{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "Cs8Se12",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -63.73513497389694,
  "input_cartesian_polarization_e_A2": [
    -2.256152770653678e-17,
    -9.831615764396228e-18,
    -0.0011852745667101255
  ],
  "input_reduced_polarization": [
    -2.2651263034241337e-15,
    -6.821428434199141e-16,
    -0.11326376239774481
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -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": "Cmce",
      "spacegroup_number": 64,
      "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": 1.2429269767364679e-15,
      "parent_symmetrization_rmsd_A": 0.3885784126376819,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -59.621226262092115,
      "reduced_polarization": [
        1.0537711600195351e-15,
        -5.198394220774861e-16,
        4.052169629525457e-16
      ],
      "cartesian_polarization_e_A2": [
        1.0495965362810256e-17,
        -7.492362496142892e-18,
        4.2404856594869274e-18
      ],
      "ranking_score": 0.3885784126376844
    },
    {
      "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": 3.1944986479170364e-15,
      "parent_symmetrization_rmsd_A": 0.7631225208992968,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -48.41983673678996,
      "reduced_polarization": [
        9.16535772301621e-17,
        -3.1888407662986297e-15,
        1.6648063105556122e-16
      ],
      "cartesian_polarization_e_A2": [
        9.129048207844316e-19,
        -4.596025224117407e-17,
        1.742174669662373e-18
      ],
      "ranking_score": 0.7631225208993032
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 0.0002548322244432464,
      "parent_symmetrization_rmsd_A": 0.05268296984787682,
      "parent_cell_rmsd_A": 0.05597742154821222,
      "energy_eV": -63.58949592609528,
      "reduced_polarization": [
        3.753901566328542e-14,
        -7.402684197169394e-14,
        0.0002548322244432464
      ],
      "cartesian_polarization_e_A2": [
        3.7277645780534923e-16,
        -1.0781822575187125e-15,
        2.686682170546941e-06
      ],
      "ranking_score": 0.5671869896838164
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "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": 2.2979065110855946e-15,
      "parent_symmetrization_rmsd_A": 0.3885900531277634,
      "parent_cell_rmsd_A": 0.05597742154821222,
      "energy_eV": -59.751972463458415,
      "reduced_polarization": [
        2.1740071831191644e-15,
        -5.474241191511691e-16,
        -5.043747963641852e-16
      ],
      "cartesian_polarization_e_A2": [
        2.158779677163264e-17,
        -7.973266907395425e-18,
        -5.317595824568405e-18
      ],
      "ranking_score": 0.4025844085148211
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 9.074950413356951e-08,
      "parent_symmetrization_rmsd_A": 0.21474209679246944,
      "parent_cell_rmsd_A": 0.24468643366448892,
      "energy_eV": -62.94622612589967,
      "reduced_polarization": [
        -5.949037311660674e-15,
        -1.586494257549947e-15,
        -0.5000000907495041
      ],
      "cartesian_polarization_e_A2": [
        2.0336052883192345e-16,
        3.3109742704217675e-16,
        -0.005071997537241656
      ],
      "ranking_score": 0.7759138867075999
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00012692492453631447,
      "parent_symmetrization_rmsd_A": 0.1302283123838589,
      "parent_cell_rmsd_A": 0.28881029573819883,
      "energy_eV": -61.37886357832874,
      "reduced_polarization": [
        -0.5000230232784032,
        -1.6147604484368265e-15,
        -0.00012481932991375116
      ],
      "cartesian_polarization_e_A2": [
        -0.004964166837873787,
        -1.0239778767571343e-15,
        -0.00020998617756454987
      ],
      "ranking_score": 0.7026847361674813
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0008796519381753008,
      "parent_symmetrization_rmsd_A": 0.34041402244505375,
      "parent_cell_rmsd_A": 0.5043558618777677,
      "energy_eV": -62.33385982356414,
      "reduced_polarization": [
        -9.195882338780165e-15,
        -0.5000215516414743,
        -0.0008793878888666396
      ],
      "cartesian_polarization_e_A2": [
        -2.779367331676754e-15,
        -0.007309898829612482,
        0.0003565439663119925
      ],
      "ranking_score": 0.9682622917908463
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00892274394339755,
      "parent_symmetrization_rmsd_A": 0.3018531587280316,
      "parent_cell_rmsd_A": 0.6025858438047698,
      "energy_eV": -59.82077012842274,
      "reduced_polarization": [
        -0.5036884601907817,
        1.3714682387868474e-14,
        -0.5081246920495768
      ],
      "cartesian_polarization_e_A2": [
        -0.005609310548365491,
        -1.4983899327198016e-15,
        -0.005599930063006534
      ],
      "ranking_score": 0.9703451075660191
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 6.935559927975876e-06,
      "parent_symmetrization_rmsd_A": 0.4347557819851962,
      "parent_cell_rmsd_A": 0.572106040019485,
      "energy_eV": -61.553927742191384,
      "reduced_polarization": [
        -3.0538404660146718e-15,
        -0.49999340450002694,
        -0.49999785491920434
      ],
      "cartesian_polarization_e_A2": [
        -3.927231549774147e-15,
        -0.006638408865876622,
        -0.004706579242393987
      ],
      "ranking_score": 1.0777961631099235
    },
    {
      "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": 5.088544906742302e-06,
      "parent_symmetrization_rmsd_A": 0.356930137097165,
      "parent_cell_rmsd_A": 0.5856834385175671,
      "energy_eV": -59.975363965335944,
      "reduced_polarization": [
        -0.4999957841092652,
        -0.4999981421037251,
        -2.160503647763095e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.0049507833434636675,
        -0.007334280171357363,
        0.0001391215885202697
      ],
      "ranking_score": 1.0033611738163701
    },
    {
      "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": 0.021194514182050265,
      "parent_symmetrization_rmsd_A": 0.4635744827621869,
      "parent_cell_rmsd_A": 0.732573853998222,
      "energy_eV": -58.34899094710305,
      "reduced_polarization": [
        -0.4847145509190013,
        -0.49239994072050847,
        -0.48743809024258095
      ],
      "cartesian_polarization_e_A2": [
        -0.0052308546241980995,
        -0.006627908039150239,
        -0.005002621833823538
      ],
      "ranking_score": 1.189106974625843
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "target_residual": 0.11326376239774481,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.04057916421527687,
            "max_log_strain_component": 0.010506125529412305,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0030643281210787,
              0.9999998807416961,
              0.9895488710386198
            ],
            "cell_volume_ratio": 0.9925810550977784,
            "cell_rmsd_from_input_A": 0.05597742154821222
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.753901566328542e-14,
              -7.402684197169394e-14,
              0.0002548322244432464
            ],
            "branch_aligned_reduced_polarization": [
              3.753901566328542e-14,
              -7.402684197169394e-14,
              0.0002548322244432464
            ],
            "target_residual": 0.0002548322244432464,
            "energy_eV": -63.58949592609528
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmce",
        "spacegroup_number": 64,
        "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": 1.2429269767364679e-15,
        "parent_symmetrization_rmsd_A": 0.3885784126376819,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -59.621226262092115,
        "reduced_polarization": [
          1.0537711600195351e-15,
          -5.198394220774861e-16,
          4.052169629525457e-16
        ],
        "cartesian_polarization_e_A2": [
          1.0495965362810256e-17,
          -7.492362496142892e-18,
          4.2404856594869274e-18
        ],
        "ranking_score": 0.3885784126376844
      },
      "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": [
          -63.73513497389696,
          -63.67661527946496,
