{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "I12Nb4O4",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -96.71296985473887,
  "input_cartesian_polarization_e_A2": [
    -1.2103112736759395e-11,
    -0.008216994005225195,
    -1.2533408086788608e-11
  ],
  "input_reduced_polarization": [
    -8.915846353326514e-10,
    -1.44535070124465,
    -7.81272327223504e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.0,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.5275950522564593e-15,
      "parent_symmetrization_rmsd_A": 0.17112779756284915,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -96.46591765836084,
      "reduced_polarization": [
        -1.7579352343684831e-15,
        -1.736331882002197e-15,
        -5.324960614876578e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.394453158052349e-17,
        -9.871257303301665e-18,
        -8.542463633584218e-18
      ],
      "ranking_score": 0.1711277975628542
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.000260423136262622,
      "parent_symmetrization_rmsd_A": 0.004081853063077074,
      "parent_cell_rmsd_A": 0.00030596556950105233,
      "energy_eV": -96.72367783015163,
      "reduced_polarization": [
        -2.743715882606181e-12,
        -1.4997395768637374,
        -2.719056428808615e-12
      ],
      "cartesian_polarization_e_A2": [
        1.6840061610648553e-13,
        -0.008526700841522263,
        5.5726446431221716e-14
      ],
      "ranking_score": 0.5046791907279776
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.499999999999996,
      "parent_symmetrization_rmsd_A": 0.1711278200850755,
      "parent_cell_rmsd_A": 0.00030596556950105233,
      "energy_eV": -96.46662233171965,
      "reduced_polarization": [
        1.2640429584405192e-16,
        3.962303737014042e-15,
        -3.3448002178071487e-15
      ],
      "cartesian_polarization_e_A2": [
        3.6280722220348273e-17,
        2.2527496859862918e-17,
        -5.366208794723549e-17
      ],
      "ranking_score": 1.1712043114774429
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.0340848776889686e-05,
      "parent_symmetrization_rmsd_A": 0.03216539778759161,
      "parent_cell_rmsd_A": 0.002418095399482027,
      "energy_eV": -96.58050126948638,
      "reduced_polarization": [
        -1.0403361783682474e-14,
        -0.9999796591512231,
        -8.510549914396702e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.9577651515251965e-14,
        -0.005682375225698696,
        3.9175913909474974e-14
      ],
      "ranking_score": 0.532810603335016
    },
    {
      "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,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.002155993481299921,
      "parent_symmetrization_rmsd_A": 0.5070050484771766,
      "parent_cell_rmsd_A": 0.2138252886227357,
      "energy_eV": -85.39633701528327,
      "reduced_polarization": [
        -0.49819769700986044,
        -1.500505144897029,
        0.0010699721754079859
      ],
      "cartesian_polarization_e_A2": [
        -0.01144330238030416,
        -0.009037786582844464,
        0.00011127356973070863
      ],
      "ranking_score": 1.0647733575954605
    },
    {
      "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,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.1345773066759102e-05,
      "parent_symmetrization_rmsd_A": 0.3790348579458738,
      "parent_cell_rmsd_A": 0.11701919273448252,
      "energy_eV": -91.20019961825352,
      "reduced_polarization": [
        3.770670405238782e-06,
        -1.4999986111835486,
        -0.499989389637139
      ],
      "cartesian_polarization_e_A2": [
        0.00515093744039822,
        -0.008745738365356921,
        -0.008157684726184014
      ],
      "ranking_score": 0.908312347675628
    },
    {
      "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,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0009472859465721941,
      "parent_symmetrization_rmsd_A": 0.4857382231559869,
      "parent_cell_rmsd_A": 0.17570256589923286,
      "energy_eV": -86.4958609680801,
      "reduced_polarization": [
        -0.49920466169626476,
        -1.0002462531225844,
        0.00045182634584777865
      ],
      "cartesian_polarization_e_A2": [
        -0.011339684593378628,
        -0.0060766164831209234,
        5.728350255637649e-05
      ],
      "ranking_score": 1.0315584365239396
    },
    {
      "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,
        -1.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.4952924186098877e-06,
      "parent_symmetrization_rmsd_A": 0.3556447690348753,
      "parent_cell_rmsd_A": 0.1030686280563759,
      "energy_eV": -91.82207177035158,
      "reduced_polarization": [
        6.475407573777391e-07,
        -1.0000014874148055,
        -0.49999810401149314
      ],
      "cartesian_polarization_e_A2": [
        0.00508396665427167,
        -0.005863705846128143,
        -0.00809703050708732
      ],
      "ranking_score": 0.8814169166338065
    },
    {
      "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,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 6.912639303847747e-06,
