{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 18,
  "input_formula": "C2K8O8",
  "input_spacegroup": "Cm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -88.2737686726729,
  "input_cartesian_polarization_e_A2": [
    -0.005066341040531125,
    -7.688704301845462e-18,
    0.001676385080928969
  ],
  "input_reduced_polarization": [
    -0.2501494182387931,
    -2.999457240713545e-16,
    -0.10041477040277617
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0170033031360993e-15,
      "parent_symmetrization_rmsd_A": 0.6178770454388205,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -78.8204408309276,
      "reduced_polarization": [
        7.692881516745135e-16,
        -6.185950338608975e-16,
        -2.4460507428420753e-16
      ],
      "cartesian_polarization_e_A2": [
        1.5735721096819927e-17,
        -1.585684981065129e-17,
        -1.5944943420710464e-17
      ],
      "ranking_score": 0.6178770454388225
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.203319003144401e-15,
      "parent_symmetrization_rmsd_A": 0.6178770454388205,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -78.82044083092757,
      "reduced_polarization": [
        5.741158491426222e-16,
        4.639462753956732e-16,
        -9.503270324673307e-16
      ],
      "cartesian_polarization_e_A2": [
        1.1958707565532847e-17,
        1.1892637357988468e-17,
        -2.686855106804802e-17
      ],
      "ranking_score": 0.6178770454388229
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.6693185441663893e-16,
      "parent_symmetrization_rmsd_A": 0.7021185793832092,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -74.61334499402354,
      "reduced_polarization": [
        -3.4015399120580997e-16,
        1.305922849261895e-16,
        -4.3357850155977734e-17
      ],
      "cartesian_polarization_e_A2": [
        -6.915348389645146e-18,
        3.3475571822486055e-18,
        4.096352867751584e-18
      ],
      "ranking_score": 0.70211857938321
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.9828552950452264e-05,
      "parent_symmetrization_rmsd_A": 0.11972113975556724,
      "parent_cell_rmsd_A": 0.19825498986642484,
      "energy_eV": -87.1959406617848,
      "reduced_polarization": [
        -0.5000090070435261,
        -4.254061162427058e-16,
        3.879673693811549e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.0101854078140512,
        -6.510656353454418e-17,
        0.0075612272082662925
      ],
      "ranking_score": 0.6693645443280744
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.49999999999999906,
      "parent_symmetrization_rmsd_A": 0.7026825885311555,
      "parent_cell_rmsd_A": 0.19825498986642484,
      "energy_eV": -75.36918556753312,
      "reduced_polarization": [
        -9.369702687342422e-16,
        -1.5784093106821758e-16,
        -1.520648349432504e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.820859401502297e-17,
        -4.002372114413261e-18,
        -1.6053470568800444e-17
      ],
      "ranking_score": 1.7522463359977598
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.49999999999999944,
      "parent_symmetrization_rmsd_A": 0.7026825885311552,
      "parent_cell_rmsd_A": 0.19825498986642484,
      "energy_eV": -75.3691855675331,
      "reduced_polarization": [
        5.673645456136119e-16,
        9.244968819710148e-16,
        2.2685177489867528e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0247831897343845e-17,
        2.344246524156339e-17,
        3.6505152252340735e-17
      ],
      "ranking_score": 1.7522463359977603
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1037364133842926e-06,
      "parent_symmetrization_rmsd_A": 0.08377669658434932,
      "parent_cell_rmsd_A": 0.06617241793432595,
      "energy_eV": -87.75384185637733,
      "reduced_polarization": [
        2.096392797837227e-06,
        -1.1044175687546239e-16,
        1.7562498163761117e-07
      ],
      "cartesian_polarization_e_A2": [
        4.2907787812461825e-08,
        -2.8232310019208278e-18,
        -2.65004075418935e-08
      ],
      "ranking_score": 0.6003240085407575
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.000409069450512984,
      "parent_symmetrization_rmsd_A": 0.08991091722989909,
      "parent_cell_rmsd_A": 0.2671171361632896,
      "energy_eV": -87.27140671707663,
      "reduced_polarization": [
        -0.49984769371201115,
        -3.876031550563228e-15,
        -0.49962034145606604
      ],
      "cartesian_polarization_e_A2": [
        -0.009958914351523181,
        5.092836505779861e-16,
        -0.002635964834848323
      ],
      "ranking_score": 0.6575083401717474
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0008786808128937233,
      "parent_symmetrization_rmsd_A": 0.1516279424051386,
      "parent_cell_rmsd_A": 0.4319766811178174,
      "energy_eV": -80.99771271273815,
      "reduced_polarization": [
        0.0006319106935188921,
        4.737364665338913e-15,
        -0.49938945201141594
      ],
      "cartesian_polarization_e_A2": [
        -0.000155724820278525,
        -4.1673736701066814e-17,
        -0.009519655449132986
      ],
      "ranking_score": 0.7613794743103803
    },
    {
      "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": 8.316211178021532e-05,
      "parent_symmetrization_rmsd_A": 0.23522048514176847,
      "parent_cell_rmsd_A": 0.26748651406384155,
      "energy_eV": -83.37057871273596,
      "reduced_polarization": [
        -0.4999393485273249,
        -0.4999847798287655,
        5.4824101321227845e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.010394255237395431,
        -0.012675877755210493,
        0.007312457811881574
      ],
      "ranking_score": 0.8022584378812894
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00047715661859499246,
      "parent_symmetrization_rmsd_A": 0.19384802526615502,
      "parent_cell_rmsd_A": 0.14272529981513166,
      "energy_eV": -84.73869734161674,
      "reduced_polarization": [
        0.00019225734666621658,
        -0.49990988747616594,
        0.000427311694633003
      ],
      "cartesian_polarization_e_A2": [
        -0.00019728267700314664,
        -0.012778507992149978,
        -0.0002599788872158164
      ],
      "ranking_score": 0.7304836634571279
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 1.725086833348863e-06,
      "parent_symmetrization_rmsd_A": 0.1910970432043555,
      "parent_cell_rmsd_A": 0.2664822873397932,
      "energy_eV": -86.45450675236246,
      "reduced_polarization": [
        -0.499999527195361,
        -0.4999987850345899,
        -0.4999988702923351
      ],
      "cartesian_polarization_e_A2": [
        -0.010156483791922633,
        -0.01345424132084742,
        -0.0028922369086793786
      ],
      "ranking_score": 0.7577210652129704
    },
    {
      "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": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0019768794379403883,
      "parent_symmetrization_rmsd_A": 0.25443318434272316,
      "parent_cell_rmsd_A": 0.5319241985453749,
      "energy_eV": -82.2248526006145,