          -63.267170683712855,
          -62.537383580693955,
          -61.63376223180968,
          -60.77828008662884,
          -60.138929078516256,
          -59.75240629217204,
          -59.62122626209206
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.4814853556234024e-17,
            1.4254141886788997e-17,
            -0.0011852745667101203
          ],
          [
            -2.3486108195288223e-17,
            -2.337134958526024e-17,
            -0.0016456193371535476
          ],
          [
            -1.164488877469727e-16,
            6.463692025035583e-19,
            -0.0019975737152351227
          ],
          [
            3.72611214777101e-18,
            1.2723267459806884e-17,
            -0.002269611457525715
          ],
          [
            -5.259616691041555e-17,
            1.5785016313771106e-17,
            -0.0025080540879875916
          ],
          [
            -4.132991663797106e-17,
            -1.481546251001577e-17,
            -0.0025069262584595958
          ],
          [
            3.3660727860618564e-18,
            -3.9334967915512596e-17,
            -0.0020452031830327593
          ],
          [
            -2.457918131064595e-17,
            -4.9413224559811495e-17,
            -0.001156038118763195
          ],
          [
            -3.192486233058152e-17,
            -2.370527255039113e-17,
            -8.547750887833294e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.3579520912849822e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.484676133210508e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124204e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.02793497684904e-15,
            -0.239559599152588
          ],
          [
            3.379460870790141e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654155e-15,
            -8.168153209276079e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.357952091284982e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.4846761332105156e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124214e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.0279349768490399e-15,
            -0.239559599152588
          ],
          [
            3.3794608707901433e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654157e-15,
            -8.187894806610529e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.4432899320127035e-15,
            9.992007221626409e-16,
            -0.11326376239774433
          ],
          [
            -2.3314683517128287e-15,
            -1.609823385706477e-15,
            -0.1572538910691717
          ],
          [
            -1.1712852909795402e-14,
            0.0,
            -0.1908863321705817
          ],
          [
            3.3306690738754696e-16,
            8.881784197001252e-16,
            -0.21688201205051294
          ],
          [
            -5.2735593669694936e-15,
            1.1102230246251565e-15,
            -0.23966737351919626
          ],
          [
            -4.163336342344337e-15,
            -1.0547118733938987e-15,
            -0.239559599152588
          ],
          [
            3.3306690738754696e-16,
            -2.7200464103316335e-15,
            -0.19543776090724663
          ],
          [
            -2.4424906541753444e-15,
            -3.4416913763379853e-15,
            -0.1104699539531695
          ],
          [
            -3.219646771412954e-15,
            -1.6653345369377348e-15,
            -8.326672684688674e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -59.62122626209205,
          -59.75240629217206,
          -60.13892907851621,
          -60.77828008662884,
          -61.63376223180968,
          -62.53738358069391,
          -63.26717068371284,
          -63.67661527946497,
          -63.735134973896976
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.082757097646428e-18,
            -2.145776316302777e-17,
            -6.1370794938989346e-18
          ],
          [
            -1.491848247921606e-17,
            1.2655228596385456e-17,
            0.0011560381187631884
          ],
          [
            -8.555802663729254e-19,
            4.175885242490094e-18,
            0.002045203183032749
          ],
          [
            -3.1979723700328e-17,
            -7.892508156885553e-18,
            0.002506926258459563
          ],
          [
            1.0602198455027197e-17,
            -5.7994626208839e-17,
            0.002508054087987547
          ],
          [
            -1.5542566847957974e-17,
            3.21653726824797e-17,
            0.0022696114575256952
          ],
          [
            5.128235752786111e-17,
            -1.9391076075106747e-18,
            0.0019975737152350876
          ],
          [
            -1.9278012009866994e-17,
            2.3167232994995958e-17,
            0.0016456193371535194
          ],
          [
            -2.546491325030171e-17,
            4.7491126668156174e-17,
            0.0011852745667101444
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.102973054638908e-16,
            -1.488794917155486e-15,
            -5.86453749313461e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654257e-16,
            0.11046995395316883
          ],
          [
            -8.589832174753139e-17,
            2.897336817639947e-16,
            0.19543776090724566
          ],
          [
            -3.21069185881688e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710406e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432809e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631522e-16,
            0.19088633217057835
          ],
          [
            -1.935468761214443e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.102973054638908e-16,
            -1.488794917155486e-15,
            -5.86453749313461e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654256e-16,
            0.11046995395316883
          ],
          [
            -8.58983217475314e-17,
            2.8973368176399475e-16,
            0.19543776090724566
          ],
          [
            -3.2106918588168804e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710402e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432807e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631527e-16,
            0.19088633217057835
          ],
          [
            -1.9354687612144436e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.89774555986142e-15,
          -4.278454928296727e-15,
          0.11326376239774269
        ],
        "actual_opposite_endpoint_branch_residual": 1.0070724217186694e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.3579520912849822e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.484676133210508e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124204e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.02793497684904e-15,
            -0.239559599152588
          ],
          [
            3.379460870790141e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654155e-15,
            -8.168153209276079e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654257e-16,
            0.11046995395316883
          ],
          [
            -8.589832174753139e-17,
            2.897336817639947e-16,
            0.19543776090724566
          ],
          [
            -3.21069185881688e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710406e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432809e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631522e-16,
            0.19088633217057835
          ],
          [
            -1.935468761214443e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.357952091284982e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.4846761332105156e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124214e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.0279349768490399e-15,
            -0.239559599152588
          ],
          [
            3.3794608707901433e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654157e-15,
            -8.187894806610529e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654256e-16,
            0.11046995395316883
          ],
          [
            -8.58983217475314e-17,
            2.8973368176399475e-16,
