{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "I8Tl4Zn2",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -33.81147331097075,
  "input_cartesian_polarization_e_A2": [
    2.7678090475559897e-11,
    0.0022143091114173365,
    -5.990381150645266e-12
  ],
  "input_reduced_polarization": [
    1.9484457086423397e-09,
    0.16117724539808984,
    -3.945731861429673e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0883704498843022e-15,
      "parent_symmetrization_rmsd_A": 0.4660377676160072,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -33.759447021818616,
      "reduced_polarization": [
        8.395783440227537e-16,
        -6.922479215266003e-16,
        -2.1242776924653898e-17
      ],
      "cartesian_polarization_e_A2": [
        1.1195575150867073e-17,
        -9.510342953250587e-18,
        -3.2250628006612964e-19
      ],
      "ranking_score": 0.46603776761600935
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.9348479124383736e-15,
      "parent_symmetrization_rmsd_A": 0.7606456619356678,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -30.170368156392637,
      "reduced_polarization": [
        -1.069377432290696e-15,
        -1.1301485154845118e-15,
        -1.1501446363491181e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.477307933166836e-18,
        -1.5526373768897957e-17,
        -1.7461411449294734e-17
      ],
      "ranking_score": 0.7606456619356717
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0002004497509984146,
      "parent_symmetrization_rmsd_A": 0.07216652568424846,
      "parent_cell_rmsd_A": 0.09812639423568179,
      "energy_eV": -33.672557921641136,
      "reduced_polarization": [
        2.697181495731828e-12,
        0.0002004497509984146,
        4.558710374701852e-13
      ],
      "cartesian_polarization_e_A2": [
        3.316899942707108e-14,
        2.7643191741756063e-06,
        6.967941633518188e-15
      ],
      "ranking_score": 0.5970990237451658
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.257077091676163e-16,
      "parent_symmetrization_rmsd_A": 0.46610283761214677,
      "parent_cell_rmsd_A": 0.09812639423568179,
      "energy_eV": -33.713891484872605,
      "reduced_polarization": [
        4.466266166936024e-16,
        1.4396853095497607e-16,
        -4.1389354267405344e-16
      ],
      "cartesian_polarization_e_A2": [
        7.81363089347734e-18,
        1.9854101524295296e-18,
        -6.1782197762378966e-18
      ],
      "ranking_score": 0.4906344361710685
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00025057000017286724,
      "parent_symmetrization_rmsd_A": 0.15223051976436952,
      "parent_cell_rmsd_A": 0.18487815732859558,
      "energy_eV": -33.624254777464174,
      "reduced_polarization": [
        -1.600161155548659e-13,
        0.49974942999982713,
        -2.928400977669287e-13
      ],
      "cartesian_polarization_e_A2": [
        -8.914664232556778e-13,
        0.006814289052447083,
        -5.336070642134181e-13
      ],
      "ranking_score": 0.6989511990968642
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0003049346663935389,
      "parent_symmetrization_rmsd_A": 0.30913340825978997,
      "parent_cell_rmsd_A": 0.11535012632670522,
      "energy_eV": -33.03292098808316,
      "reduced_polarization": [
        0.4997970322451257,
        0.00022700929681048832,
        -1.6000637844901113e-05
      ],
      "cartesian_polarization_e_A2": [
        0.006499707628742081,
        -4.4114683199957435e-05,
        3.264482826011891e-07
      ],
      "ranking_score": 0.8385808091742533
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0008701170208057734,
      "parent_symmetrization_rmsd_A": 0.38468455381480476,
      "parent_cell_rmsd_A": 0.14013001346073647,
      "energy_eV": -32.605006648595776,
      "reduced_polarization": [
        6.561672328125069e-05,
        -0.0008406647752613388,
        -0.5002146644152079
      ],
      "cartesian_polarization_e_A2": [
        0.0024366674169721014,
        0.00010301598641035214,
        -0.007522242504688807
      ],
      "ranking_score": 0.9214572912216004
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.4682119578739426e-05,
      "parent_symmetrization_rmsd_A": 0.36302152829370127,
      "parent_cell_rmsd_A": 0.24376955928759347,
      "energy_eV": -31.99779973120564,
      "reduced_polarization": [
        0.5000244155872072,
        0.49999833850042713,
        -3.213338979135872e-06
      ],
      "cartesian_polarization_e_A2": [
        0.006812960777749942,
        0.006749583400605226,
        -1.1078709931042235e-05
      ],
      "ranking_score": 0.9240132823547571
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 7.031377705451161e-07,
      "parent_symmetrization_rmsd_A": 0.44206940211684226,
      "parent_cell_rmsd_A": 0.30178170880646965,
      "energy_eV": -32.120192659998864,
      "reduced_polarization": [
        -3.360520223118011e-07,
        0.49999960924117953,
        -0.5000004783087987
      ],
      "cartesian_polarization_e_A2": [
        0.0025945520142395518,
        0.006934096647158574,
        -0.008092033207437037
      ],
      "ranking_score": 1.0175162355940008
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0026173413170235906,
      "parent_symmetrization_rmsd_A": 0.5603722146804291,
      "parent_cell_rmsd_A": 0.19044183808258378,
      "energy_eV": -29.997997184737827,
      "reduced_polarization": [
        0.49980584371848125,
        0.0008843107147590977,
        -0.4975442366832474
      ],
      "cartesian_polarization_e_A2": [
        0.009022718997239616,
        0.00010117938211930491,
        -0.007606137218621744
      ],
      "ranking_score": 1.113217356835122
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.03062124331567441,
      "parent_symmetrization_rmsd_A": 0.568799678408126,
      "parent_cell_rmsd_A": 0.3480332972120773,
      "energy_eV": -29.470854013288548,
      "reduced_polarization": [
        0.4867817044144125,
        0.48352390268295414,
        -0.477830755060016
      ],
      "cartesian_polarization_e_A2": [
        0.009112586832905936,
        0.006646865231884676,
        -0.007775917403627452
      ],
      "ranking_score": 1.217050489342494
    }
  ],
  "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": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "target_residual": 0.16117724539808984,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.05897273015867022,
            "max_log_strain_component": 0.01724921614877136,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.017398842954617,
              0.9989924099929488,
              0.9973498642126284
            ],
            "cell_volume_ratio": 1.0136801936731288,
            "cell_rmsd_from_input_A": 0.09462403130086161
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.77394108670629e-11,
              0.005523906502554124,
              2.1190129010563126e-11
            ],
            "branch_aligned_reduced_polarization": [
              6.77394108670629e-11,
              0.005523906502554124,
              2.1190129010563126e-11
            ],
