{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "H7F12Sb",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -83.61239806158925,
  "input_cartesian_polarization_e_A2": [
    -1.5166348894692004e-08,
    -0.00022735704887847746,
    -1.0460271407924395e-09
  ],
  "input_reduced_polarization": [
    -6.895968187782121e-07,
    -0.00819010887028453,
    -3.481425302336753e-08
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.116376994573959e-15,
      "parent_symmetrization_rmsd_A": 0.06009185294525515,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -83.61676440788395,
      "reduced_polarization": [
        -2.921794191210151e-15,
        7.124567626007344e-16,
        -8.169024653806118e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.715043241132234e-17,
        3.11164209831252e-17,
        -2.4544606761915282e-17
      ],
      "ranking_score": 0.060091852945261384
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.473609296608933e-07,
      "parent_symmetrization_rmsd_A": 0.00917261643515018,
      "parent_cell_rmsd_A": 0.00020507259222657254,
      "energy_eV": -83.60980611718563,
      "reduced_polarization": [
        -6.470955478013232e-10,
        -6.473605988415908e-07,
        -9.790926890626057e-11
      ],
      "cartesian_polarization_e_A2": [
        -1.3538457392964316e-11,
        -1.7969645294879913e-08,
        -2.941708706663115e-12
      ],
      "ranking_score": 0.5092251793050662
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.8148936250997105e-15,
      "parent_symmetrization_rmsd_A": 0.06009210430368857,
      "parent_cell_rmsd_A": 0.00020507259222657254,
      "energy_eV": -83.61644420905905,
      "reduced_polarization": [
        5.842472571049614e-16,
        -1.9532104342078822e-15,
        -3.2244437525088255e-15
      ],
      "cartesian_polarization_e_A2": [
        4.740606696515275e-17,
        -9.46598682867479e-18,
        -9.68876533596174e-17
      ],
      "ranking_score": 0.060143372451752844
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "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": 0.002308599387149316,
      "parent_symmetrization_rmsd_A": 0.5252489349791551,
      "parent_cell_rmsd_A": 0.01896512415793374,
      "energy_eV": -75.59776278329,
      "reduced_polarization": [
        8.555291384846296e-08,
        -0.49769140061445194,
        -8.60308081795691e-09
      ],
      "cartesian_polarization_e_A2": [
        1.4165673265646865e-09,
        -0.013775835689209379,
        -5.490944234090044e-10
      ],
      "ranking_score": 1.0346074147929372
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.8537309873612235e-05,
      "parent_symmetrization_rmsd_A": 0.38599666753509326,
      "parent_cell_rmsd_A": 0.011968945299788468,
      "energy_eV": -78.39896233896553,
      "reduced_polarization": [
        -0.49997148899961963,
        7.343121730916803e-07,
        -9.806619017207593e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.011261124186786164,
        -2.4760357869600212e-05,
        2.530394556588164e-07
      ],
      "ranking_score": 0.8890459784797876
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.14326899232970683,
      "parent_symmetrization_rmsd_A": 0.466949067143707,
      "parent_cell_rmsd_A": 0.01007622586189756,
      "energy_eV": -74.3234010297798,
      "reduced_polarization": [
        -0.032984031610283855,
        0.049407716898303665,
        -0.3696277048878924
      ],
      "cartesian_polarization_e_A2": [
        0.0031699787816525378,
        0.006515436413529322,
        -0.011113180928959026
      ],
      "ranking_score": 1.2560061082685952
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.20090015624595883,
      "parent_symmetrization_rmsd_A": 0.5673942407168387,
      "parent_cell_rmsd_A": 0.052964698367074965,
      "energy_eV": -73.69432143902549,
      "reduced_polarization": [
        -0.317231912776108,
        -0.4190865416949304,
        -0.02024132745855016
      ],
      "cartesian_polarization_e_A2": [
        -0.006909745384002225,
        -0.011299448690978183,
        -0.0005344232981391586
      ],
      "ranking_score": 1.4824357278005251
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.11250407935688171,
      "parent_symmetrization_rmsd_A": 0.4828477567864452,
      "parent_cell_rmsd_A": 0.050470979048353314,
      "energy_eV": -71.4360912890335,
      "reduced_polarization": [
        -0.03179498988313554,
        -0.4465579943643208,
        -0.4062439414015986
      ],
      "cartesian_polarization_e_A2": [
        0.003559627571681354,
        -0.006671476670220446,
        -0.012105917253302245
      ],
      "ranking_score": 1.220473660262297
    },
    {
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.050495990148710077,
      "parent_symmetrization_rmsd_A": 0.5527843924289906,
      "parent_cell_rmsd_A": 0.05217142742873799,
      "energy_eV": -63.084536745175,
      "reduced_polarization": [
        -0.48135226075247045,
        0.020326757439330576,
        -0.4577042582041952
      ],
      "cartesian_polarization_e_A2": [
        -0.0058936349098438305,
        0.006802838803485507,
        -0.013773618619166593
      ],
      "ranking_score": 1.1668192295835953
    },
    {
      "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": 0.06023056611684245,
      "parent_symmetrization_rmsd_A": 0.5508768500702708,
      "parent_cell_rmsd_A": 0.08271952064956753,
      "energy_eV": -62.683381550481876,
      "reduced_polarization": [
        -0.506286973447722,
        -0.47125335845753297,
        -0.44744692530734403
      ],
      "cartesian_polarization_e_A2": [
        -0.006645484158476695,
        -0.006689204096935985,
        -0.013325591260516623
      ],
      "ranking_score": 1.1920178624663476
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "target_residual": 0.008190108899390114,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.008787822162326169,
            "max_log_strain_component": 4.347660177351915e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0000322884395358,
              0.9999876139698459,
              0.9999529454677523
            ],
            "cell_volume_ratio": 0.999972846540729,
            "cell_rmsd_from_input_A": 0.00020507259222657254
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.470955478013232e-10,
              -6.473605988415908e-07,
              -9.790926890626057e-11
            ],
            "branch_aligned_reduced_polarization": [
              -6.470955478013232e-10,
              -6.473605988415908e-07,
              -9.790926890626057e-11
            ],
            "target_residual": 6.473609296608933e-07,
            "energy_eV": -83.60980611718563
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.116376994573959e-15,
        "parent_symmetrization_rmsd_A": 0.06009185294525515,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.61676440788395,
        "reduced_polarization": [
          -2.921794191210151e-15,
          7.124567626007344e-16,
          -8.169024653806118e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.715043241132234e-17,
          3.11164209831252e-17,
          -2.4544606761915282e-17
        ],
        "ranking_score": 0.060091852945261384
      },
      "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": [
          -83.61239806158925,
          -83.61352337389191,
          -83.61444713754133,
          -83.61519220759394,
          -83.6157775826299,
          -83.6162182442411,
          -83.61652505180982,
          -83.61670517511912,