            0.19543776090724566
          ],
          [
            -3.2106918588168804e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710402e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432807e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631527e-16,
            0.19088633217057835
          ],
          [
            -1.9354687612144436e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.4432899320127035e-15,
            9.992007221626409e-16,
            -0.11326376239774433
          ],
          [
            -2.3314683517128287e-15,
            -1.609823385706477e-15,
            -0.1572538910691717
          ],
          [
            -1.1712852909795402e-14,
            0.0,
            -0.1908863321705817
          ],
          [
            3.3306690738754696e-16,
            8.881784197001252e-16,
            -0.21688201205051294
          ],
          [
            -5.2735593669694936e-15,
            1.1102230246251565e-15,
            -0.23966737351919626
          ],
          [
            -4.163336342344337e-15,
            -1.0547118733938987e-15,
            -0.239559599152588
          ],
          [
            3.3306690738754696e-16,
            -2.7200464103316335e-15,
            -0.19543776090724663
          ],
          [
            -2.4424906541753444e-15,
            -3.4416913763379853e-15,
            -0.1104699539531695
          ],
          [
            -3.219646771412954e-15,
            -1.6653345369377348e-15,
            -8.326672684688674e-16
          ],
          [
            -1.4988010832439613e-15,
            8.881784197001252e-16,
            0.11046995395316883
          ],
          [
            -1.1102230246251565e-16,
            3.3306690738754696e-16,
            0.19543776090724563
          ],
          [
            -3.219646771412954e-15,
            -5.551115123125783e-16,
            0.23955959915258485
          ],
          [
            1.1102230246251565e-15,
            -3.9968028886505635e-15,
            0.23966737351919198
          ],
          [
            -1.5543122344752192e-15,
            2.220446049250313e-15,
            0.21688201205051105
          ],
          [
            5.10702591327572e-15,
            -1.1102230246251565e-16,
            0.19088633217057838
          ],
          [
            -1.942890293094024e-15,
            1.5543122344752192e-15,
            0.15725389106916898
          ],
          [
            -2.55351295663786e-15,
            3.3306690738754696e-15,
            0.1132637623977466
          ]
        ]
      },
      "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": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774483
            ],
            "target_residual": 0.3867362376022552,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.07724858055745491,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5575239471248881,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0202013400267558,
              1.0000002270262698,
              0.9941924366509397
            ],
            "cell_volume_ratio": 1.014276686383154,
            "cell_rmsd_from_input_A": 0.10870989958164935
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.628572203994786e-14,
              1.413263592257103e-13,
              -0.3172378717225354
            ],
            "branch_aligned_reduced_polarization": [
              -5.628572203994786e-14,
              1.413263592257103e-13,
              -0.3172378717225354
            ],
            "target_residual": 0.18276212827746458,
            "energy_eV": -63.58047741408655,
            "max_atomic_step_A": 0.07055587758280205,
            "max_log_strain_component": 0.019507809526149382,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0402986230925348,
              1.000000448465581,
              0.9885602891879665
            ],
            "cell_volume_ratio": 1.0283983688872644,
            "cell_rmsd_from_input_A": 0.21759906883774013
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0498773606589992e-13,
              1.4411140394997698e-13,
              -0.4687982527089623
            ],
            "branch_aligned_reduced_polarization": [
              -1.0498773606589992e-13,
              1.4411140394997698e-13,
              -0.4687982527089623
            ],
            "target_residual": 0.031201747291037696,
            "energy_eV": -63.06128773434796,
            "max_atomic_step_A": 0.014063843463759527,
            "max_log_strain_component": 0.003945118339797449,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0444108305082924,
              1.0000004932478717,
              0.9874251689817894
            ],
            "cell_volume_ratio": 1.031278049476514,
            "cell_rmsd_from_input_A": 0.23997774192304588
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.404644574459016e-14,
              3.08037112114889e-14,
              -0.49370675697408806
            ],
            "branch_aligned_reduced_polarization": [
              -7.404644574459016e-14,
              3.08037112114889e-14,
              -0.49370675697408806
            ],
            "target_residual": 0.006293243025911943,
            "energy_eV": -62.96335260066692,
            "max_atomic_step_A": 0.0028599962724179815,
            "max_log_strain_component": 0.0008145556777191239,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0452619078580403,
              1.0000005024941518,
              0.9871909610620764
            ],
            "cell_volume_ratio": 1.03187362589016,
            "cell_rmsd_from_input_A": 0.24461365428054055
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -4.712984810175195e-14,
              8.992541088600305e-15,
              -0.4986792882608802
            ],
            "branch_aligned_reduced_polarization": [
              -4.712984810175195e-14,
              8.992541088600305e-15,
              -0.4986792882608802
            ],
            "target_residual": 0.0013207117391197953,
            "energy_eV": -62.943578570992116,
            "max_atomic_step_A": 0.000533042741920072,
            "max_log_strain_component": 0.00013250480888410318,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6662464562811692,
            "cell_principal_stretches": [
              1.0451360838954593,
              0.9998680063970637,
              0.9870659905490726
            ],
            "cell_volume_ratio": 1.0314821168947024,
            "cell_rmsd_from_input_A": 0.24468643366448892
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -5.949037311660674e-15,
              -1.586494257549947e-15,
              -0.5000000907495041
            ],
            "branch_aligned_reduced_polarization": [
              -5.949037311660674e-15,
              -1.586494257549947e-15,
              -0.5000000907495041
            ],
            "target_residual": 9.074950413356951e-08,
            "energy_eV": -62.94622612589967
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 9.074950413356951e-08,
        "parent_symmetrization_rmsd_A": 0.21474209679246944,
        "parent_cell_rmsd_A": 0.24468643366448892,
        "energy_eV": -62.94622612589967,
        "reduced_polarization": [
          -5.949037311660674e-15,
          -1.586494257549947e-15,
          -0.5000000907495041
        ],
        "cartesian_polarization_e_A2": [
          2.0336052883192345e-16,
          3.3109742704217675e-16,
          -0.005071997537241656
        ],
        "ranking_score": 0.7759138867075999
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.275957200481571e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "target_residual": 0.5126681966657289,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.06853925016755091,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5265084674999098,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.017577207808944,
              1.001612225997074,
              0.9773053452871389
            ],
            "cell_volume_ratio": 0.9960869768192642,
            "cell_rmsd_from_input_A": 0.1382732091936944
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2621454788135735,
              -3.367257275142922e-14,
              -0.06828378620830564
