00026642642488,
            "cell_rmsd_from_input_A": 0.17686391147983271
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.2542779174917e-14,
              0.31767409851812395,
              0.032641026942537434
            ],
            "branch_aligned_reduced_polarization": [
              5.2542779174917e-14,
              0.31767409851812395,
              0.032641026942537434
            ],
            "target_residual": 0.18522465006321978,
            "energy_eV": -148.84615495923077,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0072158526592137765,
            "step_scale": 0.5130110675877861,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0224832353920121,
              1.0051743940125526,
              0.9732155045419153
            ],
            "cell_volume_ratio": 1.0002455593848827,
            "cell_rmsd_from_input_A": 0.22225861057629037
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              5.002205164804714e-14,
              0.3986953289195973,
              0.0010514947699728093
            ],
            "branch_aligned_reduced_polarization": [
              5.002205164804714e-14,
              0.3986953289195973,
              0.0010514947699728093
            ],
            "target_residual": 0.10131012794365556,
            "energy_eV": -142.48587753666504,
            "max_atomic_step_A": 0.06195188651059428,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6356028044935447,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.171506568769496,
            "cell_principal_stretches": [
              0.9970503970259771,
              0.996487726274377,
              0.9873332161919152
            ],
            "cell_volume_ratio": 0.9809634192749334,
            "cell_rmsd_from_input_A": 0.19326391871726142
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -5.924637919059633e-14,
              0.46100055150023456,
              0.001383241833770115
            ],
            "branch_aligned_reduced_polarization": [
              -5.924637919059633e-14,
              0.46100055150023456,
              0.001383241833770115
            ],
            "target_residual": 0.0390239713670527,
            "energy_eV": -141.25210530180343
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0390239713670527,
        "parent_symmetrization_rmsd_A": 0.4436831456560029,
        "parent_cell_rmsd_A": 0.19326391871726142,
        "energy_eV": -141.25210530180343,
        "reduced_polarization": [
          -5.924637919059633e-14,
          0.46100055150023456,
          0.001383241833770115
        ],
        "cartesian_polarization_e_A2": [
          1.351291433909101e-15,
          0.010440035320568931,
          5.720309744068931e-05
        ],
        "ranking_score": 1.0700470680694236
      },
      "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": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.106226635438361e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "target_residual": 0.5182221266731046,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.07471415801742744,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.5188244017500057,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0211712789487166,
              0.998228452783032,
              0.9810909286024868
            ],
            "cell_volume_ratio": 1.0000870327036504,
            "cell_rmsd_from_input_A": 0.07668564088093824
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.25554988636125453,
              3.0910474310951085e-14,
              0.05043246913407907
            ],
            "branch_aligned_reduced_polarization": [
              0.25554988636125453,
              3.0910474310951085e-14,
              0.05043246913407907
            ],
            "target_residual": 0.24959826121380616,
            "energy_eV": -157.42572966372904,
            "max_atomic_step_A": 0.07783777271864942,
            "max_log_strain_component": 0.01965158692311849,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0417992653291441,
              0.997565733913904,
              0.9623352251717665
            ],
            "cell_volume_ratio": 1.000119632459149,
            "cell_rmsd_from_input_A": 0.14360485536138037
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48139608009138485,
              1.4928184103223833e-14,
              -0.015154457923003198
            ],
            "branch_aligned_reduced_polarization": [
              0.48139608009138485,
              1.4928184103223833e-14,
              -0.015154457923003198
            ],
            "target_residual": 0.023995070971060736,
            "energy_eV": -153.68280535886305,
            "max_atomic_step_A": 0.005877049445805764,
            "max_log_strain_component": 0.001696791584794907,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0433082696002487,
              0.9980265637512212,
              0.9604778575332908
            ],
            "cell_volume_ratio": 1.0000969614068453,
            "cell_rmsd_from_input_A": 0.14616815020796864
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49766406432357874,
              -7.571243227568432e-15,
              -0.0027685193854971165
            ],
            "branch_aligned_reduced_polarization": [
              0.49766406432357874,
              -7.571243227568432e-15,
              -0.0027685193854971165
            ],
            "target_residual": 0.0036223328218498913,
            "energy_eV": -153.23735842674805,
            "max_atomic_step_A": 0.0007736548237553113,
            "max_log_strain_component": 0.00021607712555646105,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.043485786153369,