      "reduced_polarization": [
        0.0005539906842697777,
        -0.4987791698061023,
        -0.49854716818882516
      ],
      "cartesian_polarization_e_A2": [
        -0.0005106480117051963,
        -0.013734174950185155,
        -0.0098487619609376
      ],
      "ranking_score": 0.8913679928549476
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "target_residual": 0.269273911327213,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.11576162612013871,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9281422675767906,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0278938009125067,
              0.988787289984816,
              0.9866013114117688
            ],
            "cell_volume_ratio": 1.0027503231081805,
            "cell_rmsd_from_input_A": 0.20963724826458346
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.45461502631940415,
              3.892408098225553e-14,
              0.03332776678288122
            ],
            "branch_aligned_reduced_polarization": [
              -0.45461502631940415,
              3.892408098225553e-14,
              0.03332776678288122
            ],
            "target_residual": 0.05630751170778637,
            "energy_eV": -87.42896560943791,
            "max_atomic_step_A": 0.0175491942106222,
            "max_log_strain_component": 0.003396476088535121,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0273624501801104,
              0.990534353208649,
              0.9841714256382512
            ],
            "cell_volume_ratio": 1.0015300445077986,
            "cell_rmsd_from_input_A": 0.1998581791487567
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4997883461259902,
              5.071575390867167e-15,
              0.002634963779714562
            ],
            "branch_aligned_reduced_polarization": [
              -0.4997883461259902,
              5.071575390867167e-15,
              0.002634963779714562
            ],
            "target_residual": 0.0026434506772003525,
            "energy_eV": -87.19286926996345,
            "max_atomic_step_A": 0.000778245254611538,
            "max_log_strain_component": 0.00012927749927617795,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0271775094886129,
              0.9906624152903734,
              0.9841632682238839
            ],
            "cell_volume_ratio": 1.0014709135259932,
            "cell_rmsd_from_input_A": 0.19825498986642484
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000090070435261,
              -4.254061162427058e-16,
              3.879673693811549e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000090070435261,
              -4.254061162427058e-16,
              3.879673693811549e-05
            ],
            "target_residual": 3.9828552950452264e-05,
            "energy_eV": -87.1959406617848
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.9828552950452264e-05,
        "parent_symmetrization_rmsd_A": 0.11972113975556724,
        "parent_cell_rmsd_A": 0.19825498986642484,
        "energy_eV": -87.1959406617848,
        "reduced_polarization": [
          -0.5000090070435261,
          -4.254061162427058e-16,
          3.879673693811549e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.0101854078140512,
          -6.510656353454418e-17,
          0.0075612272082662925
        ],
        "ranking_score": 0.6693645443280744
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "target_residual": 0.2695512150969624,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.10173819987532534,
            "max_log_strain_component": 0.013080674265717988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.014106954440232,
              0.9984957716001194,
              0.9904331113183068
            ],
            "cell_volume_ratio": 1.0028942514101968,
            "cell_rmsd_from_input_A": 0.061980574480969844
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.02885431322905574,
              -5.220812119272633e-14,
              0.03306326596283852
            ],
            "branch_aligned_reduced_polarization": [
              0.02885431322905574,
              -5.220812119272633e-14,
              0.03306326596283852
            ],
            "target_residual": 0.04388337894977844,
            "energy_eV": -87.70378454488927,
            "max_atomic_step_A": 0.010689200993159556,
            "max_log_strain_component": 0.0013813161264880029,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.01305185371381,
              0.9996905506888281,
              0.9896286236283866
            ],
            "cell_volume_ratio": 1.0022348747607632,
            "cell_rmsd_from_input_A": 0.066193485711778
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0009546104421161475,
              1.1788004516638885e-14,
              0.0007063703691814518
            ],
            "branch_aligned_reduced_polarization": [
              0.0009546104421161475,
              1.1788004516638885e-14,
              0.0007063703691814518
            ],
            "target_residual": 0.001187535344591784,
            "energy_eV": -87.75149681396844,
            "max_atomic_step_A": 0.00036651343629512037,
            "max_log_strain_component": 3.7542313998484156e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0130172968891589,
              0.9997082502870415,
              0.9896321491615029
            ],
            "cell_volume_ratio": 1.0022220013450582,
            "cell_rmsd_from_input_A": 0.06617241793432595
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.096392797837227e-06,
              -1.1044175687546239e-16,
              1.7562498163761117e-07
            ],
            "branch_aligned_reduced_polarization": [
              2.096392797837227e-06,
              -1.1044175687546239e-16,
              1.7562498163761117e-07
            ],
            "target_residual": 2.1037364133842926e-06,
            "energy_eV": -87.75384185637733
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.1037364133842926e-06,
        "parent_symmetrization_rmsd_A": 0.08377669658434932,
        "parent_cell_rmsd_A": 0.06617241793432595,
        "energy_eV": -87.75384185637733,
        "reduced_polarization": [
          2.096392797837227e-06,
          -1.1044175687546239e-16,
          1.7562498163761117e-07
        ],
        "cartesian_polarization_e_A2": [
          4.2907787812461825e-08,
          -2.8232310019208278e-18,
          -2.65004075418935e-08
        ],
        "ranking_score": 0.6003240085407575
      },
      "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": [
          -88.2737686726729,
          -88.25183248938959,
          -88.21576280028789,
          -88.16651494072029,
          -88.10501477178832,
          -88.03216236871218,
          -87.94882097651546,
          -87.85580190731508,
          -87.75384185637735
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.005066341040531133,
            -2.2888005967153496e-17,
            0.001676385080928964
          ],
          [
            -0.004491943944195098,
            -3.387262309415232e-17,
            0.001440571388815126