            ],
            "branch_aligned_reduced_polarization": [
              -0.2621454788135735,
              -3.367257275142922e-14,
              -0.06828378620830564
            ],
            "target_residual": 0.24746201467652731,
            "energy_eV": -63.27222773029042,
            "max_atomic_step_A": 0.0642303957991044,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9670393910876137,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0347624533369535,
              1.003690797971037,
              0.954257172113324
            ],
            "cell_volume_ratio": 0.99107389529794,
            "cell_rmsd_from_input_A": 0.2760842107865053
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4813623426308883,
              -4.242356387425635e-14,
              -0.014802195256320178
            ],
            "branch_aligned_reduced_polarization": [
              -0.4813623426308883,
              -4.242356387425635e-14,
              -0.014802195256320178
            ],
            "target_residual": 0.023800572611066145,
            "energy_eV": -61.5866667177429,
            "max_atomic_step_A": 0.00810624500749639,
            "max_log_strain_component": 0.0016642774629522603,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0358223162938738,
              1.0041223174308944,
              0.9518747707500305
            ],
            "cell_volume_ratio": 0.9900376240796123,
            "cell_rmsd_from_input_A": 0.28829442178844705
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49926842417949746,
              -8.15647690918711e-15,
              -0.0013852681001468542
            ],
            "branch_aligned_reduced_polarization": [
              -0.49926842417949746,
              -8.15647690918711e-15,
              -0.0013852681001468542
            ],
            "target_residual": 0.0015665793597607618,
            "energy_eV": -61.38608787051417,
            "max_atomic_step_A": 0.0006547105694366627,
            "max_log_strain_component": 0.0001386434227768061,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.035822318767996,
              1.0041628610746964,
              0.9517428049506718
            ],
            "cell_volume_ratio": 0.9899403392330862,
            "cell_rmsd_from_input_A": 0.28881029573819883
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000230232784032,
              -1.6147604484368265e-15,
              -0.00012481932991375116
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000230232784032,
              -1.6147604484368265e-15,
              -0.00012481932991375116
            ],
            "target_residual": 0.00012692492453631447,
            "energy_eV": -61.37886357832874
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00012692492453631447,
        "parent_symmetrization_rmsd_A": 0.1302283123838589,
        "parent_cell_rmsd_A": 0.28881029573819883,
        "energy_eV": -61.37886357832874,
        "reduced_polarization": [
          -0.5000230232784032,
          -1.6147604484368265e-15,
          -0.00012481932991375116
        ],
        "cartesian_polarization_e_A2": [
          -0.004964166837873787,
          -1.0239778767571343e-15,
          -0.00020998617756454987
        ],
        "ranking_score": 0.7026847361674813
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.2651263034241337e-15,
              -6.661338147750939e-16,
              -0.11326376239774481
            ],
            "target_residual": 0.5126681966657305,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.11034650323683182,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3739944299534958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0207935398305457,
              0.9960784769049398,
              0.9807516020972923
            ],
            "cell_volume_ratio": 0.9972188867540926,
            "cell_rmsd_from_input_A": 0.1985956845609208
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.934529508530213e-14,
              -0.18933053352884496,
              -0.07542905947276325
            ],
            "branch_aligned_reduced_polarization": [
              9.934529508530213e-14,
              -0.189330533528845,
              -0.07542905947276325
            ],
            "target_residual": 0.31969526178912594,
            "energy_eV": -63.53502086761168,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.017538698035886223,
            "step_scale": 0.5679349662407454,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0394002745788056,
              0.9925462301988112,
              0.9641917235469134
            ],
            "cell_volume_ratio": 0.994711114668213,
            "cell_rmsd_from_input_A": 0.3740175397858256
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.615252034245486e-13,
              -0.3684621191401878,
              -0.041823852415294294
            ],
            "branch_aligned_reduced_polarization": [
              1.615252034245486e-13,
              -0.3684621191401878,
              -0.041823852415294294
            ],
            "target_residual": 0.13802698552075413,
            "energy_eV": -63.02375523557368,
            "max_atomic_step_A": 0.10341343229842206,
            "max_log_strain_component": 0.012143423399692753,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0527097241818237,
              0.9886794167008096,
              0.953084203530877
            ],
            "cell_volume_ratio": 0.991962829962592,
            "cell_rmsd_from_input_A": 0.4976339431156087
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.0736165685975927e-13,
              -0.4955616080847083,
              -0.014554258946447707
            ],
            "branch_aligned_reduced_polarization": [
              1.0736165685975927e-13,
              -0.4955616080847083,
              -0.014554258946447707
            ],
            "target_residual": 0.015215971092046017,
            "energy_eV": -62.385824173271246,
            "max_atomic_step_A": 0.008174103240884684,
            "max_log_strain_component": 0.001634499254730853,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.053515218048723,
              0.9870647408837331,
              0.9528089145423502
            ],
            "cell_volume_ratio": 0.990814295189503,
            "cell_rmsd_from_input_A": 0.5043558618777677
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -9.195882338780165e-15,
              -0.5000215516414743,
              -0.0008793878888666396
            ],
            "branch_aligned_reduced_polarization": [
              -9.195882338780165e-15,
              -0.5000215516414743,
              -0.0008793878888666396
            ],
            "target_residual": 0.0008796519381753008,
            "energy_eV": -62.33385982356414
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0008796519381753008,
        "parent_symmetrization_rmsd_A": 0.34041402244505375,
        "parent_cell_rmsd_A": 0.5043558618777677,
        "energy_eV": -62.33385982356414,
        "reduced_polarization": [
          -9.195882338780165e-15,
          -0.5000215516414743,
          -0.0008793878888666396
        ],
        "cartesian_polarization_e_A2": [
          -2.779367331676754e-15,
          -0.007309898829612482,
          0.0003565439663119925
        ],
        "ranking_score": 0.9682622917908463
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.275957200481571e-15,
              -6.821428434199141e-16,
              -0.11326376239774483
            ],
            "target_residual": 0.6321114755126233,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.11193120893329328,
            "max_log_strain_component": 0.02,
            "step_scale": 0.526508467500279,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0320645803976785,
              0.9945146280233258,
              0.9874063286553079
            ],
            "cell_volume_ratio": 1.0134771361624753,
            "cell_rmsd_from_input_A": 0.17352806467312187
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.17577446194326635,
              1.4397697423284274e-13,
              -0.28267030560841677
            ],
            "branch_aligned_reduced_polarization": [
              -0.17577446194326635,
              1.4397697423284274e-13,