              0.9981119200125914,
              0.9602283076224106
            ],
            "cell_volume_ratio": 1.0000927634131398,
            "cell_rmsd_from_input_A": 0.1464012372170245
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49967894018479236,
              -1.726985912261404e-15,
              -0.00038825182717779625
            ],
            "branch_aligned_reduced_polarization": [
              0.49967894018479236,
              -1.726985912261404e-15,
              -0.00038825182717779625
            ],
            "target_residual": 0.0005038044126921267,
            "energy_eV": -153.1766806661865
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005038044126921267,
        "parent_symmetrization_rmsd_A": 0.143110571029403,
        "parent_cell_rmsd_A": 0.1464012372170245,
        "energy_eV": -153.1766806661865,
        "reduced_polarization": [
          0.49967894018479236,
          -1.726985912261404e-15,
          -0.00038825182717779625
        ],
        "cartesian_polarization_e_A2": [
          0.004557736286418858,
          -3.8016937757806285e-16,
          -0.00019184512301310925
        ],
        "ranking_score": 0.6807184891590434
      },
      "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": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.030070512785107e-16,
              1.2212453270876722e-15,
              0.13621370185703002
            ],
            "target_residual": 0.6183368586107127,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0063786282944820515,
            "step_scale": 0.2555288243592488,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0076631308231108,
              0.9975966263360665,
              0.9946721175373144
            ],
            "cell_volume_ratio": 0.9998855320873271,
            "cell_rmsd_from_input_A": 0.07163413850198705
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.7723008926793675e-14,
              0.12908237571294057,
              0.22376653169366054
            ],
            "branch_aligned_reduced_polarization": [
              2.7723008926793675e-14,
              0.12908237571294057,
              0.22376653169366056
            ],
            "target_residual": 0.46247682430507325,
            "energy_eV": -157.2736250288566,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004927236576843305,
            "step_scale": 0.2777063193227232,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0130664138802141,
              0.9967274454758908,
              0.9901886427594734
            ],
            "cell_volume_ratio": 0.9998440700498646,
            "cell_rmsd_from_input_A": 0.11570396420269792
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.559123208567179e-14,
              0.22754817233769303,
              0.2794635830101591
            ],
            "branch_aligned_reduced_polarization": [
              4.559123208567179e-14,
              0.22754817233769303,
              0.2794635830101591
            ],
            "target_residual": 0.3505229088308614,
            "energy_eV": -154.6241685822448,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0053552461434579,
            "step_scale": 0.33359189743823325,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0200800726482038,
              0.9938378487764807,
              0.9861034873836697
            ],
            "cell_volume_ratio": 0.9997059812985037,
            "cell_rmsd_from_input_A": 0.18869057891800523
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.3348005254190586e-14,
              0.3064382497710056,
              0.32463817257245514
            ],
            "branch_aligned_reduced_polarization": [
              5.3348005254190586e-14,
              0.3064382497710056,
              0.32463817257245514
            ],
            "target_residual": 0.26118560770157234,
            "energy_eV": -151.37371377851025,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008350790404215658,
            "step_scale": 0.46782978089008104,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0328676916963133,
              0.9865452864863111,
              0.9807502052434628
            ],
            "cell_volume_ratio": 0.999355774952545,
            "cell_rmsd_from_input_A": 0.3508590078849459
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              5.2224057648453205e-14,
              0.3804916913418784,
              0.36676368808994403
            ],
            "branch_aligned_reduced_polarization": [
              5.2224057648453205e-14,
              0.3804916913418784,
              0.36676368808994403
            ],
            "target_residual": 0.17898086671406693,
            "energy_eV": -146.43349389891424,
            "max_atomic_step_A": 0.044521468585102586,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4357670868746348,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.93345333810808,
            "cell_principal_stretches": [
              1.0048291436191874,
              0.9890215628830502,
              0.9786908121875582
            ],
            "cell_volume_ratio": 0.972620668427782,
            "cell_rmsd_from_input_A": 0.10207603740967315
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.5331051728277675e-14,
              0.43000213677714566,
              0.4247514587229204
            ],
            "branch_aligned_reduced_polarization": [
              1.5331051728277675e-14,
              0.43000213677714566,
              0.4247514587229204
            ],
            "target_residual": 0.10277180459685319,