      "parent_symmetrization_rmsd_A": 0.3768543047722219,
      "parent_cell_rmsd_A": 0.06483913883335778,
      "energy_eV": -92.05266170694428,
      "reduced_polarization": [
        -0.49999562099116557,
        -1.4999994343183884,
        -0.49999468127194835
      ],
      "cartesian_polarization_e_A2": [
        -0.00628794569460986,
        -0.008698041159881471,
        -0.008107656398505676
      ],
      "ranking_score": 0.8930779147591691
    },
    {
      "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,
        -1.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.0158990588393532e-06,
      "parent_symmetrization_rmsd_A": 0.36016740788494295,
      "parent_cell_rmsd_A": 0.058157321170034255,
      "energy_eV": -92.40249679629885,
      "reduced_polarization": [
        -0.4999994653473158,
        -1.0000004492146584,
        -0.4999992621628935
      ],
      "cartesian_polarization_e_A2": [
        -0.006236912630487132,
        -0.005830493016151451,
        -0.008071764149441763
      ],
      "ranking_score": 0.8747087699755692
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "target_residual": 0.054649298755349976,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.003485452855711213,
            "max_log_strain_component": 4.41421259709343e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              0.9999923316326799,
              0.9999558588482788,
              0.9999490892824492
            ],
            "cell_volume_ratio": 0.9998972827395405,
            "cell_rmsd_from_input_A": 0.00030596556950105233
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.743715882606181e-12,
              -1.4997395768637374,
              -2.719056428808615e-12
            ],
            "branch_aligned_reduced_polarization": [
              -2.743715882606181e-12,
              -1.4997395768637374,
              -2.719056428808615e-12
            ],
            "target_residual": 0.000260423136262622,
            "energy_eV": -96.72367783015163
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.000260423136262622,
        "parent_symmetrization_rmsd_A": 0.004081853063077074,
        "parent_cell_rmsd_A": 0.00030596556950105233,
        "energy_eV": -96.72367783015163,
        "reduced_polarization": [
          -2.743715882606181e-12,
          -1.4997395768637374,
          -2.719056428808615e-12
        ],
        "cartesian_polarization_e_A2": [
          1.6840061610648553e-13,
          -0.008526700841522263,
          5.5726446431221716e-14
        ],
        "ranking_score": 0.5046791907279776
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "target_residual": 0.44535070124465004,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.02840381997159712,
            "max_log_strain_component": 0.00035972514201128373,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.000414980717041,
              1.0003597898508594,
              1.0000624936210731
            ],
            "cell_volume_ratio": 1.0008374619223723,
            "cell_rmsd_from_input_A": 0.0024943471239190014
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.83406635555339e-12,
              -0.9845195538432032,
              1.633937986644923e-11
            ],
            "branch_aligned_reduced_polarization": [
              7.83406635555339e-12,
              -0.9845195538432032,
              1.633937986644923e-11
            ],
            "target_residual": 0.015480446156796779,
            "energy_eV": -96.57522997550451,
            "max_atomic_step_A": 0.0009268324566398909,
            "max_log_strain_component": 1.0993084298768061e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0004022964896437,
              1.0003487928718058,
              1.0000605837783225
            ],
            "cell_volume_ratio": 1.0008118589702524,
            "cell_rmsd_from_input_A": 0.002418095399482027
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0403361783682474e-14,
              -0.9999796591512231,
              -8.510549914396702e-15
            ],
            "branch_aligned_reduced_polarization": [
              -1.0403361783682474e-14,
              -0.9999796591512231,
              -8.510549914396702e-15
            ],
            "target_residual": 2.0340848776889686e-05,
            "energy_eV": -96.58050126948638
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.5275950522564593e-15,
        "parent_symmetrization_rmsd_A": 0.17112779756284915,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -96.46591765836084,
        "reduced_polarization": [
          -1.7579352343684831e-15,
          -1.736331882002197e-15,
          -5.324960614876578e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.394453158052349e-17,
          -9.871257303301665e-18,
          -8.542463633584218e-18
        ],
        "ranking_score": 0.1711277975628542
      },
      "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": [
          -96.71296985473889,
          -96.68381836384405,
          -96.64490566521206,