          -83.61676440788393
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5166348975153794e-08,
            -0.00022735704887846264,
            -1.0460272256157128e-09
          ],
          [
            -1.3268769180442882e-08,
            -0.00019927150282156346,
            -9.156577280747368e-10
          ],
          [
            -1.1371680024450157e-08,
            -0.00017102827815363027,
            -7.851013793606924e-10
          ],
          [
            -9.475153504658709e-09,
            -0.0001426591094021998,
            -6.543689236646358e-10
          ],
          [
            -7.579214410549867e-09,
            -0.00011419664560582575,
            -5.23502889059737e-10
          ],
          [
            -5.683834750262941e-09,
            -8.56728413391572e-05,
            -3.925540496745844e-10
          ],
          [
            -3.788930898096835e-09,
            -5.711814633101947e-05,
            -2.6155860260784156e-10
          ],
          [
            -1.8943771116099995e-09,
            -2.855837279954318e-05,
            -1.306665047587959e-10
          ],
          [
            -5.868447033394205e-17,
            4.88152796199149e-17,
            -2.0333522268449424e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.923819820412303e-15,
            1.4201008256582821e-15,
            -6.767476306339381e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.92381982637012e-15,
            1.4200880055215137e-15,
            -6.767476306038354e-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": [
          [
            -6.895968236997341e-07,
            -0.008190108870285429,
            -3.48142558670439e-08
          ],
          [
            -6.033239610681029e-07,
            -0.007178380026226838,
            -3.047525115595917e-08
          ],
          [
            -5.17069944916404e-07,
            -0.006160971116564495,
            -2.6130027586113158e-08
          ],
          [
            -4.3083813955346884e-07,
            -0.00513902531554794,
            -2.1778942815853242e-08
          ],
          [
            -3.446303125653749e-07,
            -0.004113718741420025,
            -1.7423412213002365e-08
          ],
          [
            -2.584460179200221e-07,
            -0.0030862024958617784,
            -1.306512564802631e-08
          ],
          [
            -1.722821117433604e-07,
            -0.002057573471194285,
            -8.705287879440249e-09
          ],
          [
            -8.613536522927845e-08,
            -0.001028761504410669,
            -4.348889803829081e-09
          ],
          [
            -2.942091015256665e-15,
            1.4432899320127035e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.61676440788395,
          -83.61670517511915,
          -83.61652505180983,
          -83.61621824424111,
          -83.61577758262989,
          -83.61519220759392,
          -83.61444713754135,
          -83.6135233738919,
          -83.61239806158926
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.414251491598959e-17,
            5.974706638664092e-17,
            -2.174724349125582e-17
          ],
          [
            1.8943770407735428e-09,
            2.8558372799521644e-05,
            1.306663941576696e-10
          ],
          [
            3.7889308429617074e-09,
            5.7118146331017505e-05,
            2.615586205350298e-10
          ],
          [
            5.683834736637074e-09,
            8.567284133920597e-05,
            3.925540613152251e-10
          ],
          [
            7.579214433349881e-09,
            0.00011419664560581072,
            5.235027159540852e-10
          ],
          [
            9.475153426182142e-09,
            0.00014265910940218393,
            6.543687710729812e-10
          ],
          [
            1.137168002396889e-08,
            0.00017102827815352874,
            7.851014282995101e-10
          ],
          [
            1.326876911664495e-08,
            0.00019927150282153327,
            9.156576064947116e-10
          ],
          [
            1.5166348929914718e-08,
            0.0002273570488785021,
            1.046027172345494e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.7443959050718255e-15,
            1.7903709985259504e-15,
            -7.237996108703215e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7443959050718255e-15,
            1.7903709985259504e-15,
            -7.237996108703215e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.895968178327639e-07,
          0.008190108870288247,
          3.4814254492991074e-08
        ],
        "actual_opposite_endpoint_branch_residual": 3.809777551094577e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.923819820412303e-15,
            1.4201008256582821e-15,
            -6.767476306339381e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.92381982637012e-15,
            1.4200880055215137e-15,
            -6.767476306038354e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.895968236997341e-07,
            -0.008190108870285429,
            -3.48142558670439e-08
          ],
          [
            -6.033239610681029e-07,
            -0.007178380026226838,
            -3.047525115595917e-08
          ],
          [
            -5.17069944916404e-07,
            -0.006160971116564495,
            -2.6130027586113158e-08
          ],
          [
            -4.3083813955346884e-07,
            -0.00513902531554794,
            -2.1778942815853242e-08
          ],
          [
            -3.446303125653749e-07,
            -0.004113718741420025,
            -1.7423412213002365e-08
          ],
          [
            -2.584460179200221e-07,
            -0.0030862024958617784,
            -1.306512564802631e-08
          ],
          [
            -1.722821117433604e-07,
            -0.002057573471194285,
            -8.705287879440249e-09
          ],
          [
            -8.613536522927845e-08,
            -0.001028761504410669,
            -4.348889803829081e-09
          ],
          [
            -2.942091015256665e-15,
            1.4432899320127035e-15,
            -6.661338147750939e-16
          ],
          [
            8.613536039980829e-08,
            0.0010287615044081155,
            4.3488861400931e-09
          ],
          [
            1.722821095784255e-07,
            0.002057573471194507,
            8.705288490062912e-09
          ],
          [
            2.584460174759329e-07,
            0.003086202495863777,
            1.3065125981093217e-08
          ],
          [
            3.446303108445292e-07,
            0.004113718741416639,
            1.7423406384331486e-08
          ],
          [
            4.3083813372479796e-07,
            0.005139025315544776,
            2.177893776433848e-08
          ],
          [
            5.17069945638049e-07,
            0.006160971116561664,
            2.6130029251447695e-08
          ],
          [
            6.033239563496551e-07,
            0.00717838002622373,
            3.047524710364513e-08
          ],
          [
            6.895968208686654e-07,
            0.008190108870285928,
            3.4814254035175907e-08
          ]
        ]
      },
      "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,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028454,
              -3.481425302336753e-08
            ],
            "target_residual": 0.4918098911302002,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005936843190518816,