            "target_residual": 0.005523906502554124,
            "energy_eV": -33.6790966316279,
            "max_atomic_step_A": 0.002330634836210131,
            "max_log_strain_component": 0.0006276818885381225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0180376462434135,
              0.9989557639408265,
              0.997253560943373
            ],
            "cell_volume_ratio": 1.014181515932267,
            "cell_rmsd_from_input_A": 0.09812639423568179
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.697181495731828e-12,
              0.0002004497509984146,
              4.558710374701852e-13
            ],
            "branch_aligned_reduced_polarization": [
              2.697181495731828e-12,
              0.0002004497509984146,
              4.558710374701852e-13
            ],
            "target_residual": 0.0002004497509984146,
            "energy_eV": -33.672557921641136
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0883704498843022e-15,
        "parent_symmetrization_rmsd_A": 0.4660377676160072,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -33.759447021818616,
        "reduced_polarization": [
          8.395783440227537e-16,
          -6.922479215266003e-16,
          -2.1242776924653898e-17
        ],
        "cartesian_polarization_e_A2": [
          1.1195575150867073e-17,
          -9.510342953250587e-18,
          -3.2250628006612964e-19
        ],
        "ranking_score": 0.46603776761600935
      },
      "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": [
          -33.811473310970754,
          -33.79573668031943,
          -33.783284088203125,
          -33.77423695185496,
          -33.76809947976344,
          -33.764057352550026,
          -33.76147323838535,
          -33.75997314025375,
          -33.75944702181862
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.767808526938709e-11,
            0.0022143091114173357,
            -5.990383638550855e-12
          ],
          [
            2.453451100588429e-11,
            0.0017129158776531287,
            -4.5773008566649944e-12
          ],
          [
            2.1229996617729394e-11,
            0.0012842530259007078,
            -3.4026681148295314e-12
          ],
          [
            1.7786585915960503e-11,
            0.0009295408735168944,
            -2.4486040984185242e-12
          ],
          [
            1.4254788498064127e-11,
            0.0006454674416698773,
            -1.6925291291733776e-12
          ],
          [
            1.0687834301999138e-11,
            0.0004237294559968079,
            -1.1060701642373645e-12
          ],
          [
            7.117661032535831e-12,
            0.00025248667412714176,
            -6.564800541495479e-13
          ],
          [
            3.555370553714552e-12,
            0.00011698447171588873,
            -3.032543137499078e-13
          ],
          [
            1.8152496335150728e-17,
            -1.5697013418514182e-17,
            9.214465144746562e-20
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391207624e-15,
            -1.1425691971946792e-15,
            6.0693648356153985e-18
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391370707e-15,
            -1.1431827706687159e-15,
            6.069364836391662e-18
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.948445293997736e-09,
            0.16117724539808975,
            -3.945733739740831e-10
          ],
          [
            1.7450938472052258e-09,
            0.12468135606508313,
            -3.0149671648160847e-10
          ],
          [
            1.5237194839201607e-09,
            0.0934794352069237,
            -2.2412621758505225e-10
          ],
          [
            1.2864288523317668e-09,
            0.06766030844830417,
            -1.6128415269989205e-10
          ],
          [
            1.0375984516031167e-09,
            0.0469829003123744,
            -1.1148315604003756e-10
          ],
          [
            7.819525027485952e-10,
            0.03084282413844286,
            -7.285438918813725e-11
          ],
          [
            5.227106525396152e-10,
            0.01837824106205732,
            -4.3240910851949366e-11
          ],
          [
            2.617053240783207e-10,
            0.008515177401518637,
            -1.9974688569845966e-11
          ],
          [
            1.3322676295501878e-15,
            -1.1657341758564144e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -33.759447021818616,
          -33.759973140253756,
          -33.76147323838537,
          -33.76405735255009,
          -33.76809947976342,
          -33.774236951854945,
          -33.78328408820313,
          -33.795736680319386,
          -33.811473310970754
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.509789092968448e-18,
            -1.2696303370481048e-18,
            -4.607232572373281e-20
          ],
          [
            -3.5553527237244965e-12,
            -0.00011698447171590977,
            3.0324947615570677e-13
          ],
          [
            -7.117648086212302e-12,
            -0.00025248667412716377,
            6.564734197346437e-13
          ],
          [
            -1.0687818130612809e-11,
            -0.00042372945599681775,
            1.1060707171052733e-12
          ],
          [
            -1.4254779882539216e-11,
            -0.0006454674416699281,
            1.6925493549243703e-12
          ],
          [
            -1.7786563110159268e-11,
            -0.0009295408735169186,
            2.4485886641894067e-12
          ],
          [
            -2.1229982197091442e-11,
            -0.0012842530259007195,
            3.4026600982448556e-12
          ],
          [
            -2.4534481473523503e-11,
            -0.001712915877653153,
            4.577313019758986e-12
          ],
          [
            -2.767807881926149e-11,
            -0.002214309111417371,
            5.990382532815037e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.673439493300946e-16,
            -9.241506497179098e-17,
            -3.0346824178076992e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.673439493300946e-16,
            -9.241506497179098e-17,
            -3.0346824178076992e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.948442500902743e-09,
          -0.16117724539809206,
          3.945733621545475e-10
        ],
        "actual_opposite_endpoint_branch_residual": 2.3133451639573847e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391207624e-15,
            -1.1425691971946792e-15,
            6.0693648356153985e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391370707e-15,
            -1.1431827706687159e-15,
            6.069364836391662e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.948445293997736e-09,
            0.16117724539808975,
            -3.945733739740831e-10
          ],
          [
            1.7450938472052258e-09,
            0.12468135606508313,
            -3.0149671648160847e-10
          ],
          [
            1.5237194839201607e-09,
            0.0934794352069237,
            -2.2412621758505225e-10
          ],
          [
