{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "H20Al4Ba4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -95.48023473787508,
  "input_cartesian_polarization_e_A2": [
    4.3408029346928425e-17,
    -4.215607445551989e-17,
    0.00483744654503043
  ],
  "input_reduced_polarization": [
    1.5747709592141661e-15,
    -1.9909779127850843e-15,
    0.3148326803060005
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.241341796676659e-15,
      "parent_symmetrization_rmsd_A": 0.273714365430712,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -95.41520799763465,
      "reduced_polarization": [
        1.5046638748642774e-15,
        3.963800266045079e-15,
        1.1512736779658549e-16
      ],
      "cartesian_polarization_e_A2": [
        4.147555125728537e-17,
        8.392773122654088e-17,
        1.768947515374647e-18
      ],
      "ranking_score": 0.2737143654307205
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.2851384874442645e-15,
      "parent_symmetrization_rmsd_A": 0.3341666252965084,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -93.46825577312268,
      "reduced_polarization": [
        1.0162700332171363e-15,
        4.130880482755694e-15,
        5.152024003719758e-16
      ],
      "cartesian_polarization_e_A2": [
        2.801314004946285e-17,
        8.746541289064552e-17,
        7.916154286297254e-18
      ],
      "ranking_score": 0.334166625296517
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.4878817614926163e-06,
      "parent_symmetrization_rmsd_A": 0.03959166788828928,
      "parent_cell_rmsd_A": 0.005427329023180339,
      "energy_eV": -95.45828808226028,
      "reduced_polarization": [
        -2.1191531650458142e-15,
        1.7436350835280612e-15,
        0.5000024878817615
      ],
      "cartesian_polarization_e_A2": [
        -4.8452549415028005e-17,
        1.3966285999196403e-17,
        0.007685655221993036
      ],
      "ranking_score": 0.5409534759076073
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999833,
      "parent_symmetrization_rmsd_A": 0.27371790240623717,
      "parent_cell_rmsd_A": 0.005427329023180339,
      "energy_eV": -95.43158127741047,
      "reduced_polarization": [
        2.2407356121320423e-15,
        -2.451775022084263e-15,
        1.6824353415671529e-15
      ],
      "cartesian_polarization_e_A2": [
        6.186184972584795e-17,
        -5.202350438910506e-17,
        2.586110725840853e-17
      ],
      "ranking_score": 1.275074734662029
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.831043693706924e-06,
      "parent_symmetrization_rmsd_A": 0.06626254013895617,
      "parent_cell_rmsd_A": 0.00915004635052861,
      "energy_eV": -95.33889281923474,
      "reduced_polarization": [
        1.3784063365640143e-15,
        1.711786220140279e-15,
        -3.831043693706924e-06
      ],
      "cartesian_polarization_e_A2": [
        3.789561629238949e-17,
        3.611472940651763e-17,
        -5.8825244922936493e-08
      ],
      "ranking_score": 0.5685577138139757
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0007985157872008586,
      "parent_symmetrization_rmsd_A": 0.16359771184969216,
      "parent_cell_rmsd_A": 0.02140444412200831,
      "energy_eV": -94.91901995555627,
      "reduced_polarization": [
        -5.988072490152238e-15,
        -0.49944760835724955,
        0.5005766202696996
      ],
      "cartesian_polarization_e_A2": [
        4.067624627541163e-16,
        -0.010563719021783149,
        0.007647554087627582
      ],
      "ranking_score": 0.6705458544545959
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 1.7398117037503592e-05,
      "parent_symmetrization_rmsd_A": 0.21791845557124936,
      "parent_cell_rmsd_A": 0.05294037008648873,
      "energy_eV": -94.23084310948475,
      "reduced_polarization": [
        0.49999502817320257,
        -8.958864753780022e-15,
        0.5000166725947215
      ],
      "cartesian_polarization_e_A2": [
        0.013736547837135649,
        -2.9797772353134647e-16,
        0.00756609472184243
      ],
      "ranking_score": 0.7311883443269466
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.65938898038494e-05,
      "parent_symmetrization_rmsd_A": 0.17697085733801526,
      "parent_cell_rmsd_A": 0.023583926320218447,
      "energy_eV": -94.79439712932555,
      "reduced_polarization": [
        -5.279535145168587e-16,
        -0.49997927762205757,
        4.173216528607674e-05
      ],
      "cartesian_polarization_e_A2": [
        -5.326750836209188e-17,
        -0.010545684185886611,
        -4.766513400108853e-05
      ],
      "ranking_score": 0.6829600266976776
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00014121985014102753,
      "parent_symmetrization_rmsd_A": 0.22775621725359474,
      "parent_cell_rmsd_A": 0.055376815595307695,
      "energy_eV": -94.0608885124048,
      "reduced_polarization": [
        0.4999295287274896,
        -2.190987116207836e-15,
        0.00012237992410774108
      ],
      "cartesian_polarization_e_A2": [
        0.013740856629268206,
        -4.318307433316418e-16,
        -0.00012061223853256435
      ],
      "ranking_score": 0.7418828608527037
    },
    {
      "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": 1.1703417881109881e-05,
      "parent_symmetrization_rmsd_A": 0.27650513899587775,
      "parent_cell_rmsd_A": 0.05849472600935764,
      "energy_eV": -93.56802304857638,
      "reduced_polarization": [
        0.4999970656299142,
        -0.4999977391355187,
        0.5000111017095124
      ],
      "cartesian_polarization_e_A2": [
        0.013734814948123193,
        -0.010572280505307013,
        0.007513282647105008
      ],
      "ranking_score": 0.7911522273339794
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 7.938428887466632e-05,
      "parent_symmetrization_rmsd_A": 0.2878839864943535,
      "parent_cell_rmsd_A": 0.06138263682499882,
      "energy_eV": -93.39424658177444,
      "reduced_polarization": [
        0.49997682782538955,
        -0.4999705804939487,
        6.999577349852947e-05
      ],
      "cartesian_polarization_e_A2": [
        0.013739125498337062,
        -0.010541260691881526,
        -0.00017595556970565138
      ],
      "ranking_score": 0.8033884142783525
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "target_residual": 0.18516731969399952,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.03352683644387291,
            "max_log_strain_component": 0.001637015731310845,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.000083760068379,
              0.9995224260972029,
              0.9983643234480893
            ],
            "cell_volume_ratio": 0.9979711138295324,
            "cell_rmsd_from_input_A": 0.0053871196352948654