          ],
          [
            -0.0039049131014907154,
            -2.5260560134587473e-17,
            0.0012150506712014404
          ],
          [
            -0.003303548511829558,
            -4.1448403980227414e-17,
            0.0009985781526879903
          ],
          [
            -0.0026858008424550006,
            -8.234453154937251e-17,
            0.0007897479423631001
          ],
          [
            -0.0020492867648176515,
            -4.392192193501843e-17,
            0.0005870407153962677
          ],
          [
            -0.0013913462034156859,
            -1.4300476711339023e-16,
            0.00038887866902516144
          ],
          [
            -0.0007091624314947566,
            7.305380713453948e-17,
            0.00019368783484768328
          ],
          [
            4.29077878136924e-08,
            -2.444233304209702e-17,
            -2.6500407558517266e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.1956750452045903e-15,
            -0.015725285735040458
          ],
          [
            2.096392797890072e-06,
            -9.559499569093314e-16,
            1.756249808142324e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.195675045204591e-15,
            -0.015725285735040458
          ],
          [
            2.0963927978914776e-06,
            -9.559499569093314e-16,
            1.7562498081519218e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.881784197001252e-16,
            -0.1004147704027768
          ],
          [
            -0.22160227133785432,
            -9.992007221626409e-16,
            -0.09098034066484134
          ],
          [
            -0.1924762559692374,
            -4.440892098500626e-16,
            -0.08065923960038246
          ],
          [
            -0.162691154633,
            -9.43689570931383e-16,
            -0.06945511665149401
          ],
          [
            -0.1321498300538837,
            -2.4980018054066022e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -9.992007221626409e-16,
            -0.04439235867200547
          ],
          [
            -0.06833225741192223,
            -4.9960036108132044e-15,
            -0.030516870990772493
          ],
          [
            -0.03479571564887579,
            3.219646771412954e-15,
            -0.01572528573504045
          ],
          [
            2.0963927979122943e-06,
            -9.43689570931383e-16,
            1.756249807804977e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.75384185637732,
          -87.66896580700936,
          -87.57479023233041,
          -87.4714693814775,
          -87.35909968313838,
          -87.23771117833283,
          -87.10726358321938,
          -86.96764272314265,
          -86.81865887733524
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.290778782268e-08,
            -2.7302409800381668e-17,
            -2.6500407490604844e-08
          ],
          [
            0.0006451726399450627,
            3.654270750695995e-17,
            -0.00014244907164062798
          ],
          [
            0.001310054908140328,
            9.7879122830639e-17,
            -0.00028614171041595383
          ],
          [
            0.0019938770153881207,
            -2.1569909302768816e-17,
            -0.00043142923720548956
          ],
          [
            0.0026952778036074014,
            4.2332645931599875e-17,
            -0.0005784972366789055
          ],
          [
            0.0034122713740981784,
            1.1993028980913124e-16,
            -0.0007274161998768443
          ],
          [
            0.004142189666119827,
            2.1952637184887374e-16,
            -0.0008781594217802964
          ],
          [
            0.004881616205414486,
            1.8218795779869876e-16,
            -0.001030604193006504
          ],
          [
            0.005626325298673014,
            2.1343205252095912e-16,
            -0.0011845195715438554
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.096392798362894e-06,
            -1.0678055902914085e-15,
            1.756249846873225e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.506885171188373e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.096392798362894e-06,
            -1.0678055902914085e-15,
            1.756249846873225e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.5068851711883728e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.2501536378121221,
          -1.0141613900239384e-15,
          0.10041519612868756
        ],
        "actual_opposite_endpoint_branch_residual": 0.054081128165020274
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.1956750452045903e-15,
            -0.015725285735040458
          ],
          [
            2.096392797890072e-06,
            -9.559499569093314e-16,
            1.756249808142324e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.506885171188373e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.195675045204591e-15,
            -0.015725285735040458
          ],
          [
            2.0963927978914776e-06,
            -9.559499569093314e-16,
            1.7562498081519218e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837798e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.5068851711883728e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.881784197001252e-16,
            -0.1004147704027768
          ],
          [
            -0.22160227133785432,
            -9.992007221626409e-16,
            -0.09098034066484134
          ],
          [
            -0.1924762559692374,
            -4.440892098500626e-16,
            -0.08065923960038246
          ],
          [
            -0.162691154633,
            -9.43689570931383e-16,
            -0.06945511665149401
          ],
          [
            -0.1321498300538837,
            -2.4980018054066022e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -9.992007221626409e-16,
            -0.04439235867200547
          ],
          [
            -0.06833225741192223,
            -4.9960036108132044e-15,
            -0.030516870990772493
          ],
          [
            -0.03479571564887579,
            3.219646771412954e-15,
            -0.01572528573504045
          ],
          [
            2.0963927979122943e-06,
            -9.43689570931383e-16,
            1.756249807804977e-07
          ],
          [
            0.03167254686217469,
            1.1102230246251565e-15,
            0.01606770552882053
          ],
          [
            0.0643816278138668,
            3.3306690738754696e-15,
            0.032904347134624645
          ],
          [
            0.09809260382725227,
            -1.4988010832439613e-15,
            0.05046831104890448
          ],
          [
            0.1327415195446927,
            8.881784197001252e-16,
            0.06870476501962575
          ],
          [
            0.1682332744546433,
            3.9968028886505635e-15,
            0.08754152863694653
          ],
          [
            0.20443860277328485,
            7.993605777301127e-15,
            0.10688575775346765
          ],