            1.2864288523317668e-09,
            0.06766030844830417,
            -1.6128415269989205e-10
          ],
          [
            1.0375984516031167e-09,
            0.0469829003123744,
            -1.1148315604003756e-10
          ],
          [
            7.819525027485952e-10,
            0.03084282413844286,
            -7.285438918813725e-11
          ],
          [
            5.227106525396152e-10,
            0.01837824106205732,
            -4.3240910851949366e-11
          ],
          [
            2.617053240783207e-10,
            0.008515177401518637,
            -1.9974688569845966e-11
          ],
          [
            1.3322676295501878e-15,
            -1.1657341758564144e-15,
            0.0
          ],
          [
            -2.6170415834414484e-10,
            -0.008515177401520135,
            1.997435550293858e-11
          ],
          [
            -5.22709875383498e-10,
            -0.018378241062058986,
            4.3240411251588284e-11
          ],
          [
            -7.819512815032681e-10,
            -0.03084282413844358,
            7.285438918813725e-11
          ],
          [
            -1.037597341380092e-09,
            -0.04698290031237812,
            1.1148448830766711e-10
          ],
          [
            -1.2864275755752885e-09,
            -0.06766030844830595,
            1.6128309798801865e-10
          ],
          [
            -1.523718595741741e-09,
            -0.09347943520692459,
            2.2412571798469116e-10
          ],
          [
            -1.7450912936922691e-09,
            -0.1246813560650849,
            3.014974936377257e-10
          ],
          [
            -1.948444794397375e-09,
            -0.16117724539809236,
            3.9457326295178063e-10
          ]
        ]
      },
      "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": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808986,
              -3.945731861429673e-10
            ],
            "target_residual": 0.33882275460191014,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.0683772871353136,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5515587663996426,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0030815779851907,
              1.001169545736918,
              0.9801986733067553
            ],
            "cell_volume_ratio": 0.9843691518207252,
            "cell_rmsd_from_input_A": 0.10589313136781346
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.315946261085584e-10,
              0.3517549685000353,
              -1.36354663497288e-10
            ],
            "branch_aligned_reduced_polarization": [
              9.315946261085584e-10,
              0.3517549685000353,
              -1.36354663497288e-10
            ],
            "target_residual": 0.1482450314999647,
            "energy_eV": -33.79570326951742,
            "max_atomic_step_A": 0.05382129899316111,
            "max_log_strain_component": 0.01602105501725999,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.005556933318531,
              1.0021074002057881,
              0.9646199831789121
            ],
            "cell_volume_ratio": 0.9720244488124961,
            "cell_rmsd_from_input_A": 0.18786766974137534
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.455597911948391e-11,
              0.5052899499846404,
              3.561530258474858e-11
            ],
            "branch_aligned_reduced_polarization": [
              6.455597911948391e-11,
              0.5052899499846404,
              3.561530258474858e-11
            ],
            "target_residual": 0.005289949984640385,
            "energy_eV": -33.61519024606477,
            "max_atomic_step_A": 0.0019719412893610165,
            "max_log_strain_component": 0.0005928840650573339,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0054652201906202,
              1.0020726777928446,
              0.9651920605668004
            ],
            "cell_volume_ratio": 0.9724785132025001,
            "cell_rmsd_from_input_A": 0.18487815732859558
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.600161155548659e-13,
              0.49974942999982713,
              -2.928400977669287e-13
            ],
            "branch_aligned_reduced_polarization": [
              -1.600161155548659e-13,
              0.49974942999982713,
              -2.928400977669287e-13
            ],
            "target_residual": 0.00025057000017286724,
            "energy_eV": -33.624254777464174
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00025057000017286724,
        "parent_symmetrization_rmsd_A": 0.15223051976436952,
        "parent_cell_rmsd_A": 0.18487815732859558,
        "energy_eV": -33.624254777464174,
        "reduced_polarization": [
          -1.600161155548659e-13,
          0.49974942999982713,
          -2.928400977669287e-13
        ],
        "cartesian_polarization_e_A2": [
          -8.914664232556778e-13,
          0.006814289052447083,
          -5.336070642134181e-13
        ],
        "ranking_score": 0.6989511990968642
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484456825757945e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "target_residual": 0.5253361804460743,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008483043783944788,
            "step_scale": 0.491793005990829,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0095121484882204,
              0.998779001329102,
              0.998437992874839
            ],
            "cell_volume_ratio": 1.0067045956780614,
            "cell_rmsd_from_input_A": 0.05130029706463801
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24055540373057258,
              0.08107491793117813,
              0.00038582257926367296
            ],
            "branch_aligned_reduced_polarization": [
              0.2405554037305726,
              0.08107491793117813,
              0.00038582257926367296
            ],
            "target_residual": 0.2718175669636091,
            "energy_eV": -33.62587795849035,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007670155032964621,
            "step_scale": 0.8908568105893352,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0184215152059413,
              0.9976432180533736,
              0.9968348039244012
            ],
            "cell_volume_ratio": 1.0128054110771338,
            "cell_rmsd_from_input_A": 0.09975404088303763
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4517027857598542,
              0.015373692409524905,
              -0.0015227739495401057
            ],
            "branch_aligned_reduced_polarization": [
              0.4517027857598542,
              0.015373692409524905,
              -0.0015227739495401057
            ],
            "target_residual": 0.050707890531579265,
            "energy_eV": -33.1827568663378,
            "max_atomic_step_A": 0.02984377096678047,
            "max_log_strain_component": 0.002138554020798941,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0209402065955508,
              0.9973075062240586,
              0.9963873783385682
            ],
            "cell_volume_ratio": 1.0145129913842283,