            "step_scale": 0.2274005257231196,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0006427634898662,
              1.0001691498219814,
              0.9995591972497213
            ],
            "cell_volume_ratio": 1.0003708613433517,
            "cell_rmsd_from_input_A": 0.0028001495460966974
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.218559123286334e-07,
              -0.11889969454957929,
              -1.793117677492247e-08
            ],
            "branch_aligned_reduced_polarization": [
              -5.218559123286334e-07,
              -0.11889969454957927,
              -1.793117677492247e-08
            ],
            "target_residual": 0.3811003054507785,
            "energy_eV": -83.1863028067578,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0006243382401622902,
            "step_scale": 0.2934998453270612,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0013191607224132,
              1.0003470642848724,
              0.9990958439822636
            ],
            "cell_volume_ratio": 1.0007610198818013,
            "cell_rmsd_from_input_A": 0.005744500794923143
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.4552168305597453e-07,
              -0.22722209634167426,
              1.5693147206916563e-09
            ],
            "branch_aligned_reduced_polarization": [
              -3.4552168305597453e-07,
              -0.22722209634167423,
              1.5693147206916563e-09
            ],
            "target_residual": 0.2727779036585446,
            "energy_eV": -81.86885668745191,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0007356142513129274,
            "step_scale": 0.4220830643120891,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0021166991980328,
              1.000556729113632,
              0.9985501827268789
            ],
            "cell_volume_ratio": 1.0012209117755617,
            "cell_rmsd_from_input_A": 0.009213133752047922
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.021157262635966e-07,
              -0.33662049216583617,
              2.4202359197527993e-08
            ],
            "branch_aligned_reduced_polarization": [
              -2.021157262635966e-07,
              -0.33662049216583617,
              2.4202359197527993e-08
            ],
            "target_residual": 0.16337950783429064,
            "energy_eV": -79.60547112200274,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0010690422333740983,
            "step_scale": 0.8540744625517905,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0032768662317357,
              1.0008615059488521,
              0.9977577236847937
            ],
            "cell_volume_ratio": 1.0018896332011746,
            "cell_rmsd_from_input_A": 0.014253051429271016
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.151914027557399e-07,
              -0.4627176826328349,
              2.020041640483867e-08
            ],
            "branch_aligned_reduced_polarization": [
              -3.151914027557399e-07,
              -0.4627176826328349,
              2.020041640483867e-08
            ],
            "target_residual": 0.037282317368502904,
            "energy_eV": -76.21390324739525,
            "max_atomic_step_A": 0.02374174912229617,
            "max_log_strain_component": 0.0020054609328327513,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 0.8653798169286685,
            "cell_principal_stretches": [
              1.0050482995699088,
              1.0012447420563277,
              0.9978721857794537
            ],
            "cell_volume_ratio": 1.00415810744219,
            "cell_rmsd_from_input_A": 0.01896512415793374
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              8.555291384846296e-08,
              -0.49769140061445194,
              -8.60308081795691e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.555291384846296e-08,
              -0.49769140061445194,
              -8.60308081795691e-09
            ],
            "target_residual": 0.002308599387149316,
            "energy_eV": -75.59776278329
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "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": 0.002308599387149316,
        "parent_symmetrization_rmsd_A": 0.5252489349791551,
        "parent_cell_rmsd_A": 0.01896512415793374,
        "energy_eV": -75.59776278329,
        "reduced_polarization": [
          8.555291384846296e-08,
          -0.49769140061445194,
          -8.60308081795691e-09
        ],
        "cartesian_polarization_e_A2": [
          1.4165673265646865e-09,
          -0.013775835689209379,
          -5.490944234090044e-10
        ],
        "ranking_score": 1.0346074147929372
      },
      "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": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187592416e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "target_residual": 0.5000663838801456,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000636769675434745,
            "step_scale": 0.4317843750856788,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0006342681316875,
              1.000013894746659,
              0.9993405405133755
            ],
            "cell_volume_ratio": 0.999988284761746,
            "cell_rmsd_from_input_A": 0.003480981069480634
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.20452874498600065,
              -0.006658058537519572,
              -0.003051310275379884
            ],
            "branch_aligned_reduced_polarization": [
              -0.20452874498600065,
              -0.006658058537519572,
              -0.003051310275379884
            ],
            "target_residual": 0.2955620117292368,
            "energy_eV": -82.90757960758347,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000660168649128639,
            "step_scale": 0.5821226501240425,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0013026423728446,
              1.0000303289455659,
              0.9986433080960863
            ],
            "cell_volume_ratio": 0.9999745104372703,
            "cell_rmsd_from_input_A": 0.006985527377421518
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3565564975591972,
              -0.005565767150561236,
              -0.007505832011915331
            ],
            "branch_aligned_reduced_polarization": [
              -0.3565564975591972,
              -0.005565767150561236,
              -0.007505832011915331
            ],
            "target_residual": 0.143747534485465,
            "energy_eV": -81.04918719899105,
            "max_atomic_step_A": 0.09998530643946567,
            "max_log_strain_component": 0.0006752544645312211,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.001970597740375,
              1.000046146387538,
              0.9979484983883877
            ],
            "cell_volume_ratio": 0.9999611959118846,
            "cell_rmsd_from_input_A": 0.010708578645004019
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4614749140000999,
              -0.003555072087480999,
              -0.00924663024299588
            ],
            "branch_aligned_reduced_polarization": [
              -0.4614749140000999,
              -0.003555072087480999,
              -0.00924663024299588
            ],
            "target_residual": 0.03977839815399274,
            "energy_eV": -79.25394237608552,
            "max_atomic_step_A": 0.026120741830837655,
            "max_log_strain_component": 0.00021666463935033958,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0022219851452008,
              1.000045324708618,
              0.9976995752101244
            ],