          -96.60161766782757,
          -96.55886286897878,
          -96.52090757823352,
          -96.4912249486373,
          -96.47237474631864,
          -96.46591765836088
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2103113400347874e-11,
            -0.008216994005225166,
            -1.2533397825927942e-11
          ],
          [
            -1.015958021678854e-11,
            -0.007256475574408959,
            -1.0828388423703857e-11
          ],
          [
            -8.374558398438069e-12,
            -0.006268974562382791,
            -9.167609045734443e-12
          ],
          [
            -6.73706651668065e-12,
            -0.005258231117914438,
            -7.551751017507063e-12
          ],
          [
            -5.229080002962344e-12,
            -0.004228385525303436,
            -5.979269802170936e-12
          ],
          [
            -3.8276205685417705e-12,
            -0.003183684693087375,
            -4.4458512426485284e-12
          ],
          [
            -2.506959387571739e-12,
            -0.0021282286082586724,
            -2.944570119664908e-12
          ],
          [
            -1.2400905086549956e-12,
            -0.0010658224225606966,
            -1.466344452344158e-12
          ],
          [
            6.086195829376813e-18,
            1.211544850462179e-19,
            -3.454621814949768e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.916838043619391e-16,
            2.1310800495793528e-17,
            -2.1534449419929853e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.9168380436769045e-16,
            2.7755575615628914e-17,
            -2.1534449419980747e-15
          ]
        ],
        "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": [
          [
            -8.915843618950703e-10,
            -0.44535070124464493,
            -7.81271713989895e-10
          ],
          [
            -7.569977977794906e-10,
            -0.27639767698105144,
            -6.749896197533189e-10
          ],
          [
            -6.307414035511272e-10,
            -0.10269847757744821,
            -5.714645978649457e-10
          ],
          [
            -5.123428903353044e-10,
            0.07508901323875439,
            -4.707397804892821e-10
          ],
          [
            -4.009522713843694e-10,
            0.25623652880314385,
            -3.727188557789418e-10
          ],
          [
            -2.954205213789862e-10,
            0.43999704748846447,
            -2.7713292771736064e-10
          ],
          [
            -1.9440260512482155e-10,
            -0.37435060916431767,
            -1.8355034159256434e-10
          ],
          [
            -9.643613685383912e-11,
            -0.18747575875931977,
            -9.140482815084283e-11
          ],
          [
            -6.661338147750939e-16,
            0.0,
            -2.1649348980190553e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -96.46591765836088,
          -96.47237474631866,
          -96.49122494863732,
          -96.5209075782335,
          -96.55886286897876,
          -96.60161766782757,
          -96.64490566521204,
          -96.683818363844,
          -96.7129698547389
        ],
        "cartesian_polarizations_e_A2": [
          [
            9.161482737467132e-19,
            1.0751144242182218e-18,
            -3.5620835313838423e-17
          ],
          [
            1.2400565418387274e-12,
            0.001065822422560695,
            1.4662954805048116e-12
          ],
          [
            2.506947499928868e-12,
            0.0021282286082586837,
            2.944578399664441e-12
          ],
          [
            3.827596642215368e-12,
            0.0031836846930873752,
            4.445834043821746e-12
          ],
          [
            5.229034230213727e-12,
            0.004228385525303388,
            5.9792695446589885e-12
          ],
          [
            6.737001103693904e-12,
            0.005258231117914433,
            7.551802034585529e-12
          ],
          [
            8.374548887828556e-12,
            0.006268974562382791,
            9.167592446118153e-12
          ],
          [
            1.0159586961620696e-11,
            0.0072564755744088634,
            1.0828375142029963e-11
          ],
          [
            1.2103145299640337e-11,
            0.008216994005225096,
            1.253329789148381e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.531120820250866e-16,
            1.8911020088050538e-16,
            -2.220431403061288e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.531120820250866e-16,
            1.8911020088050538e-16,
            -2.220431403061288e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.91582995305543e-10,
          1.445350701244645,
          7.812673807209596e-10
        ],
        "actual_opposite_endpoint_branch_residual": 1.2362875153224023e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.916838043619391e-16,
            2.1310800495793528e-17,
            -2.1534449419929853e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.9168380436769045e-16,
