{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "Al2Ca6Na6Sb8",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -75.14158095162111,
  "input_cartesian_polarization_e_A2": [
    2.0256006400747562e-17,
    0.00013184096637721486,
    1.428822760463745e-11
  ],
  "input_reduced_polarization": [
    5.498028593837369e-10,
    0.011667442754268472,
    1.099603127323307e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.2615286310102967e-15,
      "parent_symmetrization_rmsd_A": 0.6547187441040799,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -73.71899672609743,
      "reduced_polarization": [
        -4.490049427379209e-16,
        -2.541877160945394e-16,
        2.201884400976324e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.325565651602288e-17,
        -2.8722964266407814e-18,
        2.861125500509812e-17
      ],
      "ranking_score": 0.6547187441040845
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 8.968100919865799e-07,
      "parent_symmetrization_rmsd_A": 0.0017797164863250993,
      "parent_cell_rmsd_A": 0.0027098090473966713,
      "energy_eV": -75.13779608958268,
      "reduced_polarization": [
        -8.448380845502134e-14,
        -8.96810091986564e-07,
        -1.4701623193693953e-13
      ],
      "cartesian_polarization_e_A2": [
        -1.646766755434457e-16,
        -1.0129320828522164e-08,
        -1.9103838074052683e-15
      ],
      "ranking_score": 0.5024589623683582
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 4.4186568325199685e-15,
      "parent_symmetrization_rmsd_A": 0.6547187490799184,
      "parent_cell_rmsd_A": 0.0027098090473966713,
      "energy_eV": -73.71886473419318,
      "reduced_polarization": [
        -4.1685661001681486e-15,
        -9.214490838450867e-16,
        -1.139524663175556e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.39955597861491e-17,
        -1.0407614143683826e-17,
        -1.4806562733120215e-17
      ],
      "ranking_score": 0.6553962013417765
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 7.744041160751003e-05,
      "parent_symmetrization_rmsd_A": 0.07516761746337879,
      "parent_cell_rmsd_A": 0.1146300085057028,
      "energy_eV": -75.02999227971364,
      "reduced_polarization": [
        -5.391214094939287e-14,
        0.5000774404116075,
        -1.2378533800065405e-13
      ],
      "cartesian_polarization_e_A2": [
        1.6484290013766617e-16,
        0.005759991099977295,
        1.7844106913493376e-13
      ],
      "ranking_score": 0.6039800004130195
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0008880019724551561,
      "parent_symmetrization_rmsd_A": 0.11964934113711127,
      "parent_cell_rmsd_A": 0.05316571112397704,
      "energy_eV": -74.7029050676167,
      "reduced_polarization": [
        -6.45446491369748e-10,
        0.0002822437048602919,
        0.49915804632303756
      ],
      "cartesian_polarization_e_A2": [
        -0.0037447520235219128,
        -4.270152769587852e-05,
        0.006486101613419943
      ],
      "ranking_score": 0.6347167728630159
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0008880018630936249,
      "parent_symmetrization_rmsd_A": 0.11964934120744093,
      "parent_cell_rmsd_A": 0.053165711083265337,
      "energy_eV": -74.70290506527893,
      "reduced_polarization": [
        0.49915804643048617,
        0.00028224368131156825,
        -6.006188982589845e-10
      ],
      "cartesian_polarization_e_A2": [
        0.007489504775636803,
        -4.270152778820542e-05,
        -5.794330810874708e-12
      ],
      "ranking_score": 0.6347167727044445
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.50338924474101e-05,
      "parent_symmetrization_rmsd_A": 0.1442267338654625,
      "parent_cell_rmsd_A": 0.12973072460877938,
      "energy_eV": -74.49860979763899,
      "reduced_polarization": [
        1.2676199089948752e-11,
        0.5000224733928437,
        0.5000110291606735
      ],
      "cartesian_polarization_e_A2": [
        -0.0037379387940824644,
        0.0057157682907014494,
        0.006474300488295618
      ],
      "ranking_score": 0.6767094828025522
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.503386604865014e-05,
      "parent_symmetrization_rmsd_A": 0.144226733018706,
      "parent_cell_rmsd_A": 0.12973072414308448,
      "energy_eV": -74.49860976164524,
      "reduced_polarization": [
        0.5000110291471802,
        0.5000224733700592,
        6.577991998319735e-12
      ],
      "cartesian_polarization_e_A2": [
        0.007475877901046401,
        0.005715768292697626,
        -2.4449307218239877e-10
      ],
      "ranking_score": 0.6767094817865744
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 6.773731295601368e-06,
      "parent_symmetrization_rmsd_A": 0.11985968679584066,
      "parent_cell_rmsd_A": 0.03369344312935168,
      "energy_eV": -74.70127168216635,
      "reduced_polarization": [
        0.4999997512051179,
        6.764587086412677e-06,
        0.49999975120626616
      ],
      "cartesian_polarization_e_A2": [
        0.0037510750539355123,
        -4.5977559941846e-05,
        0.006497052155158146
      ],
      "ranking_score": 0.6282965950407697
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 2.735518461466254e-05,
      "parent_symmetrization_rmsd_A": 0.1442266749568354,
      "parent_cell_rmsd_A": 0.12306129848004647,
      "energy_eV": -74.49861284383476,
      "reduced_polarization": [
        0.5000110290765093,
        0.5000224727598556,
        0.5000110290825153
      ],
      "cartesian_polarization_e_A2": [
        0.003737939106881485,
        0.005715768049818081,
        0.006474300242304381
      ],
      "ranking_score": 0.6750467099460763