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.907820364470629e-15,
              1.2393280162320953e-14,
              0.498668496217411
            ],
            "branch_aligned_reduced_polarization": [
              -1.907820364470629e-15,
              1.2393280162320953e-14,
              0.498668496217411
            ],
            "target_residual": 0.0013315037825890053,
            "energy_eV": -95.45874967024652,
            "max_atomic_step_A": 0.0002471755323926968,
            "max_log_strain_component": 1.2232054342334995e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.000084385963974,
              0.9995188584440334,
              0.9983521114761204
            ],
            "cell_volume_ratio": 0.9979559691584273,
            "cell_rmsd_from_input_A": 0.005427329023180339
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.1191531650458142e-15,
              1.7436350835280612e-15,
              0.5000024878817615
            ],
            "branch_aligned_reduced_polarization": [
              -2.1191531650458142e-15,
              1.7436350835280612e-15,
              0.5000024878817615
            ],
            "target_residual": 2.4878817614926163e-06,
            "energy_eV": -95.45828808226028
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.4878817614926163e-06,
        "parent_symmetrization_rmsd_A": 0.03959166788828928,
        "parent_cell_rmsd_A": 0.005427329023180339,
        "energy_eV": -95.45828808226028,
        "reduced_polarization": [
          -2.1191531650458142e-15,
          1.7436350835280612e-15,
          0.5000024878817615
        ],
        "cartesian_polarization_e_A2": [
          -4.8452549415028005e-17,
          1.3966285999196403e-17,
          0.007685655221993036
        ],
        "ranking_score": 0.5409534759076073
      },
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "target_residual": 0.3148326803060005,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.05700435582935872,
            "max_log_strain_component": 0.00278335319236347,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0027872303161607,
              1.0008125239202954,
              0.9998576021674256
            ],
            "cell_volume_ratio": 1.0034591081754969,
            "cell_rmsd_from_input_A": 0.0091864620687951
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.5726950865755479e-15,
              -1.8420579215580024e-14,
              -0.001269534616807975
            ],
            "branch_aligned_reduced_polarization": [
              1.5726950865755479e-15,
              -1.8420579215580024e-14,
              -0.001269534616807975
            ],
            "target_residual": 0.001269534616807975,
            "energy_eV": -95.33790342252155,
            "max_atomic_step_A": 0.00023067492749692022,
            "max_log_strain_component": 1.1013061873180151e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0027761866191602,
              1.000809307657175,
              0.9998581655615807
            ],
            "cell_volume_ratio": 1.0034453977617654,
            "cell_rmsd_from_input_A": 0.00915004635052861
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.3784063365640143e-15,
              1.711786220140279e-15,
              -3.831043693706924e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.3784063365640143e-15,
              1.711786220140279e-15,
              -3.831043693706924e-06
            ],
            "target_residual": 3.831043693706924e-06,
            "energy_eV": -95.33889281923474
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.241341796676659e-15,
        "parent_symmetrization_rmsd_A": 0.273714365430712,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -95.41520799763465,
        "reduced_polarization": [
          1.5046638748642774e-15,
          3.963800266045079e-15,
          1.1512736779658549e-16
        ],
        "cartesian_polarization_e_A2": [
          4.147555125728537e-17,
          8.392773122654088e-17,
          1.768947515374647e-18
        ],
        "ranking_score": 0.2737143654307205
      },
      "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": [
          -95.48023473787507,
          -95.48279407400383,
          -95.4759269800289,
          -95.4621021860102,
          -95.44595051380963,
          -95.43260245534361,
          -95.42319493650221,
          -95.41729722480385,
          -95.41520799763464
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.249887884087892e-17,
            -4.910676177794572e-17,
            0.004837446545030459
          ],
          [
            7.064973661060634e-18,
            9.14290709078435e-18,
            0.004232627093696013
          ],
          [
            -1.5231252039874838e-17,
            3.112744277726127e-17,
            0.0036268278380754406
          ],
          [
            4.297166332668645e-17,
            6.037435580062256e-17,
            0.0030219513610516262
          ],
          [
            -8.581865064758947e-18,
            -4.301322199528092e-18,
            0.002419008690432661
          ],
          [
            4.3491146684117375e-17,
            -6.8675699852368814e-18,
            0.0018170802317674004
          ],
          [
            -1.961569157659188e-17,
            2.1246869318924997e-17,
            0.0012134191705771235
          ],
          [
            4.220282795768867e-17,
            -1.3184487611596978e-17,
            0.0006073235095662657
          ],
          [
            4.640025348573058e-17,
            9.419272236937605e-17,
            -1.0593251110030171e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662597e-16,
            4.3180790221833e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641915e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.11335761682839e-16,
            -2.0314599036180525e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322035e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475689e-15,
            -6.226866226307509e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.894343139670465e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662596e-16,
            4.318079022183299e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641917e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.113357616828391e-16,
            -2.0314599036180523e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322037e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475687e-15,
            -6.22686622630751e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.869504964868156e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.2212453270876722e-15,
            -2.3314683517128287e-15,