            "cell_volume_ratio": 0.9999617697673008,
            "cell_rmsd_from_input_A": 0.01169259543077731
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4966861234249197,
              -0.00015899991341409585,
              -0.0005346402533050834
            ],
            "branch_aligned_reduced_polarization": [
              -0.4966861234249197,
              -0.00015899991341409585,
              -0.0005346402533050834
            ],
            "target_residual": 0.003360490905773414,
            "energy_eV": -78.4777740686929,
            "max_atomic_step_A": 0.00273478754250624,
            "max_log_strain_component": 0.00014698670029633513,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 0.8290685745465053,
            "cell_principal_stretches": [
              1.0023255541586311,
              1.0001897852570798,
              0.997770393022855
            ],
            "cell_volume_ratio": 1.000280564592098,
            "cell_rmsd_from_input_A": 0.011968945299788468
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49997148899961963,
              7.343121730916803e-07,
              -9.806619017207593e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997148899961963,
              7.343121730916803e-07,
              -9.806619017207593e-07
            ],
            "target_residual": 2.8537309873612235e-05,
            "energy_eV": -78.39896233896553
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.8537309873612235e-05,
        "parent_symmetrization_rmsd_A": 0.38599666753509326,
        "parent_cell_rmsd_A": 0.011968945299788468,
        "energy_eV": -78.39896233896553,
        "reduced_polarization": [
          -0.49997148899961963,
          7.343121730916803e-07,
          -9.806619017207593e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.011261124186786164,
          -2.4760357869600212e-05,
          2.530394556588164e-07
        ],
        "ranking_score": 0.8890459784797876
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.4814253035975185e-08
            ],
            "target_residual": 0.5000670385753603,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.000845750222316093,
            "step_scale": 0.2680090211155286,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.000963570263157,
              0.9996039041276015,
              0.9992039682737505
            ],
            "cell_volume_ratio": 0.9997706095745043,
            "cell_rmsd_from_input_A": 0.007676192789768147
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0016902488368760423,
              -0.003311035425419794,
              -0.13058097433637728
            ],
            "branch_aligned_reduced_polarization": [
              -0.0016902488368760423,
              -0.003311035425419794,
              -0.13058097433637728
            ],
            "target_residual": 0.3694377300966691,
            "energy_eV": -82.79029025027799,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0009147209446609982,
            "step_scale": 0.36729002873865857,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0019831223054592,
              0.9992272541039465,
              0.9983427586462933
            ],
            "cell_volume_ratio": 0.9995495992598757,
            "cell_rmsd_from_input_A": 0.01573281626338004
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.025927853612056517,
              0.019000628407101827,
              -0.22184004464830517
            ],
            "branch_aligned_reduced_polarization": [
              -0.025927853612056517,
              0.019000628407101827,
              -0.2218400446483052
            ],
            "target_residual": 0.2800111394820746,
            "energy_eV": -80.29602384653401,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006477054521116777,
            "step_scale": 0.6245220698991687,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0028255303886668,
              0.9987076625547208,
              0.9977275364069472
            ],
            "cell_volume_ratio": 0.9992536019844549,
            "cell_rmsd_from_input_A": 0.022693602710890857
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.04887726014420322,
              0.05612548983279934,
              -0.2619607101353412
            ],
            "branch_aligned_reduced_polarization": [
              -0.04887726014420322,
              0.05612548983279934,
              -0.2619607101353412
            ],
            "target_residual": 0.24940280809855936,
            "energy_eV": -78.92024775378717,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0012304861220864948,
            "step_scale": 0.6673878357628492,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0041288639660537,
              0.9983824478028567,
              0.9965679065080973
            ],
            "cell_volume_ratio": 0.9990639434890114,
            "cell_rmsd_from_input_A": 0.0329908784231486
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.05849673665820759,
              0.06978665095294281,
              -0.2995174864251729
            ],
            "branch_aligned_reduced_polarization": [
              -0.05849673665820759,
              0.06978665095294281,
              -0.2995174864251729
            ],
            "target_residual": 0.2201937399204807,
            "energy_eV": -74.43633822124353,
            "max_atomic_step_A": 0.09049486812146973,
            "max_log_strain_component": 0.0027069342698422855,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.5183547857109942,
            "cell_principal_stretches": [
              1.0014463464982042,
              1.0003376664130363,
              0.9979984958392536
            ],
            "cell_volume_ratio": 0.9997794254463633,
            "cell_rmsd_from_input_A": 0.01007622586189756
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.032984031610283855,
              0.049407716898303665,
              -0.3696277048878924
            ],
            "branch_aligned_reduced_polarization": [
              -0.032984031610283855,
              0.049407716898303665,
              -0.3696277048878924
            ],
            "target_residual": 0.14326899232970683,
            "energy_eV": -74.3234010297798
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.49999999999999917,
        "parent_symmetrization_rmsd_A": 0.06009185294525515,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.61676440788395,
        "reduced_polarization": [
          -2.921794191210151e-15,
          7.124567626007344e-16,
          -8.169024653806118e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.715043241132234e-17,
          3.11164209831252e-17,
          -2.4544606761915282e-17
        ],
        "ranking_score": 1.0600918529452534
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187592416e-07,
              -0.00819010887028454,
              -3.481425302336753e-08
            ],
            "target_residual": 0.7013389190802694,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000525347618741642,
            "step_scale": 0.20122474756785894,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0007263279985117,
              0.9999924849241786,
              0.9996096424329969
            ],
            "cell_volume_ratio": 1.0003281693053439,
            "cell_rmsd_from_input_A": 0.002843052756724409
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.09945701716658048,
              -0.1064805429187538,
              -0.00034379679787455977
            ],
            "branch_aligned_reduced_polarization": [