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "target_residual": 0.011667442754268538,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.00245353690372594,
            "max_log_strain_component": 0.00022433971651614627,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0002243652744454,
              1.0002243642982405,
              0.9998030167906176
            ],
            "cell_volume_ratio": 1.0002517083007536,
            "cell_rmsd_from_input_A": 0.0027098090473966713
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.448380845502134e-14,
              -8.96810091986564e-07,
              -1.4701623193693953e-13
            ],
            "branch_aligned_reduced_polarization": [
              -8.448380845502134e-14,
              -8.96810091986564e-07,
              -1.4701623193693953e-13
            ],
            "target_residual": 8.968100919865799e-07,
            "energy_eV": -75.13779608958268
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 8.968100919865799e-07,
        "parent_symmetrization_rmsd_A": 0.0017797164863250993,
        "parent_cell_rmsd_A": 0.0027098090473966713,
        "energy_eV": -75.13779608958268,
        "reduced_polarization": [
          -8.448380845502134e-14,
          -8.96810091986564e-07,
          -1.4701623193693953e-13
        ],
        "cartesian_polarization_e_A2": [
          -1.646766755434457e-16,
          -1.0129320828522164e-08,
          -1.9103838074052683e-15
        ],
        "ranking_score": 0.5024589623683582
      },
      "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": [
          -75.14158095162108,
          -75.14112255340672,
          -75.14065994543341,
          -75.1401931312246,
          -75.13972211429828,
          -75.13924689816672,
          -75.13876748633697,
          -75.13828388231036,
          -75.13779608958272
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.134974910569407e-17,
            0.00013184096637723644,
            1.4288163430148631e-11
          ],
          [
            6.483417452048443e-17,
            0.00011535157760483675,
            1.2502693511266909e-11
          ],
          [
            -6.806846361942589e-17,
            9.886445123178433e-05,
            1.0716949641467811e-11
          ],
          [
            9.305246558012142e-17,
            8.237959918176496e-05,
            8.93103808099071e-12
          ],
          [
            2.6187640841232625e-17,
            6.589703337273232e-05,
            7.144813216323025e-12
          ],
          [
            8.795959265720127e-17,
            4.941676571593395e-05,
            5.358456015168815e-12
          ],
          [
            -2.138231020704377e-17,
            3.293880811642594e-05,
            3.5718414644113126e-12
          ],
          [
            -8.396656070940352e-17,
            1.6463172473346828e-05,
            1.7849798249589066e-12
          ],
          [
            -1.590083773622338e-16,
            -1.012932085920614e-08,
            -2.0095597193837607e-15
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851285e-14,
            -8.968100947032019e-07,
            -1.5464888780246087e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851276e-14,
            -8.968100947031373e-07,
            -1.5464888780247155e-13
          ]
        ],
        "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": [
          [
            5.497997612735617e-10,
            0.01166744275427034,
            1.0995981902794938e-09
          ],
          [
            4.810952747291708e-10,
            0.010208764769662038,
            9.621821117633544e-10
          ],
          [
            4.1236913883579973e-10,
            0.00875012336064751,
            8.247473815004014e-10
          ],
          [
            3.4365732481944633e-10,
            0.00729151960252894,
            6.873023261633193e-10
          ],
          [
            2.749195315843167e-10,
            0.005832954570340387,
            5.498356214772571e-10
          ],
          [
            2.061864012858905e-10,
            0.004374429338761754,
            4.1236114523002243e-10
          ],
          [
            1.3743328697302104e-10,
            0.002915944982164298,
            2.7486934950360364e-10
          ],
          [
            6.867495461193585e-11,
            0.001457502574634395,
            1.3736101145411794e-10
          ],
          [
            -8.79296635503124e-14,
            -8.968100946860069e-07,
            -1.546540673302843e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -75.13779608958271,
          -75.13816117361762,
          -75.13852207132008,
          -75.13887878603104,
          -75.13923132108111,
          -75.13957967979022,
          -75.13992386546781,
          -75.14026388141284,
          -75.14059973091372
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1098744068171266e-16,
            -1.0129320832743785e-08,
            -2.0466816667367385e-15
          ],
          [
            -4.201159699483308e-17,
            -1.4611463080619072e-05,
            -1.774613552211712e-12
          ],
          [
            -9.171533418569086e-17,
            -2.921688412838146e-05,
            -3.547497672061581e-12
          ],
          [
            -4.198592199040874e-17,
            -4.382638264331459e-05,
            -5.3203529826002956e-12
          ],
          [
            -8.927534619066297e-17,
            -5.8439948787309874e-05,
            -7.093344717747449e-12
          ],
          [
            1.5691967399243008e-17,
            -7.305757270568821e-05,
            -8.866418234845566e-12
          ],
          [
            -8.232684744287624e-17,
            -8.767924452632311e-05,
            -1.0639687607281575e-11
          ],