            "energy_eV": -145.8624787606367
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 0.10277180459685319,
        "parent_symmetrization_rmsd_A": 0.4216417164337423,
        "parent_cell_rmsd_A": 0.10207603740967315,
        "energy_eV": -145.8624787606367,
        "reduced_polarization": [
          1.5331051728277675e-14,
          0.43000213677714566,
          0.4247514587229204
        ],
        "cartesian_polarization_e_A2": [
          2.5970689932901176e-15,
          0.009961743383117345,
          0.002931242838292391
        ],
        "ranking_score": 1.152704334979867
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.106226635438361e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "target_residual": 0.6183368586107133,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.08436631979144321,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.5188244017500945,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0178165955692178,
              1.0047467017551825,
              0.9776264445755471
            ],
            "cell_volume_ratio": 0.9997675986491145,
            "cell_rmsd_from_input_A": 0.11687475450721845
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24622552901949532,
              -4.7324599824900526e-14,
              0.30154008726382564
            ],
            "branch_aligned_reduced_polarization": [
              0.24622552901949535,
              -4.7324599824900526e-14,
              0.30154008726382564
            ],
            "target_residual": 0.3221611694240709,
            "energy_eV": -156.8707019955595,
            "max_atomic_step_A": 0.07234380819123505,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9074198863788229,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0353584457570308,
              1.0107711115615903,
              0.9550543274796974
            ],
            "cell_volume_ratio": 0.9994742930366953,
            "cell_rmsd_from_input_A": 0.2550539536385624
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.44682469767667676,
              -6.740847356914822e-14,
              0.42956118500641455
            ],
            "branch_aligned_reduced_polarization": [
              0.44682469767667676,
              -6.740847356914822e-14,
              0.42956118500641455
            ],
            "target_residual": 0.08825666793436847,
            "energy_eV": -150.69219034501248,
            "max_atomic_step_A": 0.018176022749124617,
            "max_log_strain_component": 0.005576359452775726,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0397583384461557,
              1.0136325811040308,
              0.9481966014134706
            ],
            "cell_volume_ratio": 0.9993356207541995,
            "cell_rmsd_from_input_A": 0.31436775130620614
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4886803664797925,
              -2.9549492611079925e-14,
              0.4833853310080339
            ],
            "branch_aligned_reduced_polarization": [
              0.4886803664797925,
              -2.9549492611079925e-14,
              0.4833853310080339
            ],
            "target_residual": 0.020104261457323056,
            "energy_eV": -148.26943003460067,
            "max_atomic_step_A": 0.004157062213966242,
            "max_log_strain_component": 0.001234858343766496,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.040706464764938,
              1.0143324821321358,
              0.9466470128233463
            ],
            "cell_volume_ratio": 0.9993017647218979,
            "cell_rmsd_from_input_A": 0.32876851005689267
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4973449911783956,
              -9.68012934026208e-15,
              0.49620087952123226
            ],
            "branch_aligned_reduced_polarization": [
              0.4973449911783956,
              -9.68012934026208e-15,
              0.49620087952123226
            ],
            "target_residual": 0.004634909735365904,
            "energy_eV": -147.70758746135374,
            "max_atomic_step_A": 0.0010984452795976373,
            "max_log_strain_component": 0.0001422548107046812,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.3642302011117016,
            "cell_principal_stretches": [
              1.0406990932152425,
              1.0144295184037158,
              0.9469047027344408
            ],
            "cell_volume_ratio": 0.9996623314604803,
            "cell_rmsd_from_input_A": 0.33022563810651
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000004363919085,
              1.5646023497163987e-16,
              0.4999998114247223
            ],
            "branch_aligned_reduced_polarization": [
              0.5000004363919085,
              1.5646023497163987e-16,
              0.4999998114247223
            ],
            "target_residual": 4.7539303021005655e-07,
            "energy_eV": -147.6393589398295
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.7539303021005655e-07,
        "parent_symmetrization_rmsd_A": 0.18034661771367694,
        "parent_cell_rmsd_A": 0.33022563810651,
        "energy_eV": -147.6393589398295,
        "reduced_polarization": [
          0.5000004363919085,
          1.5646023497163987e-16,
          0.4999998114247223
        ],
        "cartesian_polarization_e_A2": [
          0.004334566148137951,
          -7.155363901017417e-16,
          0.003125098045204629
        ],
        "ranking_score": 0.7629039780263649
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.106226635438361e-16,
              1.2212453270876722e-15,
              0.13621370185703002