              -0.09945701716658051,
              -0.1064805429187538,
              -0.00034379679787455977
            ],
            "target_residual": 0.5615090047317585,
            "energy_eV": -83.13468288541202,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0005517938861425427,
            "step_scale": 0.2525687360125801,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0014980716458446,
              0.9999761060599541,
              0.9992000122672732
            ],
            "cell_volume_ratio": 1.000672974882793,
            "cell_rmsd_from_input_A": 0.0058598582324085316
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.1908897705437422,
              -0.2031734320325778,
              -0.001975856624905004
            ],
            "branch_aligned_reduced_polarization": [
              -0.19088977054374223,
              -0.20317343203257776,
              -0.001975856624905004
            ],
            "target_residual": 0.4285546049399321,
            "energy_eV": -81.60944981050456,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006247275277671363,
            "step_scale": 0.30817285626883983,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0024632392048938,
              0.9998682619248761,
              0.9987352717070301
            ],
            "cell_volume_ratio": 1.001063500029371,
            "cell_rmsd_from_input_A": 0.009580723748263537
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.2692355603503128,
              -0.2864402551797084,
              -0.002892601671228251
            ],
            "branch_aligned_reduced_polarization": [
              -0.2692355603503128,
              -0.2864402551797084,
              -0.002892601671228251
            ],
            "target_residual": 0.3144333925634658,
            "energy_eV": -79.073283986266,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0009664776077193308,
            "step_scale": 0.4392978872750164,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0039805911736375,
              0.9997051744817773,
              0.9979907696184677
            ],
            "cell_volume_ratio": 1.0016679584996846,
            "cell_rmsd_from_input_A": 0.0155151129562147
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.3265827474423772,
              -0.3716535612113826,
              -0.01670617270884305
            ],
            "branch_aligned_reduced_polarization": [
              -0.3265827474423772,
              -0.3716535612113826,
              -0.01670617270884305
            ],
            "target_residual": 0.21639188533984435,
            "energy_eV": -76.04704280389913,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007348593685892405,
            "step_scale": 0.5537530564457431,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.1869384419317346,
            "cell_principal_stretches": [
              1.009370888282745,
              1.0032220822583504,
              0.9923391604006597
            ],
            "cell_volume_ratio": 1.0048656206775906,
            "cell_rmsd_from_input_A": 0.052964698367074965
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.317231912776108,
              -0.4190865416949304,
              -0.02024132745855016
            ],
            "branch_aligned_reduced_polarization": [
              -0.317231912776108,
              -0.4190865416949304,
              -0.02024132745855016
            ],
            "target_residual": 0.20090015624595883,
            "energy_eV": -73.69432143902549
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.707106781186545,
        "parent_symmetrization_rmsd_A": 0.06009185294525515,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.61676440788395,
        "reduced_polarization": [
          -2.921794191210151e-15,
          7.124567626007344e-16,
          -8.169024653806118e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.715043241132234e-17,
          3.11164209831252e-17,
          -2.4544606761915282e-17
        ],
        "ranking_score": 1.4743054153183452
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028454,
              -3.4814253035975185e-08
            ],
            "target_residual": 0.7013393858890618,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0008663639485749936,
            "step_scale": 0.2745432507678425,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.000818873090226,
              1.000380220814645,
              0.9990218990710642
            ],
            "cell_volume_ratio": 1.0002201311891317,
            "cell_rmsd_from_input_A": 0.006851039257004798
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0017853984557774309,
              -0.13917789987778764,
              -0.1316460044774332
            ],
            "branch_aligned_reduced_polarization": [
              -0.0017853984557774309,
              -0.13917789987778761,
              -0.1316460044774332
            ],
            "target_residual": 0.5156359584064022,
            "energy_eV": -82.74659364745743,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0009134701247785572,
            "step_scale": 0.3554717629679744,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0016801994488993,
              1.0007646844188487,
              0.998004054010123
            ],
            "cell_volume_ratio": 1.0004453402796223,
            "cell_rmsd_from_input_A": 0.01393080108728102
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.019964712411247747,
              -0.25164388808907734,
              -0.23300521536332314
            ],
            "branch_aligned_reduced_polarization": [
              -0.019964712411247747,
              -0.25164388808907734,
              -0.23300521536332314
            ],
            "target_residual": 0.3651925014131041,
            "energy_eV": -80.28457253758017,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0008589809386776717,
            "step_scale": 0.5886603242548862,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0025031641295215,
              1.0012302207939698,
              0.9969845720949222
            ],
            "cell_volume_ratio": 1.000709769424055,
            "cell_rmsd_from_input_A": 0.021179350103219818
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.049131732066085364,
              -0.3317376826459876,
              -0.27851221726135533
            ],
            "branch_aligned_reduced_polarization": [
              -0.049131732066085364,
              -0.3317376826459876,
              -0.27851221726135533
            ],
            "target_residual": 0.2824587977734754,
            "energy_eV": -78.34106872071636,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013105557148644358,
            "step_scale": 0.7566232924669007,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0037450277240163,
              1.0016230130412258,
              0.9955912082323904
            ],
            "cell_volume_ratio": 1.000941633854889,
            "cell_rmsd_from_input_A": 0.031151597089300497
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.04851674930214476,
              -0.3919108614363774,
              -0.3244098208495436
            ],
            "branch_aligned_reduced_polarization": [
              -0.04851674930214476,
              -0.3919108614363774,
              -0.3244098208495436
            ],
            "target_residual": 0.21182315230484733,
            "energy_eV": -72.38618083096281,
            "max_atomic_step_A": 0.06953808027332734,