            2.7755575615628914e-17,
            -2.1534449419980747e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-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": [
          [
            -8.915843618950703e-10,
            -0.44535070124464493,
            -7.81271713989895e-10
          ],
          [
            -7.569977977794906e-10,
            -0.27639767698105144,
            -6.749896197533189e-10
          ],
          [
            -6.307414035511272e-10,
            -0.10269847757744821,
            -5.714645978649457e-10
          ],
          [
            -5.123428903353044e-10,
            0.07508901323875439,
            -4.707397804892821e-10
          ],
          [
            -4.009522713843694e-10,
            0.25623652880314385,
            -3.727188557789418e-10
          ],
          [
            -2.954205213789862e-10,
            0.43999704748846447,
            -2.7713292771736064e-10
          ],
          [
            -1.9440260512482155e-10,
            -0.37435060916431767,
            -1.8355034159256434e-10
          ],
          [
            -9.643613685383912e-11,
            -0.18747575875931977,
            -9.140482815084283e-11
          ],
          [
            -6.661338147750939e-16,
            0.0,
            -2.1649348980190553e-15
          ],
          [
            9.643330578512632e-11,
            0.18747575875931943,
            9.140177503752511e-11
          ],
          [
            1.9440227205791416e-10,
            0.3743506091643196,
            1.8355084119292542e-10
          ],
          [
            2.954189115556005e-10,
            -0.43999704748846424,
            2.7713187300548725e-10
          ],
          [
            4.0095027298292507e-10,
            -0.2562365288031523,
            3.727188557789418e-10
          ],
          [
            5.123413915342212e-10,
            -0.07508901323875539,
            4.707430001360535e-10
          ],
          [
            6.307405708838587e-10,
            0.10269847757744821,
            5.714635431530724e-10
          ],
          [
            7.569977977794906e-10,
            0.27639767698103457,
            6.749887315748992e-10
          ],
          [
            8.915830296274407e-10,
            0.4453507012446327,
            7.812654967409571e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846394508264e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "target_residual": 0.5029776783942473,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00705222673349411,
            "step_scale": 0.33509547262292383,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0071134067397425,
              0.999984372955428,
              0.9929181746051869
            ],
            "cell_volume_ratio": 0.9999655786895675,
            "cell_rmsd_from_input_A": 0.03889843702336366
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.16445151392677743,
              -1.4427848213669532,
              0.000346642627317384
            ],
            "branch_aligned_reduced_polarization": [
              -0.16445151392677743,
              -1.4427848213669532,
              0.000346642627317384
            ],
            "target_residual": 0.3403916616680764,
            "energy_eV": -96.03161680430307,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006951309455714025,
            "step_scale": 0.4516879257215099,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.014065772606196,
              0.9997864221412388,
              0.9858763571905063
            ],
            "cell_volume_ratio": 0.9995299467789719,
            "cell_rmsd_from_input_A": 0.07730017444748058
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3046083237931893,
              -1.4630445157451142,
              0.0018004594952880694
            ],
            "branch_aligned_reduced_polarization": [
              -0.3046083237931893,
              -1.4630445157451142,
              0.0018004594952880694
            ],
            "target_residual": 0.19886391478047102,
            "energy_eV": -94.1191055683691,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007974383190971287,
            "step_scale": 0.6504158062673278,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0219276989483528,
              0.9993082779878404,
              0.9777245425233351
            ],
            "cell_volume_ratio": 0.9984726483575604,
            "cell_rmsd_from_input_A": 0.12117214287126755
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4058263365375686,
              -1.5017833174914788,
              0.006919261143511568
            ],
            "branch_aligned_reduced_polarization": [
              -0.4058263365375686,
              -1.5017833174914788,
              0.006919261143511568
            ],
            "target_residual": 0.09444435020679008,
            "energy_eV": -90.92014622012643,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011877244238690365,
            "step_scale": 0.9646964305127189,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0334583588716908,