              -0.28267030560841677
            ],
            "target_residual": 0.3903260119342771,
            "energy_eV": -63.29915390947095,
            "max_atomic_step_A": 0.056269539808284995,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4654306483694421,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0611593549099978,
              0.9906062288103581,
              0.9734068789085837
            ],
            "cell_volume_ratio": 1.0232366154063472,
            "cell_rmsd_from_input_A": 0.33657272007334943
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2632359593935102,
              1.7454176646583186e-13,
              -0.3422208593684439
            ],
            "branch_aligned_reduced_polarization": [
              -0.2632359593935102,
              1.7454176646583186e-13,
              -0.3422208593684439
            ],
            "target_residual": 0.28451971485776506,
            "energy_eV": -62.74308443306613,
            "max_atomic_step_A": 0.059812354695308385,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.6189101743196288,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0913523386418646,
              0.9866253114920234,
              0.959654920388561
            ],
            "cell_volume_ratio": 1.0333140409304273,
            "cell_rmsd_from_input_A": 0.507717995523844
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3377853356695064,
              1.847157216741662e-13,
              -0.3868609090335055
            ],
            "branch_aligned_reduced_polarization": [
              -0.3377853356695064,
              1.847157216741662e-13,
              -0.3868609090335055
            ],
            "target_residual": 0.1977727261999981,
            "energy_eV": -61.98736391361502,
            "max_atomic_step_A": 0.058579987206018105,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8120928986388787,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.1225845168221313,
              0.9825964983722887,
              0.9461566759745373
            ],
            "cell_volume_ratio": 1.0436558651872272,
            "cell_rmsd_from_input_A": 0.6869825018881022
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.3917750542885999,
              2.0584603619094756e-13,
              -0.41484864390024584
            ],
            "branch_aligned_reduced_polarization": [
              -0.3917750542885999,
              2.0584603619094756e-13,
              -0.41484864390024584
            ],
            "target_residual": 0.13770763348435935,
            "energy_eV": -60.71478166330451,
            "max_atomic_step_A": 0.03836351278481952,
            "max_log_strain_component": 0.01740465220120746,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.617305750257817,
            "cell_principal_stretches": [
              1.0962392301627506,
              0.9755077235660136,
              0.9397596916710961
            ],
            "cell_volume_ratio": 1.0049694624614225,
            "cell_rmsd_from_input_A": 0.6025858438047698
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5036884601907817,
              1.3714682387868474e-14,
              -0.5081246920495768
            ],
            "branch_aligned_reduced_polarization": [
              -0.5036884601907817,
              1.3714682387868474e-14,
              -0.5081246920495768
            ],
            "target_residual": 0.00892274394339755,
            "energy_eV": -59.82077012842274
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00892274394339755,
        "parent_symmetrization_rmsd_A": 0.3018531587280316,
        "parent_cell_rmsd_A": 0.6025858438047698,
        "energy_eV": -59.82077012842274,
        "reduced_polarization": [
          -0.5036884601907817,
          1.3714682387868474e-14,
          -0.5081246920495768
        ],
        "cartesian_polarization_e_A2": [
          -0.005609310548365491,
          -1.4983899327198016e-15,
          -0.005599930063006534
        ],
        "ranking_score": 0.9703451075660191
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.2651263034241337e-15,
              -6.661338147750939e-16,
              -0.11326376239774483
            ],
            "target_residual": 0.6321114755126245,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.018462815690086162,
            "step_scale": 0.3452495114672661,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0168883612852957,
              1.0124621136719996,
              0.9798517008996183
            ],
            "cell_volume_ratio": 1.0088170378815233,
            "cell_rmsd_from_input_A": 0.19262769533455623
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.788429452955426e-14,
              -0.17340769020525762,
              -0.24516979346530934
            ],
            "branch_aligned_reduced_polarization": [
              7.788429452955426e-14,
              -0.1734076902052576,
              -0.24516979346530932
            ],
            "target_residual": 0.41424747552589636,
            "energy_eV": -63.54040492561785,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.017652032456263785,
            "step_scale": 0.526351823427379,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.033070927028636,
              1.0262712319456364,
              0.9607052656434167
            ],
            "cell_volume_ratio": 1.0185502644241515,
            "cell_rmsd_from_input_A": 0.3784617262380701
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.629925980199966e-13,
              -0.3452319943581813,
              -0.3672404568192296
            ],
            "branch_aligned_reduced_polarization": [
              2.629925980199966e-13,
              -0.3452319943581813,
              -0.3672404568192296
            ],
            "target_residual": 0.20390741005640983,
            "energy_eV": -62.84859893494746,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014959298016504105,
            "step_scale": 0.9556999370231851,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0464496824468978,
              1.041738933683488,
              0.9443000725070826
            ],
            "cell_volume_ratio": 1.0294073605251586,
            "cell_rmsd_from_input_A": 0.5415577227789359
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.862110598646719e-13,
              -0.47713044816873285,
              -0.47245273511779523
            ],
            "branch_aligned_reduced_polarization": [
              5.862110598646719e-13,
              -0.47713044816873285,
              -0.47245273511779523
            ],
            "target_residual": 0.03580318705720717,
            "energy_eV": -61.826935280534556,
            "max_atomic_step_A": 0.024868383831597365,
            "max_log_strain_component": 0.003917819825697195,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0488311531113939,
              1.0458282845703375,
              0.9410816368534335
            ],
            "cell_volume_ratio": 1.0322698930512768,
            "cell_rmsd_from_input_A": 0.5745684591503234
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              4.300814507764113e-13,
              -0.4964368593707006,
              -0.49405274963069445
            ],
            "branch_aligned_reduced_polarization": [
              4.300814507764113e-13,
              -0.4964368593707006,
              -0.49405274963069445
            ],
            "target_residual": 0.006932947288085288,
            "energy_eV": -61.57610825205754,
            "max_atomic_step_A": 0.005006511480728567,
            "max_log_strain_component": 0.000689126782890008,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.2090421669544007,
            "cell_principal_stretches": [
              1.048377344201544,
              1.045107824561792,
              0.9409234650982604
            ],
            "cell_volume_ratio": 1.0309391341586034,
            "cell_rmsd_from_input_A": 0.572106040019485
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -3.0538404660146718e-15,
              -0.49999340450002694,
              -0.49999785491920434
            ],
            "branch_aligned_reduced_polarization": [
              -3.0538404660146718e-15,
              -0.49999340450002694,