          [
            0.24119060259190706,
            6.772360450213455e-15,
            0.1266211478626964
          ],
          [
            0.2782815201597588,
            8.326672684688674e-15,
            0.14660600320367656
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277619
            ],
            "target_residual": 0.47126814969683617,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.08267014310393477,
            "max_log_strain_component": 0.02,
            "step_scale": 0.871695496515638,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0192395846254718,
              0.9988178829949973,
              0.9723991728893592
            ],
            "cell_volume_ratio": 0.9899361237655846,
            "cell_rmsd_from_input_A": 0.21386747877884754
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.46230759980581726,
              3.447826892974592e-14,
              -0.4247439894270904
            ],
            "branch_aligned_reduced_polarization": [
              -0.46230759980581726,
              3.447826892974592e-14,
              -0.4247439894270904
            ],
            "target_residual": 0.08416759566334485,
            "energy_eV": -87.66783190248901,
            "max_atomic_step_A": 0.01816970902152974,
            "max_log_strain_component": 0.004466076331114667,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0238017663529762,
              0.9985980157232869,
              0.9660435635051654
            ],
            "cell_volume_ratio": 0.9876504922178465,
            "cell_rmsd_from_input_A": 0.2640526276853134
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49810530406112064,
              8.824521418033719e-15,
              -0.4952624046603936
            ],
            "branch_aligned_reduced_polarization": [
              -0.49810530406112064,
              8.824521418033719e-15,
              -0.4952624046603936
            ],
            "target_residual": 0.0051024192597890336,
            "energy_eV": -87.29566752412556,
            "max_atomic_step_A": 0.001174634176385913,
            "max_log_strain_component": 0.0002687817388873506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0240769825569007,
              0.9985884599481192,
              0.9656621181533152
            ],
            "cell_volume_ratio": 0.9875164587407704,
            "cell_rmsd_from_input_A": 0.2671171361632896
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49984769371201115,
              -3.876031550563228e-15,
              -0.49962034145606604
            ],
            "branch_aligned_reduced_polarization": [
              -0.49984769371201115,
              -3.876031550563228e-15,
              -0.49962034145606604
            ],
            "target_residual": 0.000409069450512984,
            "energy_eV": -87.27140671707663
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.000409069450512984,
        "parent_symmetrization_rmsd_A": 0.08991091722989909,
        "parent_cell_rmsd_A": 0.2671171361632896,
        "energy_eV": -87.27140671707663,
        "reduced_polarization": [
          -0.49984769371201115,
          -3.876031550563228e-15,
          -0.49962034145606604
        ],
        "cartesian_polarization_e_A2": [
          -0.009958914351523181,
          5.092836505779861e-16,
          -0.002635964834848323
        ],
        "ranking_score": 0.6575083401717474
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277619
            ],
            "target_residual": 0.47142665087739016,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.10429541164714186,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4907331720907012,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0160794327553457,
              1.008988245555006,
              0.9698364408471337
            ],
            "cell_volume_ratio": 0.9942881552347046,
            "cell_rmsd_from_input_A": 0.2351690350187615
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.09079142168213533,
              -5.174876326325566e-15,
              -0.2767501796268396
            ],
            "branch_aligned_reduced_polarization": [
              -0.09079142168213533,
              -5.174876326325566e-15,
              -0.2767501796268396
            ],
            "target_residual": 0.24100532057967453,
            "energy_eV": -87.04595819332859,
            "max_atomic_step_A": 0.09838413390969444,
            "max_log_strain_component": 0.015587611710476972,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0310815988914488,
              1.014120358454611,
              0.9453110523522363
            ],
            "cell_volume_ratio": 0.9884558434703259,
            "cell_rmsd_from_input_A": 0.4286821902012406
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0277491733040051,
              -4.612045112618928e-15,
              -0.48386631438015026
            ],
            "branch_aligned_reduced_polarization": [
              0.0277491733040051,
              -4.612045112618928e-15,
              -0.48386631438015026
            ],
            "target_residual": 0.03209848019355209,
            "energy_eV": -80.49178345945268,
            "max_atomic_step_A": 0.008603114823307901,
            "max_log_strain_component": 0.0010360404557422285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0316096339368128,
              1.0135135565303892,
              0.9450502968817274
            ],
            "cell_volume_ratio": 0.9880976677672305,
            "cell_rmsd_from_input_A": 0.4319766811178174
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0006319106935188921,
              4.737364665338913e-15,
              -0.49938945201141594
            ],
            "branch_aligned_reduced_polarization": [
              0.0006319106935188921,
              4.737364665338913e-15,
              -0.49938945201141594
            ],
            "target_residual": 0.0008786808128937233,
            "energy_eV": -80.99771271273815
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0008786808128937233,
        "parent_symmetrization_rmsd_A": 0.1516279424051386,
        "parent_cell_rmsd_A": 0.4319766811178174,
        "energy_eV": -80.99771271273815,
        "reduced_polarization": [
          0.0006319106935188921,
          4.737364665338913e-15,
          -0.49938945201141594
        ],
        "cartesian_polarization_e_A2": [
          -0.000155724820278525,
          -4.1673736701066814e-17,
          -0.009519655449132986
        ],
        "ranking_score": 0.7613794743103803
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.7755575615628914e-16,
              -0.10041477040277617
            ],
            "target_residual": 0.5678982649396417,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.011517596321988644,
            "step_scale": 0.5226824888760624,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0181597219196956,
              1.0038876789382472,
              0.9798750366856995
            ],
            "cell_volume_ratio": 1.0015479127729578,
            "cell_rmsd_from_input_A": 0.13691867263357974