            "cell_rmsd_from_input_A": 0.1136400194986906
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4972032778299829,
              0.0020382178336631456,
              -0.0003706210477729733
            ],
            "branch_aligned_reduced_polarization": [
              0.4972032778299829,
              0.0020382178336631456,
              -0.0003706210477729733
            ],
            "target_residual": 0.0034804233643020927,
            "energy_eV": -33.043069180709516,
            "max_atomic_step_A": 0.001972094431610193,
            "max_log_strain_component": 0.00029846357179750497,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0212496283383983,
              0.9972638523491065,
              0.996363313404493
            ],
            "cell_volume_ratio": 1.0147515356889558,
            "cell_rmsd_from_input_A": 0.11535012632670522
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4997970322451257,
              0.00022700929681048832,
              -1.6000637844901113e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4997970322451257,
              0.00022700929681048832,
              -1.6000637844901113e-05
            ],
            "target_residual": 0.0003049346663935389,
            "energy_eV": -33.03292098808316
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0003049346663935389,
        "parent_symmetrization_rmsd_A": 0.30913340825978997,
        "parent_cell_rmsd_A": 0.11535012632670522,
        "energy_eV": -33.03292098808316,
        "reduced_polarization": [
          0.4997970322451257,
          0.00022700929681048832,
          -1.6000637844901113e-05
        ],
        "cartesian_polarization_e_A2": [
          0.006499707628742081,
          -4.4114683199957435e-05,
          3.264482826011891e-07
        ],
        "ranking_score": 0.8385808091742533
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945732074406294e-10
            ],
            "target_residual": 0.5253361819250059,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00797137949100939,
            "step_scale": 0.4621299527046041,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0104787280723224,
              0.9995197973879287,
              0.9963419926075425
            ],
            "cell_volume_ratio": 1.0062989298819291,
            "cell_rmsd_from_input_A": 0.06399991241394602
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0007208303039409626,
              0.07894302104768318,
              -0.2257481950296834
            ],
            "branch_aligned_reduced_polarization": [
              -0.0007208303039409626,
              0.07894302104768318,
              -0.2257481950296834
            ],
            "target_residual": 0.28538845929353657,
            "energy_eV": -33.57255662683122,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0053024352166562,
            "step_scale": 0.7578293866403712,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0184402902822787,
              0.9992433237944944,
              0.9923992559215828
            ],
            "cell_volume_ratio": 1.0099346141001797,
            "cell_rmsd_from_input_A": 0.11726879504167445
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0004433017014095971,
              0.00912742565105924,
              -0.415157836575358
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004433017014095971,
              0.00912742565105924,
              -0.415157836575358
            ],
            "target_residual": 0.08533287238800619,
            "energy_eV": -33.00242305559986,
            "max_atomic_step_A": 0.06638935768820275,
            "max_log_strain_component": 0.0033713670135585424,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0205372147846035,
              0.9993233465530009,
              0.9892242688077729
            ],
            "cell_volume_ratio": 1.008857071243681,
            "cell_rmsd_from_input_A": 0.13952881503517206
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0004631642944348495,
              -0.006018558046850734,
              -0.4939787220349997
            ],
            "branch_aligned_reduced_polarization": [
              0.0004631642944348495,
              -0.006018558046850734,
              -0.4939787220349997
            ],
            "target_residual": 0.008526039552966496,
            "energy_eV": -32.63185813465861,
            "max_atomic_step_A": 0.006082515897660435,
            "max_log_strain_component": 0.0010008350795600205,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0202233180974913,
              0.9993833412289288,
              0.9886894616916535
            ],
            "cell_volume_ratio": 1.0080620293126177,
            "cell_rmsd_from_input_A": 0.14013001346073647
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              6.561672328125069e-05,
              -0.0008406647752613388,
              -0.5002146644152079
            ],
            "branch_aligned_reduced_polarization": [
              6.561672328125069e-05,
              -0.0008406647752613388,
              -0.5002146644152079
            ],
            "target_residual": 0.0008701170208057734,
            "energy_eV": -32.605006648595776
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0008701170208057734,
        "parent_symmetrization_rmsd_A": 0.38468455381480476,
        "parent_cell_rmsd_A": 0.14013001346073647,
        "energy_eV": -32.605006648595776,
        "reduced_polarization": [
          6.561672328125069e-05,
          -0.0008406647752613388,
          -0.5002146644152079
        ],
        "cartesian_polarization_e_A2": [
          0.0024366674169721014,
          0.00010301598641035214,
          -0.007522242504688807
        ],
        "ranking_score": 0.9214572912216004
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484456825757945e-09,
              0.16117724539808986,
              -3.945731861429673e-10
            ],
            "target_residual": 0.6039874643463891,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01566220417199768,
            "step_scale": 0.4319312987490466,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0024291574907924,
              1.001343803386548,
              0.9840225506491869
            ],
            "cell_volume_ratio": 0.9877384413899212,
            "cell_rmsd_from_input_A": 0.0854056675976474
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21113182314991133,
              0.3043005178414432,
              -0.0012498976440497795
            ],
            "branch_aligned_reduced_polarization": [
              0.2111318231499113,
              0.3043005178414432,
              -0.0012498976440497795
            ],
            "target_residual": 0.3489192931867512,
            "energy_eV": -33.694844144812194,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0183172102649816,
            "step_scale": 0.7278772791792846,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.005267555480269,
              1.0029002743696134,
              0.9656866285921463
            ],
            "cell_volume_ratio": 0.973588945801348,
            "cell_rmsd_from_input_A": 0.18197973733069714