          [
            -6.180372205987483e-17,
            -0.00010230495435973367,
            -1.2413050753954624e-11
          ],
          [
            -1.2325600945770761e-17,
            -0.0001169346922995549,
            -1.4186486467190434e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.615021566787274e-14,
            -8.968100923603295e-07,
            -1.5750582194827903e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.615021566787274e-14,
            -8.968100923603295e-07,
            -1.5750582194827903e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.499756446890347e-10,
          -0.011669235569880155,
          -1.099907494663728e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0013209434882708194
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851285e-14,
            -8.968100947032019e-07,
            -1.5464888780246087e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851276e-14,
            -8.968100947031373e-07,
            -1.5464888780247155e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "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": [
          [
            5.497997612735617e-10,
            0.01166744275427034,
            1.0995981902794938e-09
          ],
          [
            4.810952747291708e-10,
            0.010208764769662038,
            9.621821117633544e-10
          ],
          [
            4.1236913883579973e-10,
            0.00875012336064751,
            8.247473815004014e-10
          ],
          [
            3.4365732481944633e-10,
            0.00729151960252894,
            6.873023261633193e-10
          ],
          [
            2.749195315843167e-10,
            0.005832954570340387,
            5.498356214772571e-10
          ],
          [
            2.061864012858905e-10,
            0.004374429338761754,
            4.1236114523002243e-10
          ],
          [
            1.3743328697302104e-10,
            0.002915944982164298,
            2.7486934950360364e-10
          ],
          [
            6.867495461193585e-11,
            0.001457502574634395,
            1.3736101145411794e-10
          ],
          [
            -8.79296635503124e-14,
            -8.968100946860069e-07,
            -1.546540673302843e-13
          ],
          [
            -6.828509979683872e-11,
            -0.0012935687270272944,
            -1.3656459296740309e-10
          ],
          [
            -1.3650519603558564e-10,
            -0.0025864574810204877,
            -2.729981796179004e-10
          ],
          [
            -2.0471857542503358e-10,
            -0.0038795621540423375,
            -4.0943159973494403e-10
          ],
          [
            -2.7294477789041593e-10,
            -0.005172881826732534,
            -5.458776763944684e-10
          ],
          [
            -3.411649851514653e-10,
            -0.006466415578465501,
            -6.823321352378287e-10
          ],
          [
            -4.0940728585070474e-10,
            -0.0077601624872727926,
            -8.188037470269194e-10
          ],
          [
            -4.77646422414324e-10,
            -0.009054121629852196,
            -9.552846291782657e-10
          ],
          [
            -5.458873908459339e-10,
            -0.010348292081609312,
            -1.0917732828907845e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268453,
              1.099603127323307e-09
            ],
            "target_residual": 0.48833255724573155,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.1026910502779109,
            "max_log_strain_component": 0.009389580027554285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0082794918902895,
              0.9906543886534026,
              0.990654348185959
            ],
            "cell_volume_ratio": 0.9895215385352182,
            "cell_rmsd_from_input_A": 0.11251974914424881
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.598491812096316e-12,
              0.4916441090506436,
              9.246854334415929e-12
            ],
            "branch_aligned_reduced_polarization": [
              4.598491812096316e-12,
              0.4916441090506436,
              9.246854334415929e-12
            ],
            "target_residual": 0.008355890949356404,
            "energy_eV": -75.03699254872032,
            "max_atomic_step_A": 0.0018056737852659012,
            "max_log_strain_component": 0.00017749289342134658,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0084366589647102,
              0.9904785706011003,
              0.9904785293760111
            ],
            "cell_volume_ratio": 0.9893245233496647,
            "cell_rmsd_from_input_A": 0.1146300085057028
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.391214094939287e-14,
              0.5000774404116075,
              -1.2378533800065405e-13
            ],
            "branch_aligned_reduced_polarization": [
              -5.391214094939287e-14,
              0.5000774404116075,
              -1.2378533800065405e-13
            ],
            "target_residual": 7.744041160751003e-05,
            "energy_eV": -75.02999227971364
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 7.744041160751003e-05,
        "parent_symmetrization_rmsd_A": 0.07516761746337879,
        "parent_cell_rmsd_A": 0.1146300085057028,
        "energy_eV": -75.02999227971364,
        "reduced_polarization": [
          -5.391214094939287e-14,
          0.5000774404116075,
          -1.2378533800065405e-13
        ],
        "cartesian_polarization_e_A2": [
          1.6484290013766617e-16,
          0.005759991099977295,
          1.7844106913493376e-13
        ],
        "ranking_score": 0.6039800004130195
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.0996031307719534e-09