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.36017836102592654,
              -0.26334743545786127,
              -0.029883807041617565
            ],
            "branch_aligned_reduced_polarization": [
              -0.36017836102592654,
              -0.26334743545786127,
              -0.029883807041617565
            ],
            "target_residual": 0.2764915350477622,
            "energy_eV": -87.1357600212602,
            "max_atomic_step_A": 0.11204780672099153,
            "max_log_strain_component": 0.011260025831077299,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0359483867414991,
              1.0058898135010745,
              0.9612543023469525
            ],
            "cell_volume_ratio": 1.0016749780269587,
            "cell_rmsd_from_input_A": 0.2602209769261917
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4799201869428674,
              -0.48758024507071807,
              0.009008410954929793
            ],
            "branch_aligned_reduced_polarization": [
              -0.4799201869428674,
              -0.48758024507071807,
              0.009008410954929793
            ],
            "target_residual": 0.02527054951610103,
            "energy_eV": -83.57140412035864,
            "max_atomic_step_A": 0.0091289290229692,
            "max_log_strain_component": 0.0011540279384850752,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0372378215544895,
              1.0057965617830493,
              0.9599219751050262
            ],
            "cell_volume_ratio": 1.00143882579402,
            "cell_rmsd_from_input_A": 0.26725508125394193
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4989664924133824,
              -0.49942001870762176,
              0.0007237821937335273
            ],
            "branch_aligned_reduced_polarization": [
              -0.4989664924133824,
              -0.49942001870762176,
              0.0007237821937335273
            ],
            "target_residual": 0.0013886601078271599,
            "energy_eV": -83.37813142754223,
            "max_atomic_step_A": 0.00043136737970660334,
            "max_log_strain_component": 6.000582471099311e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0372897390686504,
              1.005791774370752,
              0.9598637389386674
            ],
            "cell_volume_ratio": 1.001423426883764,
            "cell_rmsd_from_input_A": 0.26748651406384155
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999393485273249,
              -0.4999847798287655,
              5.4824101321227845e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999393485273249,
              -0.4999847798287655,
              5.4824101321227845e-05
            ],
            "target_residual": 8.316211178021532e-05,
            "energy_eV": -83.37057871273596
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 8.316211178021532e-05,
        "parent_symmetrization_rmsd_A": 0.23522048514176847,
        "parent_cell_rmsd_A": 0.26748651406384155,
        "energy_eV": -83.37057871273596,
        "reduced_polarization": [
          -0.4999393485273249,
          -0.4999847798287655,
          5.4824101321227845e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.010394255237395431,
          -0.012675877755210493,
          0.007312457811881574
        ],
        "ranking_score": 0.8022584378812894
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.7755575615628914e-16,
              -0.10041477040277617
            ],
            "target_residual": 0.5680298034084555,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.012174901610601424,
            "step_scale": 0.5525118000100404,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0174049417702817,
              1.0002727300564485,
              0.9841951237247908
            ],
            "cell_volume_ratio": 1.0015980739628283,
            "cell_rmsd_from_input_A": 0.08300149054076153
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1045409821761166,
              -0.2762950180329574,
              -0.03118871188817337
            ],
            "branch_aligned_reduced_polarization": [
              -0.1045409821761166,
              -0.2762950180329574,
              -0.03118871188817337
            ],
            "target_residual": 0.24888847233342382,
            "energy_eV": -87.22584601468643,
            "max_atomic_step_A": 0.09924983255101519,
            "max_log_strain_component": 0.009076500717319379,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0307255064217324,
              0.9998063841030274,
              0.9727774222962138
            ],
            "cell_volume_ratio": 1.002472369057892,
            "cell_rmsd_from_input_A": 0.1456254432032885
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.009044794164990834,
              -0.5115658216135128,
              0.006548264562222871
            ],
            "branch_aligned_reduced_polarization": [
              0.009044794164990834,
              -0.5115658216135128,
              0.006548264562222871
            ],
            "target_residual": 0.016076576123650103,
            "energy_eV": -84.55305061023789,
            "max_atomic_step_A": 0.005955518780781478,
            "max_log_strain_component": 0.00042427562057897867,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0300840276074565,
              0.9997506729432895,
              0.9733480644138929
            ],
            "cell_volume_ratio": 1.0023803115950998,
            "cell_rmsd_from_input_A": 0.14272529981513166
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.00019225734666621658,
              -0.49990988747616594,
              0.000427311694633003
            ],
            "branch_aligned_reduced_polarization": [
              0.00019225734666621658,
              -0.49990988747616594,
              0.000427311694633003
            ],
            "target_residual": 0.00047715661859499246,
            "energy_eV": -84.73869734161674
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00047715661859499246,
        "parent_symmetrization_rmsd_A": 0.19384802526615502,
        "parent_cell_rmsd_A": 0.14272529981513166,
        "energy_eV": -84.73869734161674,
        "reduced_polarization": [
          0.00019225734666621658,
          -0.49990988747616594,
          0.000427311694633003
        ],
        "cartesian_polarization_e_A2": [
          -0.00019728267700314664,
          -0.012778507992149978,
          -0.0002599788872158164
        ],
        "ranking_score": 0.7304836634571279
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.7755575615628914e-16,
              -0.10041477040277619
            ],
            "target_residual": 0.6870907283020775,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013402655066321593,
            "step_scale": 0.5841517031323337,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.023706581445526,
              0.9886765478215425,
              0.9813558020131635
            ],
            "cell_volume_ratio": 0.993244622280038,
            "cell_rmsd_from_input_A": 0.1660696381463864