            0.3148326803060024
          ],
          [
            2.220446049250313e-16,
            4.440892098500626e-16,
            0.27546957268459704
          ],
          [
            -5.551115123125783e-16,
            1.4432899320127035e-15,
            0.23604269703873815
          ],
          [
            1.5543122344752192e-15,
            2.886579864025407e-15,
            0.196675878048026
          ],
          [
            -3.3306690738754696e-16,
            -2.220446049250313e-16,
            0.1574349158389785
          ],
          [
            1.5543122344752192e-15,
            -3.3306690738754696e-16,
            0.11825996098831948
          ],
          [
            -7.216449660063518e-16,
            9.992007221626409e-16,
            0.0789722441894346
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.03952607776638317
          ],
          [
            1.6653345369377348e-15,
            4.440892098500626e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -95.41520799763464,
          -95.41729722480383,
          -95.42319493650224,
          -95.43260245534363,
          -95.44595051380962,
          -95.46210218601027,
          -95.47592698002894,
          -95.48279407400385,
          -95.48023473787508
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.835351090967087e-17,
            1.0335640879445763e-16,
            -1.9272180900615745e-18
          ],
          [
            1.9033870216269238e-17,
            1.8181917510082515e-18,
            -0.0006073235095662675
          ],
          [
            -1.3028642604367698e-17,
            2.070660662719683e-17,
            -0.0012134191705770827
          ],
          [
            4.8602862921237714e-17,
            2.597416787154645e-19,
            -0.0018170802317674522
          ],
          [
            1.3090980607259411e-17,
            1.6893598783653812e-17,
            -0.0024190086904326345
          ],
          [
            5.1054824368311704e-17,
            4.597427713263722e-17,
            -0.0030219513610517134
          ],
          [
            1.0410446482915817e-17,
            7.158480665398201e-18,
            -0.0036268278380755005
          ],
          [
            7.131467530811793e-17,
            2.4691043978692056e-17,
            -0.004232627093696033
          ],
          [
            9.440051571234842e-17,
            -1.7761135990563462e-17,
            -0.0048374465450304474
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.754184787980548e-15,
            4.88139205825903e-15,
            -1.254279982590443e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569063e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384373e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.776736479494003e-16,
            3.3808595980503335e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389036e-16,
            -0.3148326803060016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.754184787980548e-15,
            4.88139205825903e-15,
            -1.254279982590443e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569081e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384316e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.7767364794940027e-16,
            3.380859598050333e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389037e-16,
            -0.3148326803060016
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.1876425675631934e-15,
          1.1216455605520112e-14,
          -0.3148326803060037
        ],
        "actual_opposite_endpoint_branch_residual": 1.2300813672147666e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662597e-16,
            4.3180790221833e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641915e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.11335761682839e-16,
            -2.0314599036180525e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322035e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475689e-15,
            -6.226866226307509e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.894343139670465e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569063e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384373e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.776736479494003e-16,
            3.3808595980503335e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389036e-16,
            -0.3148326803060016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662596e-16,
            4.318079022183299e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641917e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.113357616828391e-16,
            -2.0314599036180523e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322037e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475687e-15,
            -6.22686622630751e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.869504964868156e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569081e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384316e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.7767364794940027e-16,
            3.380859598050333e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389037e-16,
            -0.3148326803060016
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.2212453270876722e-15,
            -2.3314683517128287e-15,
            0.3148326803060024
          ],
          [
            2.220446049250313e-16,
            4.440892098500626e-16,
            0.27546957268459704
          ],
          [
            -5.551115123125783e-16,
            1.4432899320127035e-15,
            0.23604269703873815
          ],
          [
            1.5543122344752192e-15,
            2.886579864025407e-15,
            0.196675878048026
          ],
          [
            -3.3306690738754696e-16,
            -2.220446049250313e-16,
            0.1574349158389785
          ],
          [
            1.5543122344752192e-15,
            -3.3306690738754696e-16,
            0.11825996098831948
          ],
          [
            -7.216449660063518e-16,
            9.992007221626409e-16,
            0.0789722441894346
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.03952607776638317
          ],
          [
            1.6653345369377348e-15,
            4.440892098500626e-15,
            -6.661338147750939e-16
          ],
          [
            6.661338147750939e-16,
            1.1102230246251565e-16,
            -0.03952607776638328
          ],
          [
            -4.996003610813204e-16,
            9.992007221626409e-16,
            -0.07897224418943194
          ],
          [
            1.7763568394002505e-15,
            0.0,
            -0.11825996098832281