            ],
            "target_residual": 0.7201070563281504,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010287781565454329,
            "step_scale": 0.2668776058019221,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.01256914577913,
              0.9996372742789743,
              0.9879894577861056
            ],
            "cell_volume_ratio": 1.0000447677262483,
            "cell_rmsd_from_input_A": 0.06783568254184728
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.13202225881093516,
              0.12976011312877608,
              0.09679730428370455
            ],
            "branch_aligned_reduced_polarization": [
              0.13202225881093516,
              0.1297601131287761,
              0.09679730428370455
            ],
            "target_residual": 0.5309000941397686,
            "energy_eV": -156.6277138395526,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007877179787098513,
            "step_scale": 0.28919404480686045,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0229962934522334,
              0.998711272315927,
              0.9789470092985361
            ],
            "cell_volume_ratio": 1.0001685538520146,
            "cell_rmsd_from_input_A": 0.13462063520266807
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.24082567837151805,
              0.23385819794915175,
              0.054729279797757185
            ],
            "branch_aligned_reduced_polarization": [
              0.24082567837151803,
              0.23385819794915175,
              0.054729279797757185
            ],
            "target_residual": 0.3754971129817617,
            "energy_eV": -152.38124167908217,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006177100616170876,
            "step_scale": 0.3748673703118512,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0315173548739147,
              0.9985368144802284,
              0.9710891266940845
            ],
            "cell_volume_ratio": 1.0002296212746804,
            "cell_rmsd_from_input_A": 0.1876497298207909
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3412047190017225,
              0.32360832853347876,
              0.017043424800952937
            ],
            "branch_aligned_reduced_polarization": [
              0.3412047190017225,
              0.32360832853347876,
              0.017043424800952937
            ],
            "target_residual": 0.23795050190957953,
            "energy_eV": -146.98258167499066,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0072553080941223135,
            "step_scale": 0.5706874777253086,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0384769098380555,
              0.9995779313181771,
              0.9635200054166282
            ],
            "cell_volume_ratio": 1.0001709587064078,
            "cell_rmsd_from_input_A": 0.23280349659360247
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4373947467931213,
              0.41334542021369214,
              -0.015813312506638155
            ],
            "branch_aligned_reduced_polarization": [
              0.4373947467931213,
              0.41334542021369214,
              -0.015813312506638155
            ],
            "target_residual": 0.10806708462557686,
            "energy_eV": -139.754963828002,
            "max_atomic_step_A": 0.07264858832643897,
            "max_log_strain_component": 0.02,
            "step_scale": 0.868671248855269,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.652154493989426,
            "cell_principal_stretches": [
              1.0222302265493628,
              0.9904383464514256,
              0.9637298454640247
            ],
            "cell_volume_ratio": 0.9757340791412709,
            "cell_rmsd_from_input_A": 0.2152940029211576
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4904815808979312,
              0.48652424920252757,
              0.0016931211857427616
            ],
            "branch_aligned_reduced_polarization": [
              0.4904815808979312,
              0.48652424920252757,
              0.0016931211857427616
            ],
            "target_residual": 0.016585017971284144,
            "energy_eV": -137.19013639918631
          }
        ],
        "iterations": 5
      },
      "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": 0.016585017971284144,
        "parent_symmetrization_rmsd_A": 0.4589515169087621,
        "parent_cell_rmsd_A": 0.2152940029211576,
        "energy_eV": -137.19013639918631,
        "reduced_polarization": [
          0.4904815808979312,
          0.48652424920252757,
          0.0016931211857427616
        ],
        "cartesian_polarization_e_A2": [
          0.004534095569403353,
          0.011076941649673468,
          -7.098104690277274e-05
        ],
        "ranking_score": 1.0459450535816197
      },
      "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": [
              6.030070512785107e-16,
              1.194682767743897e-15,
              0.13621370185703002
            ],
            "branch_aligned_reduced_polarization": [
              6.106226635438361e-16,
              1.2212453270876722e-15,
              0.13621370185703002
            ],
            "target_residual": 0.7951983845032409,
            "energy_eV": -158.7740580271584,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009846090851079055,
            "step_scale": 0.2554196097697369,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0114978835485164,
              1.0009000020214263,
              0.9876308269106692
            ],
            "cell_volume_ratio": 0.9998855810088229,