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4065253708411836,
              0.43794003302079776,
              -0.001947208801918815
            ],
            "branch_aligned_reduced_polarization": [
              0.4065253708411836,
              0.43794003302079776,
              -0.001947208801918815
            ],
            "target_residual": 0.11221736683756302,
            "energy_eV": -32.95055986160837,
            "max_atomic_step_A": 0.06952073204557771,
            "max_log_strain_component": 0.012097625915149776,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0071402753100023,
              1.0039426978844714,
              0.9537578920420313
            ],
            "cell_volume_ratio": 0.9643552153364753,
            "cell_rmsd_from_input_A": 0.2440080421157756
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4971598727057916,
              0.5017222865596673,
              -0.0005323899807985513
            ],
            "branch_aligned_reduced_polarization": [
              0.4971598727057916,
              0.5017222865596673,
              -0.0005323899807985513
            ],
            "target_residual": 0.0033639312021165007,
            "energy_eV": -32.011253706389155,
            "max_atomic_step_A": 0.0018176339170871412,
            "max_log_strain_component": 6.873390894427107e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0071294213758575,
              1.003958297079025,
              0.9538049916296877
            ],
            "cell_volume_ratio": 0.9644074295654199,
            "cell_rmsd_from_input_A": 0.24376955928759347
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000244155872072,
              0.49999833850042713,
              -3.213338979135872e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000244155872072,
              0.49999833850042713,
              -3.213338979135872e-06
            ],
            "target_residual": 2.4682119578739426e-05,
            "energy_eV": -31.99779973120564
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.4682119578739426e-05,
        "parent_symmetrization_rmsd_A": 0.36302152829370127,
        "parent_cell_rmsd_A": 0.24376955928759347,
        "energy_eV": -31.99779973120564,
        "reduced_polarization": [
          0.5000244155872072,
          0.49999833850042713,
          -3.213338979135872e-06
        ],
        "cartesian_polarization_e_A2": [
          0.006812960777749942,
          0.006749583400605226,
          -1.1078709931042235e-05
        ],
        "ranking_score": 0.9240132823547571
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808986,
              -3.945732074406294e-10
            ],
            "target_residual": 0.603987465632734,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015427383020554778,
            "step_scale": 0.4254554185979378,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.00363318926008,
              1.0009192590296898,
              0.9834408146281569
            ],
            "cell_volume_ratio": 0.9879211626197713,
            "cell_rmsd_from_input_A": 0.09227184547656549
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.759799239498589e-05,
              0.2988373503702661,
              -0.20782109575704014
            ],
            "branch_aligned_reduced_polarization": [
              -7.759799239498589e-05,
              0.2988373503702661,
              -0.2078210957570401
            ],
            "target_residual": 0.3547321943552914,
            "energy_eV": -33.67646037178841,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.01719892160250827,
            "step_scale": 0.6714445581289841,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0076286231756013,
              1.0019452557396524,
              0.9653705472574294
            ],
            "cell_volume_ratio": 0.9746272137202181,
            "cell_rmsd_from_input_A": 0.19136205130757833
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0007036941105536909,
              0.41984798928025296,
              -0.38240612078815744
            ],
            "branch_aligned_reduced_polarization": [
              0.0007036941105536909,
              0.41984798928025296,
              -0.38240612078815744
            ],
            "target_residual": 0.14231359891419051,
            "energy_eV": -33.08268503557089,
            "max_atomic_step_A": 0.10378040838329912,
            "max_log_strain_component": 0.015906856133560618,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0116512656808105,
              1.0029014438041768,
              0.9486537084272291
            ],
            "cell_volume_ratio": 0.9624912599537662,
            "cell_rmsd_from_input_A": 0.2826531398871641
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0021560355499670976,
              0.48859573764356273,
              -0.48334551879120485
            ],
            "branch_aligned_reduced_polarization": [
              0.0021560355499670976,
              0.48859573764356273,
              -0.48334551879120485
            ],
            "target_residual": 0.020299690478460124,
            "energy_eV": -32.28890271648545,
            "max_atomic_step_A": 0.018510811854048882,
            "max_log_strain_component": 0.0033481028432943267,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0125487116709693,
              1.0031057028798949,
              0.9451239810958596
            ],
            "cell_volume_ratio": 0.9599561776083861,
            "cell_rmsd_from_input_A": 0.30195687057724896
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.00023702286194410386,
              0.49896276114042504,
              -0.49887557651401127
            ],
            "branch_aligned_reduced_polarization": [
              0.00023702286194410386,
              0.49896276114042504,
              -0.49887557651401127
            ],
            "target_residual": 0.0015480221137760277,
            "energy_eV": -32.129767088748274,
            "max_atomic_step_A": 0.0008298872944824358,
            "max_log_strain_component": 0.00022933256641555222,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.4643583721948765,
            "cell_principal_stretches": [
              1.0122976713654843,
              1.0028711946773337,
              0.9450203712034433
            ],
            "cell_volume_ratio": 0.959388626354347,
            "cell_rmsd_from_input_A": 0.30178170880646965
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -3.360520223118011e-07,
              0.49999960924117953,
              -0.5000004783087987
            ],
            "branch_aligned_reduced_polarization": [
              -3.360520223118011e-07,
              0.49999960924117953,
              -0.5000004783087987
            ],
            "target_residual": 7.031377705451161e-07,
            "energy_eV": -32.120192659998864
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 7.031377705451161e-07,
        "parent_symmetrization_rmsd_A": 0.44206940211684226,
        "parent_cell_rmsd_A": 0.30178170880646965,
        "energy_eV": -32.120192659998864,
        "reduced_polarization": [