            ],
            "target_residual": 0.5001361095949991,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.004376351412158943,
            "step_scale": 0.855571023049244,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0050811404445934,
              1.000191957275904,
              0.9949678174463928
            ],
            "cell_volume_ratio": 1.0002153504302165,
            "cell_rmsd_from_input_A": 0.043910539633272995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.770751325881985e-08,
              -0.0027382742114972973,
              0.418860801550655
            ],
            "branch_aligned_reduced_polarization": [
              -1.770751325881985e-08,
              -0.0027382742114972973,
              0.418860801550655
            ],
            "target_residual": 0.08118539074648745,
            "energy_eV": -74.8373696071714,
            "max_atomic_step_A": 0.02423309740176332,
            "max_log_strain_component": 0.0009297955424201441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0061505024358053,
              1.0000706617244015,
              0.9938956525006756
            ],
            "cell_volume_ratio": 1.0000792724651257,
            "cell_rmsd_from_input_A": 0.05316571112397704
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.45446491369748e-10,
              0.0002822437048602919,
              0.49915804632303756
            ],
            "branch_aligned_reduced_polarization": [
              -6.45446491369748e-10,
              0.0002822437048602919,
              0.49915804632303756
            ],
            "target_residual": 0.0008880019724551561,
            "energy_eV": -74.7029050676167
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0008880019724551561,
        "parent_symmetrization_rmsd_A": 0.11964934113711127,
        "parent_cell_rmsd_A": 0.05316571112397704,
        "energy_eV": -74.7029050676167,
        "reduced_polarization": [
          -6.45446491369748e-10,
          0.0002822437048602919,
          0.49915804632303756
        ],
        "cartesian_polarization_e_A2": [
          -0.0037447520235219128,
          -4.270152769587852e-05,
          0.006486101613419943
        ],
        "ranking_score": 0.6347167728630159
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028698980306e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "target_residual": 0.5001361101446498,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005053367342976642,
            "step_scale": 0.8555710228973417,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0050811406562592,
              1.00019195681749,
              0.9949678176768296
            ],
            "cell_volume_ratio": 1.0002153504140854,
            "cell_rmsd_from_input_A": 0.04391053957537995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.41886080118610836,
              -0.0027382742586622598,
              -1.779152598646502e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.41886080118610836,
              -0.0027382742586622598,
              -1.779152598646502e-08
            ],
            "target_residual": 0.08118539111241754,
            "energy_eV": -74.83736960652593,
            "max_atomic_step_A": 0.024233097453336797,
            "max_log_strain_component": 0.0010736335320724554,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0061505024834307,
              1.000070661570465,
              0.9938956525852295
            ],
            "cell_volume_ratio": 1.0000792724436056,
            "cell_rmsd_from_input_A": 0.053165711083265337
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49915804643048617,
              0.00028224368131156825,
              -6.006188982589845e-10
            ],
            "branch_aligned_reduced_polarization": [
              0.49915804643048617,
              0.00028224368131156825,
              -6.006188982589845e-10
            ],
            "target_residual": 0.0008880018630936249,
            "energy_eV": -74.70290506527893
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0008880018630936249,
        "parent_symmetrization_rmsd_A": 0.11964934120744093,
        "parent_cell_rmsd_A": 0.053165711083265337,
        "energy_eV": -74.70290506527893,
        "reduced_polarization": [
          0.49915804643048617,
          0.00028224368131156825,
          -6.006188982589845e-10
        ],
        "cartesian_polarization_e_A2": [
          0.007489504775636803,
          -4.270152778820542e-05,
          -5.794330810874708e-12
        ],
        "ranking_score": 0.6347167727044445
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268453,
              1.0996031307719534e-09
            ],
            "target_residual": 0.6989053479310002,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006392871237655249,
            "step_scale": 0.6808474104247968,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0068596960370475,
              0.993627509294121,
              0.9924136546075759
            ],
            "cell_volume_ratio": 0.9928537821061494,
            "cell_rmsd_from_input_A": 0.08424539230074964
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.69740821185041e-08,
              0.33741671795047506,
              0.33470329672133387
            ],
            "branch_aligned_reduced_polarization": [
              3.69740821185041e-08,
              0.33741671795047506,
              0.33470329672133387
            ],
            "target_residual": 0.23185410006465734,
            "energy_eV": -74.91774273163571,
            "max_atomic_step_A": 0.06290510750608118,
            "max_log_strain_component": 0.0034518255420680466,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0105823976673514,
              0.9902035876653331,