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3908732560685949,
              -0.3080301616566795,
              -0.3297790300618684
            ],
            "branch_aligned_reduced_polarization": [
              -0.3908732560685949,
              -0.3080301616566795,
              -0.3297790300618684
            ],
            "target_residual": 0.278812201457019,
            "energy_eV": -87.49537758959133,
            "max_atomic_step_A": 0.09808343835572639,
            "max_log_strain_component": 0.007857482763232802,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0346826231823787,
              0.9836939099862958,
              0.9725440090835606
            ],
            "cell_volume_ratio": 0.9898659857544765,
            "cell_rmsd_from_input_A": 0.23786501380579925
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4869139538697889,
              -0.4820725734228744,
              -0.4817815734171794
            ],
            "branch_aligned_reduced_polarization": [
              -0.4869139538697889,
              -0.4820725734228744,
              -0.4817815734171794
            ],
            "target_residual": 0.028714948966589948,
            "energy_eV": -86.5744538744581,
            "max_atomic_step_A": 0.01147076939186361,
            "max_log_strain_component": 0.0018819921216207728,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0378385698185704,
              0.9822610819216205,
              0.9701134714556434
            ],
            "cell_volume_ratio": 0.9889612593850847,
            "cell_rmsd_from_input_A": 0.2594133176321893
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.496828949046534,
              -0.4972495583915324,
              -0.4935441467098393
            ],
            "branch_aligned_reduced_polarization": [
              -0.496828949046534,
              -0.4972495583915324,
              -0.4935441467098393
            ],
            "target_residual": 0.0077005541940269396,
            "energy_eV": -86.46955634099457,
            "max_atomic_step_A": 0.0024794054428176468,
            "max_log_strain_component": 0.0005285536300418067,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.038620384922519,
              0.9819842550812232,
              0.969394185214949
            ],
            "cell_volume_ratio": 0.9886937231804815,
            "cell_rmsd_from_input_A": 0.2657754937384111
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.499182840464052,
              -0.4994008195624184,
              -0.4982282877378361
            ],
            "branch_aligned_reduced_polarization": [
              -0.499182840464052,
              -0.4994008195624184,
              -0.4982282877378361
            ],
            "target_residual": 0.002041012308604027,
            "energy_eV": -86.45594077994204,
            "max_atomic_step_A": 0.0008302731672198186,
            "max_log_strain_component": 0.00010081072057880392,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.763215170739386,
            "cell_principal_stretches": [
              1.0385819574835078,
              0.9819987837570825,
              0.9693112530397158
            ],
            "cell_volume_ratio": 0.9885871889752011,
            "cell_rmsd_from_input_A": 0.2664822873397932
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.499999527195361,
              -0.4999987850345899,
              -0.4999988702923351
            ],
            "branch_aligned_reduced_polarization": [
              -0.499999527195361,
              -0.4999987850345899,
              -0.4999988702923351
            ],
            "target_residual": 1.725086833348863e-06,
            "energy_eV": -86.45450675236246
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.725086833348863e-06,
        "parent_symmetrization_rmsd_A": 0.1910970432043555,
        "parent_cell_rmsd_A": 0.2664822873397932,
        "energy_eV": -86.45450675236246,
        "reduced_polarization": [
          -0.499999527195361,
          -0.4999987850345899,
          -0.4999988702923351
        ],
        "cartesian_polarization_e_A2": [
          -0.010156483791922633,
          -0.01345424132084742,
          -0.0028922369086793786
        ],
        "ranking_score": 0.7577210652129704
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -0.2501494182387931,
              -2.999457240713545e-16,
              -0.10041477040277617
            ],
            "branch_aligned_reduced_polarization": [
              -0.2501494182387931,
              -2.7755575615628914e-16,
              -0.10041477040277619
            ],
            "target_residual": 0.6871994522389205,
            "energy_eV": -88.2737686726729,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.019282321560420947,
            "step_scale": 0.4731237412315311,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0251371047440616,
              0.999748304038739,
              0.9703511084803667
            ],
            "cell_volume_ratio": 0.994492553155804,
            "cell_rmsd_from_input_A": 0.23655480858995373
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.10198733117635674,
              -0.23847610199527494,
              -0.2748643189589203
            ],
            "branch_aligned_reduced_polarization": [
              -0.10198733117635674,
              -0.23847610199527491,
              -0.2748643189589203
            ],
            "target_residual": 0.3598364070322686,
            "energy_eV": -86.85245503361129,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.011231123349779909,
            "step_scale": 0.8068570563096172,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0417083546070987,
              0.9982007038120009,
              0.9534360757805367
            ],
            "cell_volume_ratio": 0.9914152605658041,
            "cell_rmsd_from_input_A": 0.37195463490076314
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.013046144944179324,
              -0.40531499105088614,
              -0.4228564481061292
            ],
            "branch_aligned_reduced_polarization": [
              0.013046144944179324,
              -0.40531499105088614,
              -0.4228564481061292
            ],
            "target_residual": 0.12282744162604968,
            "energy_eV": -82.90137700311055,
            "max_atomic_step_A": 0.053373056547572746,
            "max_log_strain_component": 0.008902889812648562,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0586122278595163,
              0.99279802031044,
              0.9403745824975029
            ],
            "cell_volume_ratio": 0.9883225184060007,
            "cell_rmsd_from_input_A": 0.48493421332107367
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.02118049774174976,
              -0.47442474203800156,
              -0.45095576718727987
            ],
            "branch_aligned_reduced_polarization": [
              0.02118049774174976,
              -0.47442474203800156,
              -0.45095576718727987
            ],
            "target_residual": 0.059228743668925866,
            "energy_eV": -82.59917033161375,