          -3.360520223118011e-07,
          0.49999960924117953,
          -0.5000004783087987
        ],
        "cartesian_polarization_e_A2": [
          0.0025945520142395518,
          0.006934096647158574,
          -0.008092033207437037
        ],
        "ranking_score": 1.0175162355940008
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484456825757945e-09,
              0.16117724539808984,
              -3.945732074406294e-10
            ],
            "target_residual": 0.7252434777997643,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005121816705739122,
            "step_scale": 0.2969304040907615,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0071372689433509,
              0.9996518447343105,
              0.997274548837547
            ],
            "cell_volume_ratio": 1.0040426810120915,
            "cell_rmsd_from_input_A": 0.04048117779401526
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1453268586817746,
              0.10759488913184025,
              -0.14512933321639707
            ],
            "branch_aligned_reduced_polarization": [
              0.14532685868177464,
              0.10759488913184025,
              -0.1451293332163971
            ],
            "target_residual": 0.5131304780299741,
            "energy_eV": -33.60429832605631,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0034842250181828668,
            "step_scale": 0.34768473419634893,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0122420062034634,
              0.999466171863368,
              0.9945588051310786
            ],
            "cell_volume_ratio": 1.006196777151029,
            "cell_rmsd_from_input_A": 0.07107931490144273
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.2631754460633009,
              0.06452255838153316,
              -0.259824484093901
            ],
            "branch_aligned_reduced_polarization": [
              0.2631754460633009,
              0.06452255838153316,
              -0.259824484093901
            ],
            "target_residual": 0.34341419354501884,
            "energy_eV": -33.1545497712435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0036302528223270143,
            "step_scale": 0.40776714480067844,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0158756087309233,
              0.9994470395189645,
              0.9912957727805571
            ],
            "cell_volume_ratio": 1.0064763470450253,
            "cell_rmsd_from_input_A": 0.09641923624687013
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3586327044575638,
              0.03274421131096295,
              -0.35014244078132606
            ],
            "branch_aligned_reduced_polarization": [
              0.3586327044575638,
              0.03274421131096295,
              -0.35014244078132606
            ],
            "target_residual": 0.20860053614106044,
            "energy_eV": -32.4713363396293,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004453680184189167,
            "step_scale": 0.6190533079455606,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0190035668283848,
              0.9995916505046689,
              0.9865722654574283
            ],
            "cell_volume_ratio": 1.0049101352519703,
            "cell_rmsd_from_input_A": 0.12537588917827522
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4498415898328256,
              0.004963649733775288,
              -0.43585529419841257
            ],
            "branch_aligned_reduced_polarization": [
              0.4498415898328256,
              0.004963649733775288,
              -0.43585529419841257
            ],
            "target_residual": 0.08157847272136393,
            "energy_eV": -31.239630451714447,
            "max_atomic_step_A": 0.04669219574945584,
            "max_log_strain_component": 0.0160848026486047,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.519773926756798,
            "cell_principal_stretches": [
              1.0152382382219258,
              0.9862614995717225,
              0.9782643959854057
            ],
            "cell_volume_ratio": 0.9795267358903962,
            "cell_rmsd_from_input_A": 0.19044183808258378
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49980584371848125,
              0.0008843107147590977,
              -0.4975442366832474
            ],
            "branch_aligned_reduced_polarization": [
              0.49980584371848125,
              0.0008843107147590977,
              -0.4975442366832474
            ],
            "target_residual": 0.0026173413170235906,
            "energy_eV": -29.997997184737827
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0026173413170235906,
        "parent_symmetrization_rmsd_A": 0.5603722146804291,
        "parent_cell_rmsd_A": 0.19044183808258378,
        "energy_eV": -29.997997184737827,
        "reduced_polarization": [
          0.49980584371848125,
          0.0008843107147590977,
          -0.4975442366832474
        ],
        "cartesian_polarization_e_A2": [
          0.009022718997239616,
          0.00010117938211930491,
          -0.007606137218621744
        ],
        "ranking_score": 1.113217356835122
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9484457086423397e-09,
              0.16117724539808984,
              -3.945731861429673e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.9484456825757945e-09,
              0.16117724539808986,
              -3.945732074406294e-10
            ],
            "target_residual": 0.7840923776526637,
            "energy_eV": -33.81147331097075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010506539288341471,
            "step_scale": 0.2897486920314964,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.002683521813509,
              1.0006821970981172,
              0.9884294105000208
            ],
            "cell_volume_ratio": 0.9917579955683705,
            "cell_rmsd_from_input_A": 0.06280553031368083
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1416835915808781,
              0.2529139090807439,
              -0.1421997756091033
            ],
            "branch_aligned_reduced_polarization": [
              0.14168359158087807,
              0.2529139090807439,
              -0.1421997756091033
            ],
            "target_residual": 0.563438714894809,
            "energy_eV": -33.662473421861264,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011140957784463702,
            "step_scale": 0.33383631634882605,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0052973401172682,
              1.0013985183807803,
              0.9765464558986241
            ],
            "cell_volume_ratio": 0.9830925074577339,
            "cell_rmsd_from_input_A": 0.12650162209161073
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.25592020868601323,
              0.325699497444426,
              -0.2527317796017995
            ],
            "branch_aligned_reduced_polarization": [
              0.25592020868601323,
              0.325699497444426,
              -0.2527317796017995
            ],
            "target_residual": 0.3887122104306707,