            "cell_rmsd_from_input_A": 0.07890724151153616
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1239218031559761,
              0.12909860742980642,
              0.21845087494489243
            ],
            "branch_aligned_reduced_polarization": [
              0.12392180315597612,
              0.1290986074298064,
              0.21845087494489246
            ],
            "target_residual": 0.5985587381128588,
            "energy_eV": -156.90606769840804,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00824535791999654,
            "step_scale": 0.27722807185345166,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0209395095846074,
              1.0014974959952039,
              0.9778558936268107
            ],
            "cell_volume_ratio": 0.999826714231094,
            "cell_rmsd_from_input_A": 0.13416049651697737
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.2253147746987582,
              0.22852183200056153,
              0.26539242454075906
            ],
            "branch_aligned_reduced_polarization": [
              0.2253147746987582,
              0.22852183200056153,
              0.26539242454075906
            ],
            "target_residual": 0.45187728772531677,
            "energy_eV": -153.39300091805927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007011294282052448,
            "step_scale": 0.3413161381574003,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.0297713391903238,
              1.0026621016066164,
              0.968166344475361
            ],
            "cell_volume_ratio": 0.9996440416653453,
            "cell_rmsd_from_input_A": 0.22252210504778
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3158476913708367,
              0.310741913896842,
              0.3026043574562463
            ],
            "branch_aligned_reduced_polarization": [
              0.3158476913708367,
              0.310741913896842,
              0.3026043574562463
            ],
            "target_residual": 0.32969036325640816,
            "energy_eV": -148.84000785574287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009228656818817063,
            "step_scale": 0.5050693726092879,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.345258104681287,
            "cell_principal_stretches": [
              1.041510976750365,
              1.0024572649957806,
              0.9570287627094892
            ],
            "cell_volume_ratio": 0.9992052549611059,
            "cell_rmsd_from_input_A": 0.4146751670224089
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4033422569252149,
              0.391207070551834,
              0.3431497405358534
            ],
            "branch_aligned_reduced_polarization": [
              0.4033422569252149,
              0.391207070551834,
              0.3431497405358534
            ],
            "target_residual": 0.21396407335857787,
            "energy_eV": -142.24752641451374,
            "max_atomic_step_A": 0.04279969613188639,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4967127956065075,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.3436460256251013,
            "cell_principal_stretches": [
              1.0147247611580523,
              1.0034333478540052,
              0.9553953945548556
            ],
            "cell_volume_ratio": 0.9727918685099645,
            "cell_rmsd_from_input_A": 0.15878757410290253
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.450511730664008,
              0.44266583050867614,
              0.42256072795552174
            ],
            "branch_aligned_reduced_polarization": [
              0.450511730664008,
              0.44266583050867614,
              0.42256072795552174
            ],
            "target_residual": 0.10831960417168375,
            "energy_eV": -140.7480865717775
          }
        ],
        "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": 0.10831960417168375,
        "parent_symmetrization_rmsd_A": 0.4341128038342434,
        "parent_cell_rmsd_A": 0.15878757410290253,
        "energy_eV": -140.7480865717775,
        "reduced_polarization": [
          0.450511730664008,
          0.44266583050867614,
          0.42256072795552174
        ],
        "cartesian_polarization_e_A2": [
          0.004031411072145762,
          0.010270790746535087,
          0.002797468587769014
        ],
        "ranking_score": 1.1904489057033365
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.016782047564391302,
        "minimum_distance_A_by_image": [
          2.418012370525955,
          2.413199325620327,
          2.408389428595412,
          2.4035826908277285,
          2.3987791237836453,
          2.3939787390201097,
          2.3891815481854017,
          2.384387563019869,
          2.379596795356689
        ],
        "minimum_distance_A": 2.379596795356689,
        "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": [
          857.6236718929908,
          857.6416545768227,
          857.6596376377154,
          857.6776210756767,
          857.6956048907169,
          857.7135890828417,
          857.7315736520598,
          857.7495585983787,
          857.7675439218083
        ],
        "cell_deformation_log_strain_norm": 0.004910778481934638
      },
      "parent_reduced_polarization": [
        -3.3766243727024908e-15,
        3.934230489620395e-14,
        0.0003260607017379696
      ],
      "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": [
          -158.77405802715842,
          -158.77589453292126,
          -158.77466326489034,
          -158.7703580431886,
          -158.76297210982634,
          -158.75249812904462,