            "max_atomic_step_A": 0.019009531768120633,
            "max_log_strain_component": 0.0036626437585268066,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.8774989709248304,
            "cell_principal_stretches": [
              1.0650753426590194,
              0.9907333664385973,
              0.9350458531036624
            ],
            "cell_volume_ratio": 0.9866656950154156,
            "cell_rmsd_from_input_A": 0.5328049953218732
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.009446497833827693,
              -0.49084676976042774,
              -0.4795114388089804
            ],
            "branch_aligned_reduced_polarization": [
              0.009446497833827693,
              -0.49084676976042774,
              -0.4795114388089804
            ],
            "target_residual": 0.024347465675533586,
            "energy_eV": -82.2845673981954,
            "max_atomic_step_A": 0.010445444461843723,
            "max_log_strain_component": 0.0019834985881509717,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.663703246973086,
            "cell_principal_stretches": [
              1.0629497226470006,
              0.9906914665069545,
              0.9345766546199203
            ],
            "cell_volume_ratio": 0.9841608242192507,
            "cell_rmsd_from_input_A": 0.5319241985453749
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0005539906842697777,
              -0.4987791698061023,
              -0.49854716818882516
            ],
            "branch_aligned_reduced_polarization": [
              0.0005539906842697777,
              -0.4987791698061023,
              -0.49854716818882516
            ],
            "target_residual": 0.0019768794379403883,
            "energy_eV": -82.2248526006145
          }
        ],
        "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": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0019768794379403883,
        "parent_symmetrization_rmsd_A": 0.25443318434272316,
        "parent_cell_rmsd_A": 0.5319241985453749,
        "energy_eV": -82.2248526006145,
        "reduced_polarization": [
          0.0005539906842697777,
          -0.4987791698061023,
          -0.49854716818882516
        ],
        "cartesian_polarization_e_A2": [
          -0.0005106480117051963,
          -0.013734174950185155,
          -0.0098487619609376
        ],
        "ranking_score": 0.8913679928549476
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "bec_projection_01",
      "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
        ],
        "endpoint_rmsd_A": 0.08377669658434932,
        "minimum_distance_A_by_image": [
          1.4339027573392664,
          1.421514296847052,
          1.4092111982514712,
          1.396995719538798,
          1.3848701903700675,
          1.3728370137750046,
          1.3608986678230865,
          1.3490577072633207,
          1.3373167867109947
        ],
        "minimum_distance_A": 1.3373167867109947,
        "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": [
          315.0691133782015,
          315.1565389241743,
          315.2439887290345,
          315.33146279951313,
          315.4189611423435,
          315.50648376426113,
          315.59403067200236,
          315.6816018723064,
          315.7691973719144
        ],
        "cell_deformation_log_strain_norm": 0.016612431505437675
      },
      "parent_reduced_polarization": [
        2.096392797890072e-06,
        -9.559499569093314e-16,
        1.756249808142324e-07
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -88.2737686726729,
          -88.25183248938959,
          -88.21576280028789,
          -88.16651494072029,
          -88.10501477178832,
          -88.03216236871218,
          -87.94882097651546,
          -87.85580190731508,
          -87.75384185637735
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.005066341040531133,
            -2.2888005967153496e-17,
            0.001676385080928964
          ],
          [
            -0.004491943944195098,
            -3.387262309415232e-17,
            0.001440571388815126
          ],
          [
            -0.0039049131014907154,
            -2.5260560134587473e-17,
            0.0012150506712014404
          ],
          [
            -0.003303548511829558,
            -4.1448403980227414e-17,
            0.0009985781526879903
          ],
          [
            -0.0026858008424550006,
            -8.234453154937251e-17,
            0.0007897479423631001
          ],
          [
            -0.0020492867648176515,
            -4.392192193501843e-17,
            0.0005870407153962677
          ],
          [
            -0.0013913462034156859,
            -1.4300476711339023e-16,
            0.00038887866902516144
          ],
          [
            -0.0007091624314947566,
            7.305380713453948e-17,
            0.00019368783484768328
          ],
          [
            4.29077878136924e-08,
            -2.444233304209702e-17,
            -2.6500407558517266e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.1956750452045903e-15,
            -0.015725285735040458
          ],
          [
            2.096392797890072e-06,
            -9.559499569093314e-16,
            1.756249808142324e-07
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.195675045204591e-15,
            -0.015725285735040458
          ],
          [
            2.0963927978914776e-06,
            -9.559499569093314e-16,
            1.7562498081519218e-07
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.881784197001252e-16,
            -0.1004147704027768
          ],
          [
            -0.22160227133785432,
            -9.992007221626409e-16,
            -0.09098034066484134
          ],
          [
            -0.1924762559692374,
            -4.440892098500626e-16,
            -0.08065923960038246
          ],
          [
            -0.162691154633,
            -9.43689570931383e-16,
            -0.06945511665149401
          ],
          [
            -0.1321498300538837,
            -2.4980018054066022e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -9.992007221626409e-16,
            -0.04439235867200547
          ],
          [
            -0.06833225741192223,
            -4.9960036108132044e-15,
            -0.030516870990772493
          ],
          [
            -0.03479571564887579,
            3.219646771412954e-15,
            -0.01572528573504045
          ],
          [
            2.0963927979122943e-06,
            -9.43689570931383e-16,
            1.756249807804977e-07
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.75384185637732,
          -87.66896580700936,
          -87.57479023233041,
          -87.4714693814775,
          -87.35909968313838,
          -87.23771117833283,
          -87.10726358321938,
          -86.96764272314265,
          -86.81865887733524
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.290778782268e-08,
            -2.7302409800381668e-17,
            -2.6500407490604844e-08
          ],
          [
            0.0006451726399450627,