          ],
          [
            4.440892098500626e-16,
            7.771561172376096e-16,
            -0.15743491583897673
          ],
          [
            1.887379141862766e-15,
            2.220446049250313e-15,
            -0.19667587804803166
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.23604269703874198
          ],
          [
            2.55351295663786e-15,
            1.2212453270876722e-15,
            -0.2754695726845983
          ],
          [
            3.4416913763379853e-15,
            -8.326672684688674e-16,
            -0.3148326803060016
          ]
        ]
      },
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5747709592141661e-15,
              -1.9984014443252818e-15,
              0.3148326803060005
            ],
            "target_residual": 0.5331856489841581,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037039033873804885,
            "step_scale": 0.860659097191674,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0031136239011482,
              0.9995889579974127,
              0.9955642538631504
            ],
            "cell_volume_ratio": 0.9982535736412936,
            "cell_rmsd_from_input_A": 0.017874820112410532
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3522284932858847e-14,
              -0.4231510166890457,
              0.473376996556839
            ],
            "branch_aligned_reduced_polarization": [
              -1.3522284932858847e-14,
              -0.4231510166890457,
              0.473376996556839
            ],
            "target_residual": 0.08132988717723573,
            "energy_eV": -95.08797753588166,
            "max_atomic_step_A": 0.02332041905365778,
            "max_log_strain_component": 0.0007373261381819024,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0037445990874216,
              0.9995149595028655,
              0.9946989455336304
            ],
            "cell_volume_ratio": 0.9979394183723019,
            "cell_rmsd_from_input_A": 0.02140444412200831
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.988072490152238e-15,
              -0.49944760835724955,
              0.5005766202696996
            ],
            "branch_aligned_reduced_polarization": [
              -5.988072490152238e-15,
              -0.49944760835724955,
              0.5005766202696996
            ],
            "target_residual": 0.0007985157872008586,
            "energy_eV": -94.91901995555627
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0007985157872008586,
        "parent_symmetrization_rmsd_A": 0.16359771184969216,
        "parent_cell_rmsd_A": 0.02140444412200831,
        "energy_eV": -94.91901995555627,
        "reduced_polarization": [
          -5.988072490152238e-15,
          -0.49944760835724955,
          0.5005766202696996
        ],
        "cartesian_polarization_e_A2": [
          4.067624627541163e-16,
          -0.010563719021783149,
          0.007647554087627582
        ],
        "ranking_score": 0.6705458544545959
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "target_residual": 0.5331856489841585,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005351010244775778,
            "step_scale": 0.6414700373990837,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0046966493113672,
              1.0000537287674396,
              0.9939760436877452
            ],
            "cell_volume_ratio": 0.9986980565216004,
            "cell_rmsd_from_input_A": 0.03263968692685925
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3167222819370158,
              -1.9607842929687267e-14,
              0.4365894265970292
            ],
            "branch_aligned_reduced_polarization": [
              0.3167222819370158,
              -1.9607842929687267e-14,
              0.4365894265970292
            ],
            "target_residual": 0.19393716187896604,
            "energy_eV": -95.01942836722633,
            "max_atomic_step_A": 0.075820851007392,
            "max_log_strain_component": 0.0032812362014683627,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0076573029696174,
              1.0000809821244654,
              0.9903739241620175
            ],
            "cell_volume_ratio": 0.9980383340724166,
            "cell_rmsd_from_input_A": 0.05256707596224252
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49678861797655394,
              -7.395410469560716e-16,
              0.5000485259581144
            ],
            "branch_aligned_reduced_polarization": [
              0.49678861797655394,
              -7.395410469560716e-16,
              0.5000485259581144
            ],
            "target_residual": 0.0032117486310611946,
            "energy_eV": -94.2484247606402,
            "max_atomic_step_A": 0.0013972016926260351,
            "max_log_strain_component": 6.19554929129863e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0077206966742172,
              1.0000808931344827,
              0.9903138466008388
            ],
            "cell_volume_ratio": 0.9980404875157491,
            "cell_rmsd_from_input_A": 0.05294037008648873
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999502817320257,
              -8.958864753780022e-15,
              0.5000166725947215
            ],
            "branch_aligned_reduced_polarization": [
              0.49999502817320257,
              -8.958864753780022e-15,
              0.5000166725947215
            ],
            "target_residual": 1.7398117037503592e-05,
            "energy_eV": -94.23084310948475
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 1.7398117037503592e-05,
        "parent_symmetrization_rmsd_A": 0.21791845557124936,
        "parent_cell_rmsd_A": 0.05294037008648873,
        "energy_eV": -94.23084310948475,
        "reduced_polarization": [
          0.49999502817320257,
          -8.958864753780022e-15,
          0.5000166725947215
        ],
        "cartesian_polarization_e_A2": [
          0.013736547837135649,
          -2.9797772353134647e-16,
          0.00756609472184243
        ],
        "ranking_score": 0.7311883443269466
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5747709592141661e-15,
              -1.9984014443252818e-15,
              0.3148326803060005
            ],
            "target_residual": 0.5908634500361808,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0035000728761753882,
            "step_scale": 0.8132959331422597,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0047820918259764,
              1.0006607722921566,
              0.9973806126571694
            ],
            "cell_volume_ratio": 1.0028123714027666,
            "cell_rmsd_from_input_A": 0.018004846115891794