            "energy_eV": -33.172241225667584,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012374956801720051,
            "step_scale": 0.36625643815398545,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.0081127210508642,
              1.0021774379713908,
              0.9636230821470514
            ],
            "cell_volume_ratio": 0.9735559392504066,
            "cell_rmsd_from_input_A": 0.1951289412666212
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.34548150323510063,
              0.3820523605904453,
              -0.33607086893029214
            ],
            "branch_aligned_reduced_polarization": [
              0.34548150323510063,
              0.3820523605904453,
              -0.33607086893029214
            ],
            "target_residual": 0.25428403704920216,
            "energy_eV": -32.35957019181207,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014528469181156354,
            "step_scale": 0.49367491893417836,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7439577331056895,
            "cell_principal_stretches": [
              1.011443638974818,
              1.003057849342733,
              0.9486872188980535
            ],
            "cell_volume_ratio": 0.9624777928595861,
            "cell_rmsd_from_input_A": 0.27392644832756663
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4268108328803734,
              0.432610475350937,
              -0.408215048348374
            ],
            "branch_aligned_reduced_polarization": [
              0.4268108328803734,
              0.432610475350937,
              -0.408215048348374
            ],
            "target_residual": 0.13536055395048668,
            "energy_eV": -31.012368550240062,
            "max_atomic_step_A": 0.056403845110787366,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8144918759878401,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.543259937477484,
            "cell_principal_stretches": [
              1.0103185438584281,
              0.9806482336574175,
              0.9380261563053583
            ],
            "cell_volume_ratio": 0.9293654503538915,
            "cell_rmsd_from_input_A": 0.3480332972120773
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4867817044144125,
              0.48352390268295414,
              -0.477830755060016
            ],
            "branch_aligned_reduced_polarization": [
              0.4867817044144125,
              0.48352390268295414,
              -0.477830755060016
            ],
            "target_residual": 0.03062124331567441,
            "energy_eV": -29.470854013288548
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.03062124331567441,
        "parent_symmetrization_rmsd_A": 0.568799678408126,
        "parent_cell_rmsd_A": 0.3480332972120773,
        "energy_eV": -29.470854013288548,
        "reduced_polarization": [
          0.4867817044144125,
          0.48352390268295414,
          -0.477830755060016
        ],
        "cartesian_polarization_e_A2": [
          0.009112586832905936,
          0.006646865231884676,
          -0.007775917403627452
        ],
        "ranking_score": 1.217050489342494
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13
        ],
        "endpoint_rmsd_A": 0.4660377676160072,
        "minimum_distance_A_by_image": [
          2.6386492006292546,
          2.634525427543708,
          2.630946262583744,
          2.6279139309856503,
          2.6254303275024466,
          2.6234970105389506,
          2.6221151972939873,
          2.621285759944808,
          2.621009222901521
        ],
        "minimum_distance_A": 2.621009222901521,
        "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": [
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863,
          602.4348712513863
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.3763556391207624e-15,
        -1.1425691971946792e-15,
        6.0693648356153985e-18
      ],
      "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": [
          -33.811473310970754,
          -33.79573668031943,
          -33.783284088203125,
          -33.77423695185496,
          -33.76809947976344,
          -33.764057352550026,
          -33.76147323838535,
          -33.75997314025375,
          -33.75944702181862
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.767808526938709e-11,
            0.0022143091114173357,
            -5.990383638550855e-12
          ],
          [
            2.453451100588429e-11,
            0.0017129158776531287,
            -4.5773008566649944e-12
          ],
          [
            2.1229996617729394e-11,
            0.0012842530259007078,
            -3.4026681148295314e-12
          ],
          [
            1.7786585915960503e-11,
            0.0009295408735168944,
            -2.4486040984185242e-12
          ],
          [
            1.4254788498064127e-11,
            0.0006454674416698773,
            -1.6925291291733776e-12
          ],
          [
            1.0687834301999138e-11,
            0.0004237294559968079,
            -1.1060701642373645e-12
          ],
          [
            7.117661032535831e-12,
            0.00025248667412714176,
            -6.564800541495479e-13
          ],
          [
            3.555370553714552e-12,
            0.00011698447171588873,
            -3.032543137499078e-13
          ],
          [
            1.8152496335150728e-17,
            -1.5697013418514182e-17,
            9.214465144746562e-20
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391207624e-15,
            -1.1425691971946792e-15,
            6.0693648356153985e-18
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391370707e-15,
            -1.1431827706687159e-15,
            6.069364836391662e-18
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.948445293997736e-09,
            0.16117724539808975,
            -3.945733739740831e-10
          ],
          [
            1.7450938472052258e-09,
            0.12468135606508313,
            -3.0149671648160847e-10
          ],
          [
            1.5237194839201607e-09,
            0.0934794352069237,
            -2.2412621758505225e-10
          ],
          [
            1.2864288523317668e-09,
            0.06766030844830417,
            -1.6128415269989205e-10
          ],
          [
            1.0375984516031167e-09,
            0.0469829003123744,
            -1.1148315604003756e-10
          ],
          [
            7.819525027485952e-10,
            0.03084282413844286,
            -7.285438918813725e-11
          ],
          [
            5.227106525396152e-10,
            0.01837824106205732,
            -4.3240910851949366e-11
          ],
          [
            2.617053240783207e-10,
            0.008515177401518637,
            -1.9974688569845966e-11
          ],
          [
            1.3322676295501878e-15,
            -1.1657341758564144e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -33.759447021818616,
          -33.759973140253756,
          -33.76147323838537,
          -33.76405735255009,
          -33.76809947976342,
          -33.774236951854945,
          -33.78328408820313,
          -33.795736680319386,