            "max_log_strain_component": 0.00261298922144449,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.7464390622358623,
            "cell_principal_stretches": [
              1.0064660856495442,
              1.0032166036535537,
              0.9918643030821114
            ],
            "cell_volume_ratio": 1.001488846581398,
            "cell_rmsd_from_input_A": 0.050470979048353314
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.03179498988313554,
              -0.4465579943643208,
              -0.4062439414015986
            ],
            "branch_aligned_reduced_polarization": [
              -0.03179498988313554,
              -0.4465579943643208,
              -0.4062439414015986
            ],
            "target_residual": 0.11250407935688171,
            "energy_eV": -71.4360912890335
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.11250407935688171,
        "parent_symmetrization_rmsd_A": 0.4828477567864452,
        "parent_cell_rmsd_A": 0.050470979048353314,
        "energy_eV": -71.4360912890335,
        "reduced_polarization": [
          -0.03179498988313554,
          -0.4465579943643208,
          -0.4062439414015986
        ],
        "cartesian_polarization_e_A2": [
          0.003559627571681354,
          -0.006671476670220446,
          -0.012105917253302245
        ],
        "ranking_score": 1.220473660262297
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187592416e-07,
              -0.00819010887028453,
              -3.4814253035975185e-08
            ],
            "target_residual": 0.7071536986205418,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006853754439055623,
            "step_scale": 0.23694699909324224,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0008990004144345,
              0.9997489545668856,
              0.9991500194012655
            ],
            "cell_volume_ratio": 0.9997971981353063,
            "cell_rmsd_from_input_A": 0.007651849598480344
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1165090452419493,
              -0.006102395000211713,
              -0.11760937258420238
            ],
            "branch_aligned_reduced_polarization": [
              -0.11650904524194927,
              -0.006102395000211713,
              -0.1176093725842024
            ],
            "target_residual": 0.541594999553566,
            "energy_eV": -82.77500984062529,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0007080732727912165,
            "step_scale": 0.329004669999921,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.001846851506174,
              0.9994846073140977,
              0.9982445038712559
            ],
            "cell_volume_ratio": 0.9995726751379408,
            "cell_rmsd_from_input_A": 0.015741256942766218
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.25061561637817165,
              0.0027228241444298457,
              -0.2278371808117385
            ],
            "branch_aligned_reduced_polarization": [
              -0.25061561637817165,
              0.0027228241444298457,
              -0.22783718081173854
            ],
            "target_residual": 0.36915116783543167,
            "energy_eV": -79.95251496947508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00107295318979998,
            "step_scale": 0.4353868570283992,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0032022058399441,
              0.9990997338911568,
              0.997002760625042
            ],
            "cell_volume_ratio": 0.9992949266949039,
            "cell_rmsd_from_input_A": 0.027226335914908306
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.30547191117572026,
              -0.004160554852094313,
              -0.3448051728938423
            ],
            "branch_aligned_reduced_polarization": [
              -0.30547191117572026,
              -0.004160554852094313,
              -0.3448051728938423
            ],
            "target_residual": 0.24888535898845945,
            "energy_eV": -75.31609935131341,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00153579369891468,
            "step_scale": 0.6551208680747017,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.00526913926984,
              0.9986204342221504,
              0.9950044139126103
            ],
            "cell_volume_ratio": 0.9988673238946989,
            "cell_rmsd_from_input_A": 0.04495588631380588
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4252230429621392,
              0.009331347288449024,
              -0.40751680512046734
            ],
            "branch_aligned_reduced_polarization": [
              -0.4252230429621392,
              0.009331347288449024,
              -0.40751680512046734
            ],
            "target_residual": 0.11929714448043316,
            "energy_eV": -68.02341422098964,
            "max_atomic_step_A": 0.07808781521633018,
            "max_log_strain_component": 0.008911017220188866,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6760375126713725,
            "cell_principal_stretches": [
              1.0070531994987975,
              1.002941014862632,
              0.9875350665442004
            ],
            "cell_volume_ratio": 0.9974251886860754,
            "cell_rmsd_from_input_A": 0.05217142742873799
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.48135226075247045,
              0.020326757439330576,
              -0.4577042582041952
            ],
            "branch_aligned_reduced_polarization": [
              -0.48135226075247045,
              0.020326757439330576,
              -0.4577042582041952
            ],
            "target_residual": 0.050495990148710077,
            "energy_eV": -63.084536745175
          }
        ],
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.050495990148710077,
        "parent_symmetrization_rmsd_A": 0.5527843924289906,
        "parent_cell_rmsd_A": 0.05217142742873799,
        "energy_eV": -63.084536745175,
        "reduced_polarization": [
          -0.48135226075247045,
          0.020326757439330576,
          -0.4577042582041952
        ],
        "cartesian_polarization_e_A2": [
          -0.0058936349098438305,
          0.006802838803485507,
          -0.013773618619166593
        ],
        "ranking_score": 1.1668192295835953
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.895968187782121e-07,
              -0.00819010887028453,
              -3.481425302336753e-08
            ],
            "branch_aligned_reduced_polarization": [
              -6.895968187592416e-07,
              -0.00819010887028454,
              -3.4814253035975185e-08
            ],
            "target_residual": 0.8613223813430297,
            "energy_eV": -83.61239806158925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006983268067900749,
            "step_scale": 0.24142641020444247,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0008629690291275,
              1.0002409637318048,
              0.999090444014698
            ],
            "cell_volume_ratio": 1.000193580442081,
            "cell_rmsd_from_input_A": 0.006948735292955055
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.12018105728954565,
              -0.12470972160262264,
              -0.11864079709840598
            ],
            "branch_aligned_reduced_polarization": [
              -0.12018105728954565,
              -0.12470972160262261,
              -0.11864079709840597
            ],
            "target_residual": 0.6561555181045173,
            "energy_eV": -82.74808464774648,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0007384941562880213,