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.2691379731745875e-14,
              -0.39405718664385725,
              0.06764184799586134
            ],
            "branch_aligned_reduced_polarization": [
              1.2691379731745875e-14,
              -0.39405718664385725,
              0.06764184799586134
            ],
            "target_residual": 0.12569526364230957,
            "energy_eV": -95.06013823962627,
            "max_atomic_step_A": 0.03590708557539408,
            "max_log_strain_component": 0.0010482711874641852,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0062309513925993,
              1.0008642468719153,
              0.9966031507660389
            ],
            "cell_volume_ratio": 1.0036796144997089,
            "cell_rmsd_from_input_A": 0.023440895377998372
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.173961882097771e-15,
              -0.49767454113964876,
              0.002502015626124262
            ],
            "branch_aligned_reduced_polarization": [
              5.173961882097771e-15,
              -0.49767454113964876,
              0.002502015626124262
            ],
            "target_residual": 0.0034158221710967416,
            "energy_eV": -94.80189021128372,
            "max_atomic_step_A": 0.0009457886074755819,
            "max_log_strain_component": 2.5853877385899514e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0062715957918666,
              1.000871797689121,
              0.9965873439547792
            ],
            "cell_volume_ratio": 1.003711808394628,
            "cell_rmsd_from_input_A": 0.023583926320218447
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.279535145168587e-16,
              -0.49997927762205757,
              4.173216528607674e-05
            ],
            "branch_aligned_reduced_polarization": [
              -5.279535145168587e-16,
              -0.49997927762205757,
              4.173216528607674e-05
            ],
            "target_residual": 4.65938898038494e-05,
            "energy_eV": -94.79439712932555
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.65938898038494e-05,
        "parent_symmetrization_rmsd_A": 0.17697085733801526,
        "parent_cell_rmsd_A": 0.023583926320218447,
        "energy_eV": -94.79439712932555,
        "reduced_polarization": [
          -5.279535145168587e-16,
          -0.49997927762205757,
          4.173216528607674e-05
        ],
        "cartesian_polarization_e_A2": [
          -5.326750836209188e-17,
          -0.010545684185886611,
          -4.766513400108853e-05
        ],
        "ranking_score": 0.6829600266976776
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "target_residual": 0.5908634500361811,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005145299951557227,
            "step_scale": 0.6168098361568037,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0063097958170761,
              0.9999121652197337,
              0.9959360766533247
            ],
            "cell_volume_ratio": 1.0021322001501916,
            "cell_rmsd_from_input_A": 0.03188102403697742
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.30187522470156486,
              -2.0476459163003997e-14,
              0.12772635878984182
            ],
            "branch_aligned_reduced_polarization": [
              0.30187522470156486,
              -2.0476459163003997e-14,
              0.12772635878984182
            ],
            "target_residual": 0.23572748952289552,
            "energy_eV": -95.00036499139179,
            "max_atomic_step_A": 0.08179198351989579,
            "max_log_strain_component": 0.0036263714187844804,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.010822991808446,
              0.9998471602498226,
              0.9931181724601981
            ],
            "cell_volume_ratio": 1.0037132515726188,
            "cell_rmsd_from_input_A": 0.05452005239445396
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49361011566973134,
              -1.3913365875193558e-14,
              0.007574460421858951
            ],
            "branch_aligned_reduced_polarization": [
              0.49361011566973134,
              -1.3913365875193558e-14,
              0.007574460421858951
            ],
            "target_residual": 0.009909746335629415,
            "energy_eV": -94.10356212296182,
            "max_atomic_step_A": 0.0031830317964486837,
            "max_log_strain_component": 0.0001330376177755166,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.011012747558038,
              0.9998430266324336,
              0.9930354255641288
            ],
            "cell_volume_ratio": 1.003813877238837,
            "cell_rmsd_from_input_A": 0.055376815595307695
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999295287274896,
              -2.190987116207836e-15,
              0.00012237992410774108
            ],
            "branch_aligned_reduced_polarization": [
              0.4999295287274896,
              -2.190987116207836e-15,
              0.00012237992410774108
            ],
            "target_residual": 0.00014121985014102753,
            "energy_eV": -94.0608885124048
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00014121985014102753,
        "parent_symmetrization_rmsd_A": 0.22775621725359474,
        "parent_cell_rmsd_A": 0.055376815595307695,
        "energy_eV": -94.0608885124048,
        "reduced_polarization": [
          0.4999295287274896,
          -2.190987116207836e-15,
          0.00012237992410774108
        ],
        "cartesian_polarization_e_A2": [
          0.013740856629268206,
          -4.318307433316418e-16,
          -0.00012061223853256435
        ],
        "ranking_score": 0.7418828608527037
      },
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -1.9984014443252818e-15,
              0.3148326803060005
            ],
            "target_residual": 0.7309493390671177,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003952380672876629,
            "step_scale": 0.47380469520594326,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0039941500560434,
              0.9999833122627909,
              0.9950803622213564
            ],
            "cell_volume_ratio": 0.9990381905408875,
            "cell_rmsd_from_input_A": 0.025927932900712186
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2345487337691352,
              -0.23386822089037387,
              0.4050620677446505
            ],
            "branch_aligned_reduced_polarization": [
              0.2345487337691352,
              -0.23386822089037385,
              0.4050620677446505
            ],
            "target_residual": 0.38769022373093914,
            "energy_eV": -95.12168927785078,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0038815976434364834,