            3.654270750695995e-17,
            -0.00014244907164062798
          ],
          [
            0.001310054908140328,
            9.7879122830639e-17,
            -0.00028614171041595383
          ],
          [
            0.0019938770153881207,
            -2.1569909302768816e-17,
            -0.00043142923720548956
          ],
          [
            0.0026952778036074014,
            4.2332645931599875e-17,
            -0.0005784972366789055
          ],
          [
            0.0034122713740981784,
            1.1993028980913124e-16,
            -0.0007274161998768443
          ],
          [
            0.004142189666119827,
            2.1952637184887374e-16,
            -0.0008781594217802964
          ],
          [
            0.004881616205414486,
            1.8218795779869876e-16,
            -0.001030604193006504
          ],
          [
            0.005626325298673014,
            2.1343205252095912e-16,
            -0.0011845195715438554
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.096392798362894e-06,
            -1.0678055902914085e-15,
            1.756249846873225e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.506885171188373e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.096392798362894e-06,
            -1.0678055902914085e-15,
            1.756249846873225e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.5068851711883728e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.2501536378121221,
          -1.0141613900239384e-15,
          0.10041519612868756
        ],
        "actual_opposite_endpoint_branch_residual": 0.054081128165020274
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.1956750452045903e-15,
            -0.015725285735040458
          ],
          [
            2.096392797890072e-06,
            -9.559499569093314e-16,
            1.756249808142324e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837796e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.506885171188373e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.928890035112349e-16,
            -0.10041477040277677
          ],
          [
            -0.22160227133785432,
            -1.0078969786874353e-15,
            -0.09098034066484136
          ],
          [
            -0.1924762559692374,
            -4.4258679094295497e-16,
            -0.08065923960038245
          ],
          [
            -0.162691154633,
            -9.31568090969162e-16,
            -0.069455116651494
          ],
          [
            -0.13214983005388367,
            -2.4745665707832684e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -1.0110660215976516e-15,
            -0.04439235867200547
          ],
          [
            -0.06833225741192224,
            -5.016705726234322e-15,
            -0.030516870990772514
          ],
          [
            -0.034795715648875805,
            3.195675045204591e-15,
            -0.015725285735040458
          ],
          [
            2.0963927978914776e-06,
            -9.559499569093314e-16,
            1.7562498081519218e-07
          ],
          [
            0.03167254686217465,
            1.1272915207837798e-15,
            0.016067705528820524
          ],
          [
            0.06438162781386678,
            3.30151610016319e-15,
            0.03290434713462468
          ],
          [
            0.09809260382725221,
            -1.5068851711883728e-15,
            0.0504683110489045
          ],
          [
            0.13274151954469268,
            9.358876920650804e-16,
            0.06870476501962577
          ],
          [
            0.1682332744546433,
            4.0020410087193715e-15,
            0.08754152863694656
          ],
          [
            0.20443860277328488,
            8.018517041139275e-15,
            0.10688575775346766
          ],
          [
            0.24119060259190706,
            6.785119760739881e-15,
            0.12662114786269646
          ],
          [
            0.2782815201597589,
            8.326244451626093e-15,
            0.14660600320367653
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.2501494182387935,
            -8.881784197001252e-16,
            -0.1004147704027768
          ],
          [
            -0.22160227133785432,
            -9.992007221626409e-16,
            -0.09098034066484134
          ],
          [
            -0.1924762559692374,
            -4.440892098500626e-16,
            -0.08065923960038246
          ],
          [
            -0.162691154633,
            -9.43689570931383e-16,
            -0.06945511665149401
          ],
          [
            -0.1321498300538837,
            -2.4980018054066022e-15,
            -0.05736796152959234
          ],
          [
            -0.10073903022078695,
            -9.992007221626409e-16,
            -0.04439235867200547
          ],
          [
            -0.06833225741192223,
            -4.9960036108132044e-15,
            -0.030516870990772493
          ],
          [
            -0.03479571564887579,
            3.219646771412954e-15,
            -0.01572528573504045
          ],
          [
            2.0963927979122943e-06,
            -9.43689570931383e-16,
            1.756249807804977e-07
          ],
          [
            0.03167254686217469,
            1.1102230246251565e-15,
            0.01606770552882053
          ],
          [
            0.0643816278138668,
            3.3306690738754696e-15,
            0.032904347134624645
          ],
          [
            0.09809260382725227,
            -1.4988010832439613e-15,
            0.05046831104890448
          ],
          [
            0.1327415195446927,
            8.881784197001252e-16,
            0.06870476501962575
          ],
          [
            0.1682332744546433,
            3.9968028886505635e-15,
            0.08754152863694653
          ],
          [
            0.20443860277328485,
            7.993605777301127e-15,
            0.10688575775346765
          ],
          [
            0.24119060259190706,
            6.772360450213455e-15,
            0.1266211478626964
          ],
          [
            0.2782815201597588,
            8.326672684688674e-15,
            0.14660600320367656
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.1037364133842926e-06,
        "parent_symmetrization_rmsd_A": 0.08377669658434932,
        "parent_cell_rmsd_A": 0.06617241793432595,
        "energy_eV": -87.75384185637733,
        "reduced_polarization": [
          2.096392797837227e-06,
          -1.1044175687546239e-16,
          1.7562498163761117e-07
        ],
        "cartesian_polarization_e_A2": [
          4.2907787812461825e-08,
          -2.8232310019208278e-18,
          -2.65004075418935e-08
        ],
        "ranking_score": 0.6003240085407575
      }
    }
  ],
  "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": 89,
      "full_response": 30,
      "energy_polarization": 59
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 114,
      "full_response": 55,
      "energy_polarization": 59
    },
    "elapsed_seconds": 290.88218861300265
  }
}