            "step_scale": 0.3315309181558085,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0017790178103592,
              1.0005160282014507,
              0.998123450768067
            ],
            "cell_volume_ratio": 1.0004151063136915,
            "cell_rmsd_from_input_A": 0.014284193062179089
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.24787913448764792,
              -0.2422836153491973,
              -0.23579135634548942
            ],
            "branch_aligned_reduced_polarization": [
              -0.24787913448764792,
              -0.2422836153491973,
              -0.23579135634548942
            ],
            "target_residual": 0.4469774861510747,
            "energy_eV": -79.88414863937497,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0010583659974371705,
            "step_scale": 0.4692995663773646,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.00302852197041,
              1.0008827350759724,
              0.9967855344105732
            ],
            "cell_volume_ratio": 1.000686883644844,
            "cell_rmsd_from_input_A": 0.0245497134789139
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.29702738131639117,
              -0.34441416404332986,
              -0.3487193239987749
            ],
            "branch_aligned_reduced_polarization": [
              -0.29702738131639117,
              -0.34441416404332986,
              -0.3487193239987749
            ],
            "target_residual": 0.29713747528207407,
            "energy_eV": -74.96339959852051,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013758249827536147,
            "step_scale": 0.7648986854716104,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17519775237393007,
            "cell_principal_stretches": [
              1.0049880016203896,
              1.0013286954370046,
              0.9948508118470016
            ],
            "cell_volume_ratio": 1.00114157645131,
            "cell_rmsd_from_input_A": 0.03952808992163892
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4133020447990113,
              -0.41552022797325067,
              -0.3930817947410521
            ],
            "branch_aligned_reduced_polarization": [
              -0.4133020447990113,
              -0.41552022797325067,
              -0.3930817947410521
            ],
            "target_residual": 0.16150811104560261,
            "energy_eV": -69.24681141497106,
            "max_atomic_step_A": 0.0825095624733566,
            "max_log_strain_component": 0.006159881882169944,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.410589525111613,
            "cell_principal_stretches": [
              1.0107203346083211,
              1.004651756849583,
              0.9904192967688386
            ],
            "cell_volume_ratio": 1.0056935033961414,
            "cell_rmsd_from_input_A": 0.08271952064956753
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.506286973447722,
              -0.47125335845753297,
              -0.44744692530734403
            ],
            "branch_aligned_reduced_polarization": [
              -0.506286973447722,
              -0.47125335845753297,
              -0.44744692530734403
            ],
            "target_residual": 0.06023056611684245,
            "energy_eV": -62.683381550481876
          }
        ],
        "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": 0.06023056611684245,
        "parent_symmetrization_rmsd_A": 0.5508768500702708,
        "parent_cell_rmsd_A": 0.08271952064956753,
        "energy_eV": -62.683381550481876,
        "reduced_polarization": [
          -0.506286973447722,
          -0.47125335845753297,
          -0.44744692530734403
        ],
        "cartesian_polarization_e_A2": [
          -0.006645484158476695,
          -0.006689204096935985,
          -0.013325591260516623
        ],
        "ranking_score": 1.1920178624663476
      },
      "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": 0.06009185294525515,
        "minimum_distance_A_by_image": [
          0.9939442132910989,
          0.9935600727165309,
          0.9932270307084277,
          0.9929451386834347,
          0.9927144402153297,
          0.9925349710014197,
          0.9924067588349692,
          0.9923298235836974,
          0.9923041771743983
        ],
        "minimum_distance_A": 0.9923041771743983,
        "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": [
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317,
          230.68764069074317
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.923819820412303e-15,
        1.4201008256582821e-15,
        -6.767476306339381e-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": [
          -83.61239806158925,
          -83.61352337389191,
          -83.61444713754133,
          -83.61519220759394,
          -83.6157775826299,
          -83.6162182442411,
          -83.61652505180982,
          -83.61670517511912,
          -83.61676440788393
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5166348975153794e-08,
            -0.00022735704887846264,
            -1.0460272256157128e-09
          ],
          [
            -1.3268769180442882e-08,
            -0.00019927150282156346,
            -9.156577280747368e-10
          ],
          [
            -1.1371680024450157e-08,
            -0.00017102827815363027,
            -7.851013793606924e-10
          ],
          [
            -9.475153504658709e-09,
            -0.0001426591094021998,
            -6.543689236646358e-10
          ],
          [
            -7.579214410549867e-09,
            -0.00011419664560582575,
            -5.23502889059737e-10
          ],
          [
            -5.683834750262941e-09,
            -8.56728413391572e-05,
            -3.925540496745844e-10
          ],
          [
            -3.788930898096835e-09,
            -5.711814633101947e-05,
            -2.6155860260784156e-10
          ],
          [
            -1.8943771116099995e-09,
            -2.855837279954318e-05,
            -1.306665047587959e-10
          ],
          [
            -5.868447033394205e-17,
            4.88152796199149e-17,
            -2.0333522268449424e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.923819820412303e-15,
            1.4201008256582821e-15,
            -6.767476306339381e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.92381982637012e-15,
            1.4200880055215137e-15,
            -6.767476306038354e-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": [
          [
            -6.895968236997341e-07,
            -0.008190108870285429,
            -3.48142558670439e-08
          ],
          [
            -6.033239610681029e-07,
            -0.007178380026226838,
            -3.047525115595917e-08
          ],
          [
            -5.17069944916404e-07,
            -0.006160971116564495,
            -2.6130027586113158e-08
          ],
          [
            -4.3083813955346884e-07,
            -0.00513902531554794,
            -2.1778942815853242e-08
          ],
          [
            -3.446303125653749e-07,
            -0.004113718741420025,
            -1.7423412213002365e-08
          ],
          [
            -2.584460179200221e-07,
            -0.0030862024958617784,
            -1.306512564802631e-08
          ],
          [
            -1.722821117433604e-07,
            -0.002057573471194285,
            -8.705287879440249e-09
          ],
          [
            -8.613536522927845e-08,
            -0.001028761504410669,
            -4.348889803829081e-09
          ],
          [
            -2.942091015256665e-15,