            "step_scale": 0.824939991181996,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0080122774327815,
              0.999967959776259,
              0.9903254914865788
            ],
            "cell_volume_ratio": 0.9982282695912327,
            "cell_rmsd_from_input_A": 0.05136109924777502
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4471512169520618,
              -0.4442277221013994,
              0.48430412084570895
            ],
            "branch_aligned_reduced_polarization": [
              0.4471512169520618,
              -0.4442277221013994,
              0.48430412084570895
            ],
            "target_residual": 0.07842130752590705,
            "energy_eV": -94.00755732373975,
            "max_atomic_step_A": 0.03285946493004856,
            "max_log_strain_component": 0.0010678253219302577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0091735035605829,
              0.9999628561103441,
              0.9890284564247878
            ],
            "cell_volume_ratio": 0.9980642391263014,
            "cell_rmsd_from_input_A": 0.05842936872255833
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4995615625744486,
              -0.4993297686557764,
              0.500833096292611
            ],
            "branch_aligned_reduced_polarization": [
              0.4995615625744486,
              -0.4993297686557764,
              0.500833096292611
            ],
            "target_residual": 0.0011556326681372684,
            "energy_eV": -93.5722491755347,
            "max_atomic_step_A": 0.0003639093918863722,
            "max_log_strain_component": 9.614901877290343e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0091908080633774,
              0.9999629787817477,
              0.9890221419577909
            ],
            "cell_volume_ratio": 0.9980751033107396,
            "cell_rmsd_from_input_A": 0.05849472600935764
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999970656299142,
              -0.4999977391355187,
              0.5000111017095124
            ],
            "branch_aligned_reduced_polarization": [
              0.4999970656299142,
              -0.4999977391355187,
              0.5000111017095124
            ],
            "target_residual": 1.1703417881109881e-05,
            "energy_eV": -93.56802304857638
          }
        ],
        "iterations": 4
      },
      "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": 1.1703417881109881e-05,
        "parent_symmetrization_rmsd_A": 0.27650513899587775,
        "parent_cell_rmsd_A": 0.05849472600935764,
        "energy_eV": -93.56802304857638,
        "reduced_polarization": [
          0.4999970656299142,
          -0.4999977391355187,
          0.5000111017095124
        ],
        "cartesian_polarization_e_A2": [
          0.013734814948123193,
          -0.010572280505307013,
          0.007513282647105008
        ],
        "ranking_score": 0.7911522273339794
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              1.5747709592141661e-15,
              -1.9909779127850843e-15,
              0.3148326803060005
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -1.9984014443252818e-15,
              0.3148326803060005
            ],
            "target_residual": 0.774028175578032,
            "energy_eV": -95.48023473787508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003873200513634044,
            "step_scale": 0.4643127119376009,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0051917119033558,
              1.0000292564177533,
              0.9964022863511363
            ],
            "cell_volume_ratio": 1.0016046224676884,
            "cell_rmsd_from_input_A": 0.02573517812583639
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2282999521386641,
              -0.2273055404527131,
              0.1745686701703859
            ],
            "branch_aligned_reduced_polarization": [
              0.2282999521386641,
              -0.22730554045271312,
              0.1745686701703859
            ],
            "target_residual": 0.4226788436634794,
            "energy_eV": -95.10162768251928,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0038883508068032523,
            "step_scale": 0.7940913918354927,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.01052063933446,
              1.000064605153416,
              0.9928435571430642
            ],
            "cell_volume_ratio": 1.003353723757009,
            "cell_rmsd_from_input_A": 0.05183356711492934
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4356338089440865,
              -0.43175510966831054,
              0.04748585953442622
            ],
            "branch_aligned_reduced_polarization": [
              0.4356338089440865,
              -0.43175510966831054,
              0.04748585953442622
            ],
            "target_residual": 0.10514408429937434,
            "energy_eV": -93.97324884859313,
            "max_atomic_step_A": 0.0420341763051748,
            "max_log_strain_component": 0.001353420517782883,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0124781645700864,
              1.0000851252473169,
              0.9916292721095764
            ],
            "cell_volume_ratio": 1.0040884513619106,
            "cell_rmsd_from_input_A": 0.0611336897987148
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49862576651094925,
              -0.4979186258427567,
              0.0028311251800941994
            ],
            "branch_aligned_reduced_polarization": [
              0.49862576651094925,
              -0.4979186258427567,
              0.0028311251800941994
            ],
            "target_residual": 0.0037730499400660277,
            "energy_eV": -93.41137498474744,
            "max_atomic_step_A": 0.0012426531570746613,
            "max_log_strain_component": 3.260460094711514e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8216263287615687,
            "cell_principal_stretches": [
              1.0125406105270014,
              1.00008673047779,
              0.9916065391566397
            ],
            "cell_volume_ratio": 1.0041289715931203,
            "cell_rmsd_from_input_A": 0.06138263682499882
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49997682782538955,
              -0.4999705804939487,
              6.999577349852947e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49997682782538955,
              -0.4999705804939487,
              6.999577349852947e-05
            ],
            "target_residual": 7.938428887466632e-05,
            "energy_eV": -93.39424658177444
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 7.938428887466632e-05,