              0.9883420811221237
            ],
            "cell_volume_ratio": 0.9890164425415054,
            "cell_rmsd_from_input_A": 0.12933862207378174
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.9247033007875303e-08,
              0.4989673863687222,
              0.49761230009142493
            ],
            "branch_aligned_reduced_polarization": [
              1.9247033007875303e-08,
              0.4989673863687222,
              0.49761230009142493
            ],
            "target_residual": 0.002601423026975931,
            "energy_eV": -74.50520792127763,
            "max_atomic_step_A": 0.000818166599749639,
            "max_log_strain_component": 2.8956694194920594e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0106196526992643,
              0.9901784669125673,
              0.9883025921112922
            ],
            "cell_volume_ratio": 0.9889882945766207,
            "cell_rmsd_from_input_A": 0.12973072460877938
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.2676199089948752e-11,
              0.5000224733928437,
              0.5000110291606735
            ],
            "branch_aligned_reduced_polarization": [
              1.2676199089948752e-11,
              0.5000224733928437,
              0.5000110291606735
            ],
            "target_residual": 2.50338924474101e-05,
            "energy_eV": -74.49860979763899
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.50338924474101e-05,
        "parent_symmetrization_rmsd_A": 0.1442267338654625,
        "parent_cell_rmsd_A": 0.12973072460877938,
        "energy_eV": -74.49860979763899,
        "reduced_polarization": [
          1.2676199089948752e-11,
          0.5000224733928437,
          0.5000110291606735
        ],
        "cartesian_polarization_e_A2": [
          -0.0037379387940824644,
          0.0057157682907014494,
          0.006474300488295618
        ],
        "ranking_score": 0.6767094828025522
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028698980306e-10,
              0.011667442754268453,
              1.099603127323307e-09
            ],
            "target_residual": 0.6989053483243298,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006392871236113985,
            "step_scale": 0.6808474092869501,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0068596946574346,
              0.9936275251372164,
              0.9924136401428418
            ],
            "cell_volume_ratio": 0.9928537821053373,
            "cell_rmsd_from_input_A": 0.08424539242097467
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3347033041970556,
              0.337416716960331,
              4.116999676087986e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.3347033041970556,
              0.337416716960331,
              4.116999676087986e-08
            ],
            "target_residual": 0.23185409542928062,
            "energy_eV": -74.91774271384456,
            "max_atomic_step_A": 0.06290510611883143,
            "max_log_strain_component": 0.00345182555517503,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.010582395456416,
              0.9902036119650091,
              0.9883420590137099
            ],
            "cell_volume_ratio": 0.9890164425247945,
            "cell_rmsd_from_input_A": 0.129338621705247
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49761230378212573,
              0.49896738603452806,
              2.0960474346974837e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49761230378212573,
              0.49896738603452806,
              2.0960474346974837e-08
            ],
            "target_residual": 0.0026014197721586792,
            "energy_eV": -74.50520787962544,
            "max_atomic_step_A": 0.0008181658737245784,
            "max_log_strain_component": 3.3436341648182424e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.01061965045212,
              0.9901784912715782,
              0.9883025699760954
            ],
            "cell_volume_ratio": 0.9889882945567506,
            "cell_rmsd_from_input_A": 0.12973072414308448
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000110291471802,
              0.5000224733700592,
              6.577991998319735e-12
            ],
            "branch_aligned_reduced_polarization": [
              0.5000110291471802,
              0.5000224733700592,
              6.577991998319735e-12
            ],
            "target_residual": 2.503386604865014e-05,
            "energy_eV": -74.49860976164524
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.503386604865014e-05,
        "parent_symmetrization_rmsd_A": 0.144226733018706,
        "parent_cell_rmsd_A": 0.12973072414308448,
        "energy_eV": -74.49860976164524,
        "reduced_polarization": [
          0.5000110291471802,
          0.5000224733700592,
          6.577991998319735e-12
        ],
        "cartesian_polarization_e_A2": [
          0.007475877901046401,
          0.005715768292697626,
          -2.4449307218239877e-10
        ],
        "ranking_score": 0.6767094817865744
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028698980306e-10,
              0.011667442754268472,
              1.0996031307719534e-09
            ],
            "target_residual": 0.7072030313644152,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00437634562026906,
            "step_scale": 0.8555672568388369,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0050811421081298,
              1.0001919557217496,
              0.9949678164023898
            ],
            "cell_volume_ratio": 1.0002153494819999,
            "cell_rmsd_from_input_A": 0.027823593183800774
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4188590304197883,
              -0.002738224609631897,