          -33.811473310970754
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.509789092968448e-18,
            -1.2696303370481048e-18,
            -4.607232572373281e-20
          ],
          [
            -3.5553527237244965e-12,
            -0.00011698447171590977,
            3.0324947615570677e-13
          ],
          [
            -7.117648086212302e-12,
            -0.00025248667412716377,
            6.564734197346437e-13
          ],
          [
            -1.0687818130612809e-11,
            -0.00042372945599681775,
            1.1060707171052733e-12
          ],
          [
            -1.4254779882539216e-11,
            -0.0006454674416699281,
            1.6925493549243703e-12
          ],
          [
            -1.7786563110159268e-11,
            -0.0009295408735169186,
            2.4485886641894067e-12
          ],
          [
            -2.1229982197091442e-11,
            -0.0012842530259007195,
            3.4026600982448556e-12
          ],
          [
            -2.4534481473523503e-11,
            -0.001712915877653153,
            4.577313019758986e-12
          ],
          [
            -2.767807881926149e-11,
            -0.002214309111417371,
            5.990382532815037e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.673439493300946e-16,
            -9.241506497179098e-17,
            -3.0346824178076992e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.673439493300946e-16,
            -9.241506497179098e-17,
            -3.0346824178076992e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.948442500902743e-09,
          -0.16117724539809206,
          3.945733621545475e-10
        ],
        "actual_opposite_endpoint_branch_residual": 2.3133451639573847e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391207624e-15,
            -1.1425691971946792e-15,
            6.0693648356153985e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.948445253614021e-09,
            0.16117724539808978,
            -3.9457335001581786e-10
          ],
          [
            1.7450938385101507e-09,
            0.12468135606508313,
            -3.0149670572375765e-10
          ],
          [
            1.5237195185222699e-09,
            0.09347943520692374,
            -2.2412623933132387e-10
          ],
          [
            1.2864289059286443e-09,
            0.06766030844830416,
            -1.6128414810661148e-10
          ],
          [
            1.0375984749466966e-09,
            0.0469829003123744,
            -1.114831584741123e-10
          ],
          [
            7.819525143575393e-10,
            0.030842824138442877,
            -7.285440071769082e-11
          ],
          [
            5.227106748204407e-10,
            0.018378241062057373,
            -4.324089237246496e-11
          ],
          [
            2.617053789683274e-10,
            0.00851517740151863,
            -1.99746923908191e-11
          ],
          [
            1.3763556391370707e-15,
            -1.1431827706687159e-15,
            6.069364836391662e-18
          ],
          [
            -2.6170414776517545e-10,
            -0.008515177401520161,
            1.997437374916523e-11
          ],
          [
            -5.227098573065769e-10,
            -0.018378241062058976,
            4.32404553781968e-11
          ],
          [
            -7.819512766829289e-10,
            -0.030842824138443595,
            7.285443713387984e-11
          ],
          [
            -1.0375973274021546e-09,
            -0.0469829003123781,
            1.1148449069969372e-10
          ],
          [
            -1.2864275576026037e-09,
            -0.06766030844830592,
            1.6128313148800152e-10
          ],
          [
            -1.523718623258685e-09,
            -0.0934794352069246,
            2.2412571129658317e-10
          ],
          [
            -1.7450913050844054e-09,
            -0.12468135606508492,
            3.0149750687991595e-10
          ],
          [
            -1.948444792437327e-09,
            -0.16117724539809236,
            3.9457327718343977e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.948445293997736e-09,
            0.16117724539808975,
            -3.945733739740831e-10
          ],
          [
            1.7450938472052258e-09,
            0.12468135606508313,
            -3.0149671648160847e-10
          ],
          [
            1.5237194839201607e-09,
            0.0934794352069237,
            -2.2412621758505225e-10
          ],
          [
            1.2864288523317668e-09,
            0.06766030844830417,
            -1.6128415269989205e-10
          ],
          [
            1.0375984516031167e-09,
            0.0469829003123744,
            -1.1148315604003756e-10
          ],
          [
            7.819525027485952e-10,
            0.03084282413844286,
            -7.285438918813725e-11
          ],
          [
            5.227106525396152e-10,
            0.01837824106205732,
            -4.3240910851949366e-11
          ],
          [
            2.617053240783207e-10,
            0.008515177401518637,
            -1.9974688569845966e-11
          ],
          [
            1.3322676295501878e-15,
            -1.1657341758564144e-15,
            0.0
          ],
          [
            -2.6170415834414484e-10,
            -0.008515177401520135,
            1.997435550293858e-11
          ],
          [
            -5.22709875383498e-10,
            -0.018378241062058986,
            4.3240411251588284e-11
          ],
          [
            -7.819512815032681e-10,
            -0.03084282413844358,
            7.285438918813725e-11
          ],
          [
            -1.037597341380092e-09,
            -0.04698290031237812,
            1.1148448830766711e-10
          ],
          [
            -1.2864275755752885e-09,
            -0.06766030844830595,
            1.6128309798801865e-10
          ],
          [
            -1.523718595741741e-09,
            -0.09347943520692459,
            2.2412571798469116e-10
          ],
          [
            -1.7450912936922691e-09,
            -0.1246813560650849,
            3.014974936377257e-10
          ],
          [
            -1.948444794397375e-09,
            -0.16117724539809236,
            3.9457326295178063e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0883704498843022e-15,
        "parent_symmetrization_rmsd_A": 0.4660377676160072,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -33.759447021818616,
        "reduced_polarization": [
          8.395783440227537e-16,
          -6.922479215266003e-16,
          -2.1242776924653898e-17
        ],
        "cartesian_polarization_e_A2": [
          1.1195575150867073e-17,
          -9.510342953250587e-18,
          -3.2250628006612964e-19
        ],
        "ranking_score": 0.46603776761600935
      }
    }
  ],
  "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": 102,
      "full_response": 33,
      "energy_polarization": 69
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 127,
      "full_response": 58,
      "energy_polarization": 69
    },
    "elapsed_seconds": 145.08162600098876
  }
}