              -0.49999785491920434
            ],
            "target_residual": 6.935559927975876e-06,
            "energy_eV": -61.553927742191384
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 6.935559927975876e-06,
        "parent_symmetrization_rmsd_A": 0.4347557819851962,
        "parent_cell_rmsd_A": 0.572106040019485,
        "energy_eV": -61.553927742191384,
        "reduced_polarization": [
          -3.0538404660146718e-15,
          -0.49999340450002694,
          -0.49999785491920434
        ],
        "cartesian_polarization_e_A2": [
          -3.927231549774147e-15,
          -0.006638408865876622,
          -0.004706579242393987
        ],
        "ranking_score": 1.0777961631099235
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.275957200481571e-15,
              -6.661338147750939e-16,
              -0.11326376239774481
            ],
            "target_residual": 0.7161205763504425,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.11171486152797466,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3739944299536845,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0246612261925605,
              0.9977958069870295,
              0.9753680336163061
            ],
            "cell_volume_ratio": 0.997218886754026,
            "cell_rmsd_from_input_A": 0.22070669389559475
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.18412293993300743,
              -0.18911628248704263,
              -0.0827700031077582
            ],
            "branch_aligned_reduced_polarization": [
              -0.18412293993300743,
              -0.1891162824870426,
              -0.0827700031077582
            ],
            "target_residual": 0.4508634785671834,
            "energy_eV": -63.34041603766906,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.017038440306473075,
            "step_scale": 0.5467360949146585,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0478892798716302,
              0.9960379830722157,
              0.9526372686593819
            ],
            "cell_volume_ratio": 0.9943032648288104,
            "cell_rmsd_from_input_A": 0.42009843328343766
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.34745634755654087,
              -0.3647597658701754,
              -0.05896393746927416
            ],
            "branch_aligned_reduced_polarization": [
              -0.34745634755654087,
              -0.3647597658701754,
              -0.05896393746927416
            ],
            "target_residual": 0.21221741858330362,
            "energy_eV": -62.08725526354045,
            "max_atomic_step_A": 0.11062557752777409,
            "max_log_strain_component": 0.015389574786125595,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0675049016952514,
              0.9941679890897047,
              0.9327441245023699
            ],
            "cell_volume_ratio": 0.9899019396200336,
            "cell_rmsd_from_input_A": 0.5830864282348467
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5018754142155801,
              -0.49733212171838315,
              -0.027428535454597898
            ],
            "branch_aligned_reduced_polarization": [
              -0.5018754142155801,
              -0.49733212171838315,
              -0.027428535454597898
            ],
            "target_residual": 0.027621718089026553,
            "energy_eV": -59.86042085416225,
            "max_atomic_step_A": 0.012880055165822284,
            "max_log_strain_component": 0.00286481261128227,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0676471343526746,
              0.9929172367315623,
              0.9319004763351316
            ],
            "cell_volume_ratio": 0.9878939423911111,
            "cell_rmsd_from_input_A": 0.5887150747038488
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5014859568649003,
              -0.5012439048544904,
              -0.0032255437085027382
            ],
            "branch_aligned_reduced_polarization": [
              -0.5014859568649003,
              -0.5012439048544904,
              -0.0032255437085027382
            ],
            "target_residual": 0.0037629110150029766,
            "energy_eV": -59.934249823546025,
            "max_atomic_step_A": 0.0014599619762085,
            "max_log_strain_component": 0.0003228517878620872,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.495688111493023,
            "cell_principal_stretches": [
              1.067362054275616,
              0.9931784914250351,
              0.9322481698872902
            ],
            "cell_volume_ratio": 0.9882586046895802,
            "cell_rmsd_from_input_A": 0.5856834385175671
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999957841092652,
              -0.4999981421037251,
              -2.160503647763095e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999957841092652,
              -0.4999981421037251,
              -2.160503647763095e-06
            ],
            "target_residual": 5.088544906742302e-06,
            "energy_eV": -59.975363965335944
          }
        ],
        "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": 5.088544906742302e-06,
        "parent_symmetrization_rmsd_A": 0.356930137097165,
        "parent_cell_rmsd_A": 0.5856834385175671,
        "energy_eV": -59.975363965335944,
        "reduced_polarization": [
          -0.4999957841092652,
          -0.4999981421037251,
          -2.160503647763095e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.0049507833434636675,
          -0.007334280171357363,
          0.0001391215885202697
        ],
        "ranking_score": 1.0033611738163701
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2651263034241337e-15,
              -6.821428434199141e-16,
              -0.11326376239774481
            ],
            "branch_aligned_reduced_polarization": [
              -2.275957200481571e-15,
              -6.661338147750939e-16,
              -0.11326376239774483
            ],
            "target_residual": 0.8059559029343634,
            "energy_eV": -63.73513497389694,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01823478397447185,
            "step_scale": 0.3409853818928166,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0252236449839527,
              1.0062244960659672,
              0.9778040284863301
            ],
            "cell_volume_ratio": 1.008707667105377,
            "cell_rmsd_from_input_A": 0.21040642289668918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.13370164656595773,
              -0.1704905611296694,
              -0.2380573599368181
            ],
            "branch_aligned_reduced_polarization": [
              -0.13370164656595773,
              -0.17049056112966943,
              -0.2380573599368181
            ],
            "target_residual": 0.558000807092965,
            "energy_eV": -63.41698694711883,
            "max_atomic_step_A": 0.11735972651777114,
            "max_log_strain_component": 0.02,
            "step_scale": 0.46544522922931975,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.0573764243312467,
              1.0090085589547029,
              0.9551664590371446
            ],
            "cell_volume_ratio": 1.0190688738454337,
            "cell_rmsd_from_input_A": 0.43264235504276394
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.23767184467861768,
              -0.3180841606775392,
              -0.3259459474725571
            ],
            "branch_aligned_reduced_polarization": [
              -0.23767184467861768,
              -0.3180841606775392,
              -0.3259459474725571
            ],
            "target_residual": 0.3635990193495308,
            "energy_eV": -62.37609375291186,
            "max_atomic_step_A": 0.08964814016929654,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5318350354240319,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.087577490135366,
              1.0085171123027326,
              0.9377040703793522
            ],
            "cell_volume_ratio": 1.0285118105558901,
            "cell_rmsd_from_input_A": 0.6164180511383647
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3097692323233246,
              -0.39669473294679725,
              -0.37180690471122896
            ],