              0.9983222543881756,
              0.9655935054521854
            ],
            "cell_volume_ratio": 0.9962264559957414,
            "cell_rmsd_from_input_A": 0.18519259129654733
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.46271592103662273,
              -1.5513681012599931,
              0.010457203383931524
            ],
            "branch_aligned_reduced_polarization": [
              -0.46271592103662273,
              -1.5513681012599931,
              0.010457203383931524
            ],
            "target_residual": 0.06432835668519109,
            "energy_eV": -86.51299897418832,
            "max_atomic_step_A": 0.011996100341372041,
            "max_log_strain_component": 0.009538145808468212,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 7.244305023447555,
            "cell_principal_stretches": [
              1.0307867019904629,
              0.9919149043369313,
              0.9655822268454638
            ],
            "cell_volume_ratio": 0.9872621480512898,
            "cell_rmsd_from_input_A": 0.2138252886227357
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49819769700986044,
              -1.500505144897029,
              0.0010699721754079859
            ],
            "branch_aligned_reduced_polarization": [
              -0.49819769700986044,
              -1.500505144897029,
              0.0010699721754079859
            ],
            "target_residual": 0.002155993481299921,
            "energy_eV": -85.39633701528327
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.002155993481299921,
        "parent_symmetrization_rmsd_A": 0.5070050484771766,
        "parent_cell_rmsd_A": 0.2138252886227357,
        "energy_eV": -85.39633701528327,
        "reduced_polarization": [
          -0.49819769700986044,
          -1.500505144897029,
          0.0010699721754079859
        ],
        "cartesian_polarization_e_A2": [
          -0.01144330238030416,
          -0.009037786582844464,
          0.00011127356973070863
        ],
        "ranking_score": 1.0647733575954605
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.812723246125586e-10
            ],
            "target_residual": 0.5029776785039065,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004822448753413999,
            "step_scale": 0.4424347955728056,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0065130448709734,
              0.9999791732630835,
              0.9935046390311746
            ],
            "cell_volume_ratio": 0.9999545531005567,
            "cell_rmsd_from_input_A": 0.03490601196110965
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0012253440955745146,
              -1.4457362151144564,
              -0.21593379781455965
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012253440955745146,
              -1.4457362151144564,
              -0.21593379781455968
            ],
            "target_residual": 0.2892052334282984,
            "energy_eV": -96.1006621040298,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004575348333484401,
            "step_scale": 0.6303399360324856,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0125841693431863,
              0.9997486627087304,
              0.9872793352079615
            ],
            "cell_volume_ratio": 0.9994521628001959,
            "cell_rmsd_from_input_A": 0.06795809503242832
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0009345822891572018,
              -1.4739515279140258,
              -0.3774023558233265
            ],
            "branch_aligned_reduced_polarization": [
              -0.0009345822891572018,
              -1.4739515279140258,
              -0.3774023558233265
            ],
            "target_residual": 0.1253378582062867,
            "energy_eV": -94.48288783651117,
            "max_atomic_step_A": 0.11113963126876092,
            "max_log_strain_component": 0.004937031149521225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.019094490176234,
              0.999286858013711,
              0.9804360817778839
            ],
            "cell_volume_ratio": 0.9984444680958686,
            "cell_rmsd_from_input_A": 0.10384415898979928
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0011628825474507111,
              -1.5125997827982962,
              -0.47549987599597116
            ],
            "branch_aligned_reduced_polarization": [
              0.0011628825474507111,
              -1.5125997827982962,
              -0.47549987599597116
            ],
            "target_residual": 0.027574678576480216,
            "energy_eV": -92.06228395322385,
            "max_atomic_step_A": 0.030197319584628905,
            "max_log_strain_component": 0.00185849743723399,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.021616269869579,
              0.999073622992378,
              0.9777644084073247
            ],
            "cell_volume_ratio": 0.9979746697097266,
            "cell_rmsd_from_input_A": 0.11769664838123958
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -2.6325311194720732e-05,