              0.4188590305936205
            ],
            "branch_aligned_reduced_polarization": [
              0.4188590304197883,
              -0.002738224609631897,
              0.4188590305936205
            ],
            "target_residual": 0.11478332515934817,
            "energy_eV": -74.83737368438413,
            "max_atomic_step_A": 0.024233618072102312,
            "max_log_strain_component": 0.0009298178381060171,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0061505317042216,
              1.0000706607070984,
              0.9938956237563586
            ],
            "cell_volume_ratio": 1.000079271616468,
            "cell_rmsd_from_input_A": 0.03362884190101361
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4991580126345544,
              0.00028224760072064663,
              0.4991580125849789
            ],
            "branch_aligned_reduced_polarization": [
              0.4991580126345544,
              0.00028224760072064663,
              0.4991580125849789
            ],
            "target_residual": 0.001223743943289011,
            "energy_eV": -74.70290745275679,
            "max_atomic_step_A": 0.0002770832435110625,
            "max_log_strain_component": 9.967611513413947e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0061624423354512,
              1.0000752658005045,
              0.9938844160274208
            ],
            "cell_volume_ratio": 1.0000844379200928,
            "cell_rmsd_from_input_A": 0.03369344312935168
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999997512051179,
              6.764587086412677e-06,
              0.49999975120626616
            ],
            "branch_aligned_reduced_polarization": [
              0.4999997512051179,
              6.764587086412677e-06,
              0.49999975120626616
            ],
            "target_residual": 6.773731295601368e-06,
            "energy_eV": -74.70127168216635
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 6.773731295601368e-06,
        "parent_symmetrization_rmsd_A": 0.11985968679584066,
        "parent_cell_rmsd_A": 0.03369344312935168,
        "energy_eV": -74.70127168216635,
        "reduced_polarization": [
          0.4999997512051179,
          6.764587086412677e-06,
          0.49999975120626616
        ],
        "cartesian_polarization_e_A2": [
          0.0037510750539355123,
          -4.5977559941846e-05,
          0.006497052155158146
        ],
        "ranking_score": 0.6282965950407697
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.498028593837369e-10,
              0.011667442754268472,
              1.099603127323307e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.498028698980306e-10,
              0.011667442754268453,
              1.0996031307719534e-09
            ],
            "target_residual": 0.85934200689641,
            "energy_eV": -75.14158095162111,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0063928881264006705,
            "step_scale": 0.6808492090871688,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0068597227396003,
              0.9936275159760922,
              0.9924136028113018
            ],
            "cell_volume_ratio": 0.9928537632947774,
            "cell_rmsd_from_input_A": 0.07990288904344954
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3347042034092062,
              0.33741755077986285,
              0.3347041996035624
            ],
            "branch_aligned_reduced_polarization": [
              0.3347042034092062,
              0.33741755077986285,
              0.3347041996035624
            ],
            "target_residual": 0.2847427870793262,
            "energy_eV": -74.91774213432265,
            "max_atomic_step_A": 0.06290484724456172,
            "max_log_strain_component": 0.0034518068640194874,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0105824086128774,
              0.9902036254445176,
              0.9883420346931858
            ],
            "cell_volume_ratio": 0.9890164445267244,
            "cell_rmsd_from_input_A": 0.12272086662470376
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49761234657606784,
              0.498967423283888,
              0.49761234484201916
            ],
            "branch_aligned_reduced_polarization": [
              0.49761234657606784,
              0.498967423283888,
              0.49761234484201916
            ],
            "target_residual": 0.003531005621760481,
            "energy_eV": -74.50521076404104,
            "max_atomic_step_A": 0.000818145526196622,
            "max_log_strain_component": 2.895620935229584e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8648753469606625,
            "cell_principal_stretches": [
              1.0106196626347113,
              0.9901785056798155,
              0.9883025466887713
            ],
            "cell_volume_ratio": 0.988988297566021,
            "cell_rmsd_from_input_A": 0.12306129848004647
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000110290765093,
              0.5000224727598556,
              0.5000110290825153
            ],
            "branch_aligned_reduced_polarization": [
              0.5000110290765093,
              0.5000224727598556,
              0.5000110290825153
            ],
            "target_residual": 2.735518461466254e-05,
            "energy_eV": -74.49861284383476
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 2.735518461466254e-05,
        "parent_symmetrization_rmsd_A": 0.1442266749568354,
        "parent_cell_rmsd_A": 0.12306129848004647,
        "energy_eV": -74.49861284383476,
        "reduced_polarization": [
          0.5000110290765093,
          0.5000224727598556,
          0.5000110290825153
        ],
        "cartesian_polarization_e_A2": [