            "branch_aligned_reduced_polarization": [
              -0.3097692323233246,
              -0.39669473294679725,
              -0.37180690471122896
            ],
            "target_residual": 0.2515813841513452,
            "energy_eV": -61.20499817248708,
            "max_atomic_step_A": 0.07344418968984212,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6441374641886943,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.952392146544545,
            "cell_principal_stretches": [
              1.1184169850588166,
              1.0068898764095882,
              0.9220782257458829
            ],
            "cell_volume_ratio": 1.0383732579424367,
            "cell_rmsd_from_input_A": 0.7961790107297371
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.36360620583929176,
              -0.43966425540824094,
              -0.3984448616750397
            ],
            "branch_aligned_reduced_polarization": [
              -0.36360620583929176,
              -0.43966425540824094,
              -0.3984448616750397
            ],
            "target_residual": 0.18043590352587108,
            "energy_eV": -59.6079447573209,
            "max_atomic_step_A": 0.04284199874336935,
            "max_log_strain_component": 0.02,
            "step_scale": 0.866236765980068,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.6751000321657936,
            "cell_principal_stretches": [
              1.096891686824891,
              0.9881280932933638,
              0.9216180892587791
            ],
            "cell_volume_ratio": 0.9989137293488803,
            "cell_rmsd_from_input_A": 0.732573853998222
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4847145509190013,
              -0.49239994072050847,
              -0.48743809024258095
            ],
            "branch_aligned_reduced_polarization": [
              -0.4847145509190013,
              -0.49239994072050847,
              -0.48743809024258095
            ],
            "target_residual": 0.021194514182050265,
            "energy_eV": -58.34899094710305
          }
        ],
        "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": 0.021194514182050265,
        "parent_symmetrization_rmsd_A": 0.4635744827621869,
        "parent_cell_rmsd_A": 0.732573853998222,
        "energy_eV": -58.34899094710305,
        "reduced_polarization": [
          -0.4847145509190013,
          -0.49239994072050847,
          -0.48743809024258095
        ],
        "cartesian_polarization_e_A2": [
          -0.0052308546241980995,
          -0.006627908039150239,
          -0.005002621833823538
        ],
        "ranking_score": 1.189106974625843
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19
        ],
        "endpoint_rmsd_A": 0.3885784126376819,
        "minimum_distance_A_by_image": [
          2.405424717954235,
          2.4866390587578753,
          2.570625257868628,
          2.6571204897973484,
          2.7458876618074703,
          2.8367134995076526,
          2.929406523234401,
          3.023795024717188,
          3.1197251157269337
        ],
        "minimum_distance_A": 2.405424717954235,
        "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": [
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714,
          815.8741701404714
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.2051839014980763e-15,
        -1.6447329115654155e-15,
        -8.168153209276079e-16
      ],
      "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": [
          -63.73513497389696,
          -63.67661527946496,
          -63.267170683712855,
          -62.537383580693955,
          -61.63376223180968,
          -60.77828008662884,
          -60.138929078516256,
          -59.75240629217204,
          -59.62122626209206
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.4814853556234024e-17,
            1.4254141886788997e-17,
            -0.0011852745667101203
          ],
          [
            -2.3486108195288223e-17,
            -2.337134958526024e-17,
            -0.0016456193371535476
          ],
          [
            -1.164488877469727e-16,
            6.463692025035583e-19,
            -0.0019975737152351227
          ],
          [
            3.72611214777101e-18,
            1.2723267459806884e-17,
            -0.002269611457525715
          ],
          [
            -5.259616691041555e-17,
            1.5785016313771106e-17,
            -0.0025080540879875916
          ],
          [
            -4.132991663797106e-17,
            -1.481546251001577e-17,
            -0.0025069262584595958
          ],
          [
            3.3660727860618564e-18,
            -3.9334967915512596e-17,
            -0.0020452031830327593
          ],
          [
            -2.457918131064595e-17,
            -4.9413224559811495e-17,
            -0.001156038118763195
          ],
          [
            -3.192486233058152e-17,
            -2.370527255039113e-17,
            -8.547750887833294e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.3579520912849822e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.484676133210508e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124204e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.02793497684904e-15,
            -0.239559599152588
          ],
          [
            3.379460870790141e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654155e-15,
            -8.168153209276079e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.357952091284982e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.4846761332105156e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124214e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.0279349768490399e-15,
            -0.239559599152588
          ],
          [
            3.3794608707901433e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654157e-15,
            -8.187894806610529e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.4432899320127035e-15,
            9.992007221626409e-16,
            -0.11326376239774433
          ],
          [
            -2.3314683517128287e-15,
            -1.609823385706477e-15,
            -0.1572538910691717
          ],
          [
            -1.1712852909795402e-14,
            0.0,
            -0.1908863321705817
          ],
          [
            3.3306690738754696e-16,
            8.881784197001252e-16,
            -0.21688201205051294
          ],
          [
            -5.2735593669694936e-15,
            1.1102230246251565e-15,
            -0.23966737351919626
          ],
          [
            -4.163336342344337e-15,
            -1.0547118733938987e-15,
            -0.239559599152588
          ],
          [
            3.3306690738754696e-16,
            -2.7200464103316335e-15,
            -0.19543776090724663
          ],
          [
            -2.4424906541753444e-15,
            -3.4416913763379853e-15,
            -0.1104699539531695
          ],
          [
            -3.219646771412954e-15,
            -1.6653345369377348e-15,
            -8.326672684688674e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -59.62122626209205,
          -59.75240629217206,
          -60.13892907851621,
          -60.77828008662884,
          -61.63376223180968,
          -62.53738358069391,
          -63.26717068371284,
          -63.67661527946497,
          -63.735134973896976
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.082757097646428e-18,
            -2.145776316302777e-17,
            -6.1370794938989346e-18
          ],
          [
            -1.491848247921606e-17,
            1.2655228596385456e-17,
            0.0011560381187631884
          ],
          [
            -8.555802663729254e-19,
            4.175885242490094e-18,
            0.002045203183032749
          ],
          [
            -3.1979723700328e-17,
            -7.892508156885553e-18,
            0.002506926258459563
          ],
          [
            1.0602198455027197e-17,
            -5.7994626208839e-17,
            0.002508054087987547
          ],
          [
            -1.5542566847957974e-17,
            3.21653726824797e-17,
            0.0022696114575256952
          ],
          [
            5.128235752786111e-17,
            -1.9391076075106747e-18,