          -158.73892818782082,
          -158.7222537913766,
          -158.7024657350885
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.54978961251148e-18,
            2.705576113990587e-17,
            0.0009076729725000865
          ],
          [
            5.4330876575004927e-17,
            7.501667384471106e-17,
            0.0007942175705658991
          ],
          [
            -9.559527101591609e-18,
            1.595446279388178e-16,
            0.000680808460324544
          ],
          [
            6.555855548636656e-17,
            2.3986206636128317e-16,
            0.0005674609163677796
          ],
          [
            -6.153418137351948e-17,
            3.7790751193206054e-16,
            0.00045419009796832425
          ],
          [
            -8.433726094925546e-17,
            4.587994828194089e-16,
            0.00034101104086550846
          ],
          [
            2.0717032165871276e-17,
            5.676464786952913e-16,
            0.00022793864917299405
          ],
          [
            1.3440301075978325e-17,
            7.355757150437653e-16,
            0.0001149876786993276
          ],
          [
            -3.08220551621946e-17,
            8.79294183049498e-16,
            2.1725010256276435e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393628e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.3046136569532905e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.3766243727024908e-15,
            3.934230489620395e-14,
            0.0003260607017379696
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393624e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.304613656953291e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.376624372702491e-15,
            3.934230489620395e-14,
            0.00032606070173796936
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            1.2212453270876722e-15,
            0.13621370185702808
          ],
          [
            5.995204332975845e-15,
            3.3306690738754696e-15,
            0.11918916229976517
          ],
          [
            -9.992007221626409e-16,
            7.105427357601002e-15,
            0.10217110850033007
          ],
          [
            7.216449660063518e-15,
            1.0658141036401503e-14,
            0.08516183306976366
          ],
          [
            -6.716849298982197e-15,
            1.687538997430238e-14,
            0.06816361143659055
          ],
          [
            -9.2148511043888e-15,
            2.0539125955565396e-14,
            0.051178700612846795
          ],
          [
            2.3314683517128287e-15,
            2.5424107263916085e-14,
            0.03420933797832815
          ],
          [
            1.4432899320127035e-15,
            3.2862601528904634e-14,
            0.01725773877594816
          ],
          [
            -3.3861802251067274e-15,
            3.930189507173054e-14,
            0.00032606070173801793
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -158.70246573508854,
          -158.68649432507516,
          -158.66876716022142,
          -158.64927918212703,
          -158.62802516832576,
          -158.60499985946177,
          -158.58019796394643,
          -158.55361415723274,
          -158.52524308103474
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0985612164640513e-17,
            9.214241980024106e-16,
            2.172501025642237e-06
          ],
          [
            -4.349395938150567e-18,
            8.625508648691979e-16,
            -8.70569964064894e-05
          ],
          [
            5.199334548910661e-18,
            1.027342401414782e-15,
            -0.00017626738258150302
          ],
          [
            1.8598507997111226e-21,
            1.0663900519700099e-15,
            -0.0002654562644700695
          ],
          [
            -7.220062704778055e-17,
            1.1961785640569179e-15,
            -0.0003546214222289789
          ],
          [
            -1.2588580792758633e-16,
            1.0871460142122163e-15,
            -0.0004437605819502457
          ],
          [
            -1.0894197129832411e-16,
            1.3010168625550412e-15,
            -0.0005328714051367943
          ],
          [
            -6.249476404719055e-17,
            1.286351489206029e-15,
            -0.0006219514870560408
          ],
          [
            -1.2548540818057257e-16,
            1.3956371332503598e-15,
            -0.0007109983548671756
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.2988869465637802e-15,
            4.1227331475715714e-14,
            0.00032606070174015983
          ],
          [
            -4.913704791893165e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064747e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.166347011834207e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.2988869465637802e-15,
            4.1227331475715714e-14,
            0.00032606070174015983
          ],
          [
            -4.913704791893163e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064748e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.1663470118342026e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.166691701323177e-15,
          7.71968283698718e-14,
          -0.13556165113842214
        ],
        "actual_opposite_endpoint_branch_residual": 0.0288627398951377
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393628e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.3046136569532905e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.3766243727024908e-15,
            3.934230489620395e-14,