          0.003737939106881485,
          0.005715768049818081,
          0.006474300242304381
        ],
        "ranking_score": 0.6750467099460763
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21
        ],
        "endpoint_rmsd_A": 0.0017797164863250993,
        "minimum_distance_A_by_image": [
          2.673606079750907,
          2.6735389843255577,
          2.67347195620887,
          2.6734049953970227,
          2.673338101886175,
          2.6732712756724886,
          2.67320451675212,
          2.6731378251212137,
          2.6730712007759214
        ],
        "minimum_distance_A": 2.6730712007759214,
        "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": [
          673.7295257275339,
          673.7507213077968,
          673.7719175548754,
          673.7931144687883,
          673.8143120495582,
          673.8355102972056,
          673.8567092117514,
          673.8779087932166,
          673.8991090416217
        ],
        "cell_deformation_log_strain_norm": 0.00037345221926764747
      },
      "parent_reduced_polarization": [
        -8.792234395851285e-14,
        -8.968100947032019e-07,
        -1.5464888780246087e-13
      ],
      "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": [
          -75.14158095162108,
          -75.14112255340672,
          -75.14065994543341,
          -75.1401931312246,
          -75.13972211429828,
          -75.13924689816672,
          -75.13876748633697,
          -75.13828388231036,
          -75.13779608958272
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.134974910569407e-17,
            0.00013184096637723644,
            1.4288163430148631e-11
          ],
          [
            6.483417452048443e-17,
            0.00011535157760483675,
            1.2502693511266909e-11
          ],
          [
            -6.806846361942589e-17,
            9.886445123178433e-05,
            1.0716949641467811e-11
          ],
          [
            9.305246558012142e-17,
            8.237959918176496e-05,
            8.93103808099071e-12
          ],
          [
            2.6187640841232625e-17,
            6.589703337273232e-05,
            7.144813216323025e-12
          ],
          [
            8.795959265720127e-17,
            4.941676571593395e-05,
            5.358456015168815e-12
          ],
          [
            -2.138231020704377e-17,
            3.293880811642594e-05,
            3.5718414644113126e-12
          ],
          [
            -8.396656070940352e-17,
            1.6463172473346828e-05,
            1.7849798249589066e-12
          ],
          [
            -1.590083773622338e-16,
            -1.012932085920614e-08,
            -2.0095597193837607e-15
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851285e-14,
            -8.968100947032019e-07,
            -1.5464888780246087e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851276e-14,
            -8.968100947031373e-07,
            -1.5464888780247155e-13
          ]
        ],
        "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": [
          [
            5.497997612735617e-10,
            0.01166744275427034,
            1.0995981902794938e-09
          ],
          [
            4.810952747291708e-10,
            0.010208764769662038,
            9.621821117633544e-10
          ],
          [
            4.1236913883579973e-10,
            0.00875012336064751,
            8.247473815004014e-10
          ],
          [
            3.4365732481944633e-10,
            0.00729151960252894,
            6.873023261633193e-10
          ],
          [
            2.749195315843167e-10,
            0.005832954570340387,
            5.498356214772571e-10
          ],
          [
            2.061864012858905e-10,
            0.004374429338761754,
            4.1236114523002243e-10
          ],
          [
            1.3743328697302104e-10,
            0.002915944982164298,
            2.7486934950360364e-10
          ],
          [
            6.867495461193585e-11,
            0.001457502574634395,
            1.3736101145411794e-10
          ],
          [
            -8.79296635503124e-14,
            -8.968100946860069e-07,
            -1.546540673302843e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -75.13779608958271,
          -75.13816117361762,
          -75.13852207132008,
          -75.13887878603104,
          -75.13923132108111,
          -75.13957967979022,
          -75.13992386546781,
          -75.14026388141284,
          -75.14059973091372
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1098744068171266e-16,
            -1.0129320832743785e-08,
            -2.0466816667367385e-15
          ],
          [
            -4.201159699483308e-17,
            -1.4611463080619072e-05,
            -1.774613552211712e-12
          ],
          [
            -9.171533418569086e-17,
            -2.921688412838146e-05,
            -3.547497672061581e-12
          ],
          [
            -4.198592199040874e-17,
            -4.382638264331459e-05,
            -5.3203529826002956e-12
          ],
          [
            -8.927534619066297e-17,
            -5.8439948787309874e-05,
            -7.093344717747449e-12
          ],
          [
            1.5691967399243008e-17,
            -7.305757270568821e-05,
            -8.866418234845566e-12
          ],
          [
            -8.232684744287624e-17,
            -8.767924452632311e-05,
            -1.0639687607281575e-11
          ],
          [
            -6.180372205987483e-17,
            -0.00010230495435973367,
            -1.2413050753954624e-11
          ],
          [
            -1.2325600945770761e-17,
            -0.0001169346922995549,
            -1.4186486467190434e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.615021566787274e-14,