        "parent_symmetrization_rmsd_A": 0.2878839864943535,
        "parent_cell_rmsd_A": 0.06138263682499882,
        "energy_eV": -93.39424658177444,
        "reduced_polarization": [
          0.49997682782538955,
          -0.4999705804939487,
          6.999577349852947e-05
        ],
        "cartesian_polarization_e_A2": [
          0.013739125498337062,
          -0.010541260691881526,
          -0.00017595556970565138
        ],
        "ranking_score": 0.8033884142783525
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.273714365430712,
        "minimum_distance_A_by_image": [
          1.705194393213188,
          1.7051146945566922,
          1.7050456193743424,
          1.7049871689573246,
          1.7049393443983847,
          1.7049021465917273,
          1.704875576232931,
          1.704859633818885,
          1.7048543196477406
        ],
        "minimum_distance_A": 1.7048543196477406,
        "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": [
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773,
          333.9324448343773
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.6833238640139939e-15,
        4.44860277444475e-15,
        -6.894343139670465e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -95.48023473787507,
          -95.48279407400383,
          -95.4759269800289,
          -95.4621021860102,
          -95.44595051380963,
          -95.43260245534361,
          -95.42319493650221,
          -95.41729722480385,
          -95.41520799763464
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.249887884087892e-17,
            -4.910676177794572e-17,
            0.004837446545030459
          ],
          [
            7.064973661060634e-18,
            9.14290709078435e-18,
            0.004232627093696013
          ],
          [
            -1.5231252039874838e-17,
            3.112744277726127e-17,
            0.0036268278380754406
          ],
          [
            4.297166332668645e-17,
            6.037435580062256e-17,
            0.0030219513610516262
          ],
          [
            -8.581865064758947e-18,
            -4.301322199528092e-18,
            0.002419008690432661
          ],
          [
            4.3491146684117375e-17,
            -6.8675699852368814e-18,
            0.0018170802317674004
          ],
          [
            -1.961569157659188e-17,
            2.1246869318924997e-17,
            0.0012134191705771235
          ],
          [
            4.220282795768867e-17,
            -1.3184487611596978e-17,
            0.0006073235095662657
          ],
          [
            4.640025348573058e-17,
            9.419272236937605e-17,
            -1.0593251110030171e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662597e-16,
            4.3180790221833e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641915e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.11335761682839e-16,
            -2.0314599036180525e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322035e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475689e-15,
            -6.226866226307509e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.894343139670465e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662596e-16,
            4.318079022183299e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641917e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.113357616828391e-16,
            -2.0314599036180523e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322037e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475687e-15,
            -6.22686622630751e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.869504964868156e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.2212453270876722e-15,
            -2.3314683517128287e-15,
            0.3148326803060024
          ],
          [
            2.220446049250313e-16,
            4.440892098500626e-16,
            0.27546957268459704
          ],
          [
            -5.551115123125783e-16,
            1.4432899320127035e-15,
            0.23604269703873815
          ],
          [
            1.5543122344752192e-15,
            2.886579864025407e-15,
            0.196675878048026
          ],
          [
            -3.3306690738754696e-16,
            -2.220446049250313e-16,
            0.1574349158389785
          ],
          [
            1.5543122344752192e-15,
            -3.3306690738754696e-16,
            0.11825996098831948
          ],
          [
            -7.216449660063518e-16,
            9.992007221626409e-16,
            0.0789722441894346
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.03952607776638317
          ],
          [
            1.6653345369377348e-15,
            4.440892098500626e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -95.41520799763464,
          -95.41729722480383,
          -95.42319493650224,
          -95.43260245534363,
          -95.44595051380962,
          -95.46210218601027,
          -95.47592698002894,
          -95.48279407400385,
          -95.48023473787508
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.835351090967087e-17,
            1.0335640879445763e-16,
            -1.9272180900615745e-18
          ],
          [
            1.9033870216269238e-17,
            1.8181917510082515e-18,
            -0.0006073235095662675
          ],
          [
            -1.3028642604367698e-17,
            2.070660662719683e-17,
            -0.0012134191705770827
          ],
          [
            4.8602862921237714e-17,
            2.597416787154645e-19,
            -0.0018170802317674522
          ],
          [
            1.3090980607259411e-17,
            1.6893598783653812e-17,
            -0.0024190086904326345
          ],
          [
            5.1054824368311704e-17,
            4.597427713263722e-17,
            -0.0030219513610517134
          ],
          [
            1.0410446482915817e-17,
            7.158480665398201e-18,
            -0.0036268278380755005
          ],
          [
            7.131467530811793e-17,
            2.4691043978692056e-17,
            -0.004232627093696033
          ],
          [
            9.440051571234842e-17,
            -1.7761135990563462e-17,
            -0.0048374465450304474
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.754184787980548e-15,
            4.88139205825903e-15,
            -1.254279982590443e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569063e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384373e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.776736479494003e-16,
            3.3808595980503335e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389036e-16,