            0.0003260607017379696
          ],
          [
            -4.913704791893165e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064747e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.166347011834207e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.101124162524598e-16,
            1.206225596417751e-15,
            0.13621370185702808
          ],
          [
            5.989406257979959e-15,
            3.3451656329621383e-15,
            0.11918916229976512
          ],
          [
            -1.0173264857393624e-15,
            7.117979780730154e-15,
            0.1021711085003301
          ],
          [
            7.238955695600044e-15,
            1.0706434017864294e-14,
            0.08516183306976371
          ],
          [
            -6.709741398732299e-15,
            1.687663438423035e-14,
            0.06816361143659058
          ],
          [
            -9.211183195648518e-15,
            2.0498805228114897e-14,
            0.05117870061284675
          ],
          [
            2.304613656953291e-15,
            2.5374120349588655e-14,
            0.03420933797832809
          ],
          [
            1.4925330133929953e-15,
            3.289636563791716e-14,
            0.017257738775948158
          ],
          [
            -3.376624372702491e-15,
            3.934230489620395e-14,
            0.00032606070173796936
          ],
          [
            -4.913704791893163e-16,
            3.857650232170272e-14,
            -0.013065807742152786
          ],
          [
            5.447600416064748e-16,
            4.592634341165493e-14,
            -0.02645444503230971
          ],
          [
            -3.1663470118342026e-17,
            4.7650801658693175e-14,
            -0.03983949214851501
          ],
          [
            -7.958075454309133e-15,
            5.342627982146949e-14,
            -0.053220616081315474
          ],
          [
            -1.3853731618872375e-14,
            4.853472161900268e-14,
            -0.06659747572552614
          ],
          [
            -1.199201585452865e-14,
            5.805625164434082e-14,
            -0.07996972030136211
          ],
          [
            -6.882381707269402e-15,
            5.737567438602998e-14,
            -0.09333698910801408
          ],
          [
            -1.3795154579711907e-14,
            6.22216179664104e-14,
            -0.10669891124328444
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            1.2212453270876722e-15,
            0.13621370185702808
          ],
          [
            5.995204332975845e-15,
            3.3306690738754696e-15,
            0.11918916229976517
          ],
          [
            -9.992007221626409e-16,
            7.105427357601002e-15,
            0.10217110850033007
          ],
          [
            7.216449660063518e-15,
            1.0658141036401503e-14,
            0.08516183306976366
          ],
          [
            -6.716849298982197e-15,
            1.687538997430238e-14,
            0.06816361143659055
          ],
          [
            -9.2148511043888e-15,
            2.0539125955565396e-14,
            0.051178700612846795
          ],
          [
            2.3314683517128287e-15,
            2.5424107263916085e-14,
            0.03420933797832815
          ],
          [
            1.4432899320127035e-15,
            3.2862601528904634e-14,
            0.01725773877594816
          ],
          [
            -3.3861802251067274e-15,
            3.930189507173054e-14,
            0.00032606070173801793
          ],
          [
            -4.996003610813204e-16,
            3.852473895449293e-14,
            -0.013065807742152769
          ],
          [
            5.551115123125783e-16,
            4.596323321948148e-14,
            -0.026454445032309704
          ],
          [
            -5.551115123125783e-17,
            4.7628567756419216e-14,
            -0.03983949214851501
          ],
          [
            -7.93809462606987e-15,
            5.340172748447003e-14,
            -0.05322061608131545
          ],
          [
            -1.3877787807814457e-14,
            4.851674617611934e-14,
            -0.06659747572552616
          ],
          [
            -1.199040866595169e-14,
            5.806466418789569e-14,
            -0.07996972030136212
          ],
          [
            -6.8833827526759706e-15,
            5.739853037312059e-14,
            -0.09333698910801408
          ],
          [
            -1.3822276656583199e-14,
            6.217248937900877e-14,
            -0.10669891124328446
          ]
        ]
      },
      "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": "Ama2",
        "spacegroup_number": 40,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00032606070174159244,
        "parent_symmetrization_rmsd_A": 0.016782047564391302,
        "parent_cell_rmsd_A": 0.06857298073522305,
        "energy_eV": -158.70246573508848,
        "reduced_polarization": [
          -6.410217737722277e-15,
          3.699688011985291e-14,
          0.00032606070174159244
        ],
        "cartesian_polarization_e_A2": [
          -5.850947464774127e-17,
          8.268743487762888e-16,
          2.1725010256517823e-06
        ],
        "ranking_score": 0.5345774141516803
      }
    }
  ],
  "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": 128,
      "full_response": 33,
      "energy_polarization": 95
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 153,
      "full_response": 58,
      "energy_polarization": 95
    },
    "elapsed_seconds": 531.5355473730015
  }
}