            -8.968100923603295e-07,
            -1.5750582194827903e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.615021566787274e-14,
            -8.968100923603295e-07,
            -1.5750582194827903e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.499756446890347e-10,
          -0.011669235569880155,
          -1.099907494663728e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0013209434882708194
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851285e-14,
            -8.968100947032019e-07,
            -1.5464888780246087e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.497997964062426e-10,
            0.011667442754270382,
            1.0995981885393965e-09
          ],
          [
            4.810953293946454e-10,
            0.010208764769661984,
            9.62182111501565e-10
          ],
          [
            4.1236913772245816e-10,
            0.008750123360647507,
            8.247474300148693e-10
          ],
          [
            3.436573286354852e-10,
            0.00729151960252891,
            6.873023211876099e-10
          ],
          [
            2.749195074311354e-10,
            0.005832954570340345,
            5.498355780985998e-10
          ],
          [
            2.0618640590399873e-10,
            0.00437442933876174,
            4.1236112735703157e-10
          ],
          [
            1.37433235116654e-10,
            0.002915944982164263,
            2.7486934739478215e-10
          ],
          [
            6.867491056489246e-11,
            0.0014575025746344466,
            1.3736102726656873e-10
          ],
          [
            -8.792234395851276e-14,
            -8.968100947031373e-07,
            -1.5464888780247155e-13
          ],
          [
            -6.828508210588046e-11,
            -0.0012935687270273194,
            -1.3656457746561908e-10
          ],
          [
            -1.3650517850446098e-10,
            -0.002586457481020499,
            -2.7299815821767694e-10
          ],
          [
            -2.0471858631395743e-10,
            -0.0038795621540423254,
            -4.0943161616979227e-10
          ],
          [
            -2.7294475764053885e-10,
            -0.005172881826732542,
            -5.45877668709645e-10
          ],
          [
            -3.411649762986413e-10,
            -0.006466415578465476,
            -6.823321114624346e-10
          ],
          [
            -4.0940730880748804e-10,
            -0.00776016248727281,
            -8.188037243593262e-10
          ],
          [
            -4.776463980900765e-10,
            -0.009054121629852193,
            -9.552846521865056e-10
          ],
          [
            -5.45887399434428e-10,
            -0.010348292081609336,
            -1.0917732637454158e-09
          ]
        ],
        "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": [
          [
            5.497997612735617e-10,
            0.01166744275427034,
            1.0995981902794938e-09
          ],
          [
            4.810952747291708e-10,
            0.010208764769662038,
            9.621821117633544e-10
          ],
          [
            4.1236913883579973e-10,
            0.00875012336064751,
            8.247473815004014e-10
          ],
          [
            3.4365732481944633e-10,
            0.00729151960252894,
            6.873023261633193e-10
          ],
          [
            2.749195315843167e-10,
            0.005832954570340387,
            5.498356214772571e-10
          ],
          [
            2.061864012858905e-10,
            0.004374429338761754,
            4.1236114523002243e-10
          ],
          [
            1.3743328697302104e-10,
            0.002915944982164298,
            2.7486934950360364e-10
          ],
          [
            6.867495461193585e-11,
            0.001457502574634395,
            1.3736101145411794e-10
          ],
          [
            -8.79296635503124e-14,
            -8.968100946860069e-07,
            -1.546540673302843e-13
          ],
          [
            -6.828509979683872e-11,
            -0.0012935687270272944,
            -1.3656459296740309e-10
          ],
          [
            -1.3650519603558564e-10,
            -0.0025864574810204877,
            -2.729981796179004e-10
          ],
          [
            -2.0471857542503358e-10,
            -0.0038795621540423375,
            -4.0943159973494403e-10
          ],
          [
            -2.7294477789041593e-10,
            -0.005172881826732534,
            -5.458776763944684e-10
          ],
          [
            -3.411649851514653e-10,
            -0.006466415578465501,
            -6.823321352378287e-10
          ],
          [
            -4.0940728585070474e-10,
            -0.0077601624872727926,
            -8.188037470269194e-10
          ],
          [
            -4.77646422414324e-10,
            -0.009054121629852196,
            -9.552846291782657e-10
          ],
          [
            -5.458873908459339e-10,
            -0.010348292081609312,
            -1.0917732828907845e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 8.968100919865799e-07,
        "parent_symmetrization_rmsd_A": 0.0017797164863250993,
        "parent_cell_rmsd_A": 0.0027098090473966713,
        "energy_eV": -75.13779608958268,
        "reduced_polarization": [
          -8.448380845502134e-14,
          -8.96810091986564e-07,
          -1.4701623193693953e-13
        ],
        "cartesian_polarization_e_A2": [
          -1.646766755434457e-16,
          -1.0129320828522164e-08,
          -1.9103838074052683e-15
        ],
        "ranking_score": 0.5024589623683582
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 167.09014154801844
  }
}