            1.4432899320127035e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.61676440788395,
          -83.61670517511915,
          -83.61652505180983,
          -83.61621824424111,
          -83.61577758262989,
          -83.61519220759392,
          -83.61444713754135,
          -83.6135233738919,
          -83.61239806158926
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.414251491598959e-17,
            5.974706638664092e-17,
            -2.174724349125582e-17
          ],
          [
            1.8943770407735428e-09,
            2.8558372799521644e-05,
            1.306663941576696e-10
          ],
          [
            3.7889308429617074e-09,
            5.7118146331017505e-05,
            2.615586205350298e-10
          ],
          [
            5.683834736637074e-09,
            8.567284133920597e-05,
            3.925540613152251e-10
          ],
          [
            7.579214433349881e-09,
            0.00011419664560581072,
            5.235027159540852e-10
          ],
          [
            9.475153426182142e-09,
            0.00014265910940218393,
            6.543687710729812e-10
          ],
          [
            1.137168002396889e-08,
            0.00017102827815352874,
            7.851014282995101e-10
          ],
          [
            1.326876911664495e-08,
            0.00019927150282153327,
            9.156576064947116e-10
          ],
          [
            1.5166348929914718e-08,
            0.0002273570488785021,
            1.046027172345494e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.7443959050718255e-15,
            1.7903709985259504e-15,
            -7.237996108703215e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.7443959050718255e-15,
            1.7903709985259504e-15,
            -7.237996108703215e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.895968178327639e-07,
          0.008190108870288247,
          3.4814254492991074e-08
        ],
        "actual_opposite_endpoint_branch_residual": 3.809777551094577e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.923819820412303e-15,
            1.4201008256582821e-15,
            -6.767476306339381e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.895968236804036e-07,
            -0.008190108870285406,
            -3.481425584648634e-08
          ],
          [
            -6.033239610501791e-07,
            -0.007178380026226825,
            -3.047525115251402e-08
          ],
          [
            -5.170699449122106e-07,
            -0.006160971116564507,
            -2.6130027610327143e-08
          ],
          [
            -4.308381395669348e-07,
            -0.005139025315547934,
            -2.1778942811972166e-08
          ],
          [
            -3.446303125413098e-07,
            -0.004113718741420035,
            -1.742341219213737e-08
          ],
          [
            -2.5844601793344205e-07,
            -0.0030862024958617823,
            -1.306512563370511e-08
          ],
          [
            -1.7228211173997326e-07,
            -0.0020575734711942603,
            -8.705287861583992e-09
          ],
          [
            -8.613536524558156e-08,
            -0.0010287615044106916,
            -4.348889795445982e-09
          ],
          [
            -2.92381982637012e-15,
            1.4200880055215137e-15,
            -6.767476306038354e-16
          ],
          [
            8.613536036621314e-08,
            0.0010287615044080752,
            4.348886114379357e-09
          ],
          [
            1.7228210957394948e-07,
            0.0020575734711944875,
            8.705288458243145e-09
          ],
          [
            2.5844601751125674e-07,
            0.0030862024958637326,
            1.3065126021133117e-08
          ],
          [
            3.44630310837568e-07,
            0.004113718741416613,
            1.742340643077256e-08
          ],
          [
            4.30838133689679e-07,
            0.005139025315544824,
            2.177893773336162e-08
          ],
          [
            5.170699456586237e-07,
            0.006160971116561664,
            2.6130029239126542e-08
          ],
          [
            6.033239563109865e-07,
            0.007178380026223714,
            3.047524710604373e-08
          ],
          [
            6.895968208366559e-07,
            0.008190108870285942,
            3.481425407352768e-08
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.895968236997341e-07,
            -0.008190108870285429,
            -3.48142558670439e-08
          ],
          [
            -6.033239610681029e-07,
            -0.007178380026226838,
            -3.047525115595917e-08
          ],
          [
            -5.17069944916404e-07,
            -0.006160971116564495,
            -2.6130027586113158e-08
          ],
          [
            -4.3083813955346884e-07,
            -0.00513902531554794,
            -2.1778942815853242e-08
          ],
          [
            -3.446303125653749e-07,
            -0.004113718741420025,
            -1.7423412213002365e-08
          ],
          [
            -2.584460179200221e-07,
            -0.0030862024958617784,
            -1.306512564802631e-08
          ],
          [
            -1.722821117433604e-07,
            -0.002057573471194285,
            -8.705287879440249e-09
          ],
          [
            -8.613536522927845e-08,
            -0.001028761504410669,
            -4.348889803829081e-09
          ],
          [
            -2.942091015256665e-15,
            1.4432899320127035e-15,
            -6.661338147750939e-16
          ],
          [
            8.613536039980829e-08,
            0.0010287615044081155,
            4.3488861400931e-09
          ],
          [
            1.722821095784255e-07,
            0.002057573471194507,
            8.705288490062912e-09
          ],
          [
            2.584460174759329e-07,
            0.003086202495863777,
            1.3065125981093217e-08
          ],
          [
            3.446303108445292e-07,
            0.004113718741416639,
            1.7423406384331486e-08
          ],
          [
            4.3083813372479796e-07,
            0.005139025315544776,
            2.177893776433848e-08
          ],
          [
            5.17069945638049e-07,
            0.006160971116561664,
            2.6130029251447695e-08
          ],
          [
            6.033239563496551e-07,
            0.00717838002622373,
            3.047524710364513e-08
          ],
          [
            6.895968208686654e-07,
            0.008190108870285928,
            3.4814254035175907e-08
          ]
        ]
      },
      "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": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.116376994573959e-15,
        "parent_symmetrization_rmsd_A": 0.06009185294525515,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -83.61676440788395,
        "reduced_polarization": [
          -2.921794191210151e-15,
          7.124567626007344e-16,
          -8.169024653806118e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.715043241132234e-17,
          3.11164209831252e-17,
          -2.4544606761915282e-17
        ],
        "ranking_score": 0.060091852945261384
      }
    }
  ],
  "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": 153,
      "full_response": 37,
      "energy_polarization": 116
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 178,
      "full_response": 62,
      "energy_polarization": 116
    },
    "elapsed_seconds": 716.8760980929947
  }
}