            -0.3148326803060016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.754184787980548e-15,
            4.88139205825903e-15,
            -1.254279982590443e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569081e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384316e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.7767364794940027e-16,
            3.380859598050333e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389037e-16,
            -0.3148326803060016
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.1876425675631934e-15,
          1.1216455605520112e-14,
          -0.3148326803060037
        ],
        "actual_opposite_endpoint_branch_residual": 1.2300813672147666e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662597e-16,
            4.3180790221833e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641915e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.11335761682839e-16,
            -2.0314599036180525e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322035e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475689e-15,
            -6.226866226307509e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.894343139670465e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569063e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384373e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.776736479494003e-16,
            3.3808595980503335e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389036e-16,
            -0.3148326803060016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1790051604647946e-15,
            -2.3192500566306098e-15,
            0.31483268030600237
          ],
          [
            2.563054696662596e-16,
            4.318079022183299e-16,
            0.27546957268459704
          ],
          [
            -5.525644390157893e-16,
            1.4701096307342236e-15,
            0.2360426970387381
          ],
          [
            1.5589403272641917e-15,
            2.851404227034904e-15,
            0.19667587804802603
          ],
          [
            -3.113357616828391e-16,
            -2.0314599036180523e-16,
            0.15743491583897845
          ],
          [
            1.577786317680828e-15,
            -3.243466174617229e-16,
            0.11825996098831942
          ],
          [
            -7.116245981322037e-16,
            1.003462681859642e-15,
            0.07897224418943458
          ],
          [
            1.5310482614475687e-15,
            -6.22686622630751e-16,
            0.039526077766383165
          ],
          [
            1.6833238640139939e-15,
            4.44860277444475e-15,
            -6.869504964868156e-16
          ],
          [
            6.905170888655703e-16,
            8.587088964569081e-17,
            -0.03952607776638329
          ],
          [
            -4.726574396492495e-16,
            9.779467603649224e-16,
            -0.07897224418943193
          ],
          [
            1.7632308633805337e-15,
            1.2267269949384316e-17,
            -0.1182599609883228
          ],
          [
            4.74918958499246e-16,
            7.978632375079598e-16,
            -0.15743491583897673
          ],
          [
            1.852183938147059e-15,
            2.1713067810410345e-15,
            -0.1966758780480317
          ],
          [
            3.7767364794940027e-16,
            3.380859598050333e-16,
            -0.23604269703874198
          ],
          [
            2.587177564395892e-15,
            1.1661266813884787e-15,
            -0.2754695726845983
          ],
          [
            3.424693378511229e-15,
            -8.388359191389037e-16,
            -0.3148326803060016
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.2212453270876722e-15,
            -2.3314683517128287e-15,
            0.3148326803060024
          ],
          [
            2.220446049250313e-16,
            4.440892098500626e-16,
            0.27546957268459704
          ],
          [
            -5.551115123125783e-16,
            1.4432899320127035e-15,
            0.23604269703873815
          ],
          [
            1.5543122344752192e-15,
            2.886579864025407e-15,
            0.196675878048026
          ],
          [
            -3.3306690738754696e-16,
            -2.220446049250313e-16,
            0.1574349158389785
          ],
          [
            1.5543122344752192e-15,
            -3.3306690738754696e-16,
            0.11825996098831948
          ],
          [
            -7.216449660063518e-16,
            9.992007221626409e-16,
            0.0789722441894346
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.03952607776638317
          ],
          [
            1.6653345369377348e-15,
            4.440892098500626e-15,
            -6.661338147750939e-16
          ],
          [
            6.661338147750939e-16,
            1.1102230246251565e-16,
            -0.03952607776638328
          ],
          [
            -4.996003610813204e-16,
            9.992007221626409e-16,
            -0.07897224418943194
          ],
          [
            1.7763568394002505e-15,
            0.0,
            -0.11825996098832281
          ],
          [
            4.440892098500626e-16,
            7.771561172376096e-16,
            -0.15743491583897673
          ],
          [
            1.887379141862766e-15,
            2.220446049250313e-15,
            -0.19667587804803166
          ],
          [
            3.3306690738754696e-16,
            3.3306690738754696e-16,
            -0.23604269703874198
          ],
          [
            2.55351295663786e-15,
            1.2212453270876722e-15,
            -0.2754695726845983
          ],
          [
            3.4416913763379853e-15,
            -8.326672684688674e-16,
            -0.3148326803060016
          ]
        ]
      },
      "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": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.241341796676659e-15,
        "parent_symmetrization_rmsd_A": 0.273714365430712,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -95.41520799763465,
        "reduced_polarization": [
          1.5046638748642774e-15,
          3.963800266045079e-15,
          1.1512736779658549e-16
        ],
        "cartesian_polarization_e_A2": [
          4.147555125728537e-17,
          8.392773122654088e-17,
          1.768947515374647e-18
        ],
        "ranking_score": 0.2737143654307205
      }
    }
  ],
  "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": 57,
      "full_response": 24,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 82,
      "full_response": 49,
      "energy_polarization": 33
    },
    "elapsed_seconds": 715.059495782014
  }
}