            0.0019975737152350876
          ],
          [
            -1.9278012009866994e-17,
            2.3167232994995958e-17,
            0.0016456193371535194
          ],
          [
            -2.546491325030171e-17,
            4.7491126668156174e-17,
            0.0011852745667101444
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.102973054638908e-16,
            -1.488794917155486e-15,
            -5.86453749313461e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654257e-16,
            0.11046995395316883
          ],
          [
            -8.589832174753139e-17,
            2.897336817639947e-16,
            0.19543776090724566
          ],
          [
            -3.21069185881688e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710406e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432809e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631522e-16,
            0.19088633217057835
          ],
          [
            -1.935468761214443e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.102973054638908e-16,
            -1.488794917155486e-15,
            -5.86453749313461e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654256e-16,
            0.11046995395316883
          ],
          [
            -8.58983217475314e-17,
            2.8973368176399475e-16,
            0.19543776090724566
          ],
          [
            -3.2106918588168804e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710402e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432807e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631527e-16,
            0.19088633217057835
          ],
          [
            -1.9354687612144436e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.89774555986142e-15,
          -4.278454928296727e-15,
          0.11326376239774269
        ],
        "actual_opposite_endpoint_branch_residual": 1.0070724217186694e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.3579520912849822e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.484676133210508e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124204e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.02793497684904e-15,
            -0.239559599152588
          ],
          [
            3.379460870790141e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654155e-15,
            -8.168153209276079e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654257e-16,
            0.11046995395316883
          ],
          [
            -8.589832174753139e-17,
            2.897336817639947e-16,
            0.19543776090724566
          ],
          [
            -3.21069185881688e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710406e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432809e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631522e-16,
            0.19088633217057835
          ],
          [
            -1.935468761214443e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4873777568652675e-15,
            9.889891051658964e-16,
            -0.11326376239774433
          ],
          [
            -2.357952091284982e-15,
            -1.6215644755345363e-15,
            -0.1572538910691717
          ],
          [
            -1.1691204694606269e-14,
            4.4846761332105156e-17,
            -0.1908863321705817
          ],
          [
            3.7409322388124214e-16,
            8.827730914845948e-16,
            -0.2168820120505129
          ],
          [
            -5.2805360823837565e-15,
            1.0952051188471977e-15,
            -0.23966737351919626
          ],
          [
            -4.1494300613282975e-15,
            -1.0279349768490399e-15,
            -0.239559599152588
          ],
          [
            3.3794608707901433e-16,
            -2.7291614626445525e-15,
            -0.19543776090724665
          ],
          [
            -2.4676941573971626e-15,
            -3.428416886046454e-15,
            -0.11046995395316947
          ],
          [
            -3.2051839014980763e-15,
            -1.6447329115654157e-15,
            -8.187894806610529e-16
          ],
          [
            -1.4977818661213136e-15,
            8.780523797654256e-16,
            0.11046995395316883
          ],
          [
            -8.58983217475314e-17,
            2.8973368176399475e-16,
            0.19543776090724566
          ],
          [
            -3.2106918588168804e-15,
            -5.476025594235989e-16,
            0.23955959915258485
          ],
          [
            1.0644367219710402e-15,
            -4.023816651626639e-15,
            0.239667373519192
          ],
          [
            -1.5604385238432807e-15,
            2.2317164652371235e-15,
            0.21688201205051102
          ],
          [
            5.148632594782283e-15,
            -1.3454028399631527e-16,
            0.19088633217057835
          ],
          [
            -1.9354687612144436e-15,
            1.6074023403770296e-15,
            0.15725389106916898
          ],
          [
            -2.556619638880221e-15,
            3.295056779979931e-15,
            0.11326376239774663
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.4432899320127035e-15,
            9.992007221626409e-16,
            -0.11326376239774433
          ],
          [
            -2.3314683517128287e-15,
            -1.609823385706477e-15,
            -0.1572538910691717
          ],
          [
            -1.1712852909795402e-14,
            0.0,
            -0.1908863321705817
          ],
          [
            3.3306690738754696e-16,
            8.881784197001252e-16,
            -0.21688201205051294
          ],
          [
            -5.2735593669694936e-15,
            1.1102230246251565e-15,
            -0.23966737351919626
          ],
          [
            -4.163336342344337e-15,
            -1.0547118733938987e-15,
            -0.239559599152588
          ],
          [
            3.3306690738754696e-16,
            -2.7200464103316335e-15,
            -0.19543776090724663
          ],
          [
            -2.4424906541753444e-15,
            -3.4416913763379853e-15,
            -0.1104699539531695
          ],
          [
            -3.219646771412954e-15,
            -1.6653345369377348e-15,
            -8.326672684688674e-16
          ],
          [
            -1.4988010832439613e-15,
            8.881784197001252e-16,
            0.11046995395316883
          ],
          [
            -1.1102230246251565e-16,
            3.3306690738754696e-16,
            0.19543776090724563
          ],
          [
            -3.219646771412954e-15,
            -5.551115123125783e-16,
            0.23955959915258485
          ],
          [
            1.1102230246251565e-15,
            -3.9968028886505635e-15,
            0.23966737351919198
          ],
          [
            -1.5543122344752192e-15,
            2.220446049250313e-15,
            0.21688201205051105
          ],
          [
            5.10702591327572e-15,
            -1.1102230246251565e-16,
            0.19088633217057838
          ],
          [
            -1.942890293094024e-15,
            1.5543122344752192e-15,
            0.15725389106916898
          ],
          [
            -2.55351295663786e-15,
            3.3306690738754696e-15,
            0.1132637623977466
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmce",
        "spacegroup_number": 64,
        "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": 1.2429269767364679e-15,
        "parent_symmetrization_rmsd_A": 0.3885784126376819,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -59.621226262092115,
        "reduced_polarization": [
          1.0537711600195351e-15,
          -5.198394220774861e-16,
          4.052169629525457e-16
        ],
        "cartesian_polarization_e_A2": [
          1.0495965362810256e-17,
          -7.492362496142892e-18,
          4.2404856594869274e-18
        ],
        "ranking_score": 0.3885784126376844
      }
    }
  ],
  "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": 35,
      "energy_polarization": 93
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 153,
      "full_response": 60,
      "energy_polarization": 93
    },
    "elapsed_seconds": 235.43314939294942
  }
}