              -1.5124818858476887,
              -0.4967235742690396
            ],
            "branch_aligned_reduced_polarization": [
              -2.6325311194720732e-05,
              -1.5124818858476887,
              -0.4967235742690396
            ],
            "target_residual": 0.012904771710775852,
            "energy_eV": -91.28216880866545,
            "max_atomic_step_A": 0.00191257758829083,
            "max_log_strain_component": 0.0005313268296918812,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.954114652493591,
            "cell_principal_stretches": [
              1.0213306339002668,
              0.9987836758321833,
              0.9777887799739083
            ],
            "cell_volume_ratio": 0.9974309576510288,
            "cell_rmsd_from_input_A": 0.11701919273448252
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              3.770670405238782e-06,
              -1.4999986111835486,
              -0.499989389637139
            ],
            "branch_aligned_reduced_polarization": [
              3.770670405238782e-06,
              -1.4999986111835486,
              -0.499989389637139
            ],
            "target_residual": 1.1345773066759102e-05,
            "energy_eV": -91.20019961825352
          }
        ],
        "iterations": 5
      },
      "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,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.1345773066759102e-05,
        "parent_symmetrization_rmsd_A": 0.3790348579458738,
        "parent_cell_rmsd_A": 0.11701919273448252,
        "energy_eV": -91.20019961825352,
        "reduced_polarization": [
          3.770670405238782e-06,
          -1.4999986111835486,
          -0.499989389637139
        ],
        "cartesian_polarization_e_A2": [
          0.00515093744039822,
          -0.008745738365356921,
          -0.008157684726184014
        ],
        "ranking_score": 0.908312347675628
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846394508264e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "target_residual": 0.6695799027804799,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.007005754165720055,
            "step_scale": 0.3328872693177503,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0071526053694002,
              1.0001265187241153,
              0.9930492749761938
            ],
            "cell_volume_ratio": 1.0002787025282476,
            "cell_rmsd_from_input_A": 0.03866724102415279
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1648795716201173,
              -1.2779885364259105,
              0.0005154043761701061
            ],
            "branch_aligned_reduced_polarization": [
              -0.1648795716201173,
              -1.2779885364259105,
              0.0005154043761701061
            ],
            "target_residual": 0.4354119813962482,
            "energy_eV": -95.98885500987363,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0068702660601406935,
            "step_scale": 0.4634314334955286,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0141170397583428,
              1.000086048470793,
              0.9861814461925711
            ],
            "cell_volume_ratio": 1.0001894662463802,
            "cell_rmsd_from_input_A": 0.07664142529212446
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.31091178667680003,
              -1.1532187392355349,
              0.0019798427530678237
            ],
            "branch_aligned_reduced_polarization": [
              -0.31091178667680003,
              -1.1532187392355349,
              0.0019798427530678237
            ],
            "target_residual": 0.24338088307838332,
            "energy_eV": -93.99034404208973,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007687315633309998,
            "step_scale": 0.7115397036103095,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0218217771471045,
              0.9998331195933254,
              0.9784466361257269
            ],
            "cell_volume_ratio": 0.9996312338593184,
            "cell_rmsd_from_input_A": 0.1189541223614989
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4206085727025706,
              -1.07097406837831,
              0.007751019882858963
            ],
            "branch_aligned_reduced_polarization": [
              -0.4206085727025706,
              -1.07097406837831,
              0.007751019882858963
            ],
            "target_residual": 0.10677263422673673,
            "energy_eV": -90.67482154317332,
            "max_atomic_step_A": 0.0987721034370986,
            "max_log_strain_component": 0.00902644634287725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0307132590924015,
              0.9993105894557033,
              0.9693659015934799
            ],
            "cell_volume_ratio": 0.9984494712137191,
            "cell_rmsd_from_input_A": 0.1674568031413995
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.47629474777999736,
              -1.048264643649223,
              0.008234907099660415
            ],
            "branch_aligned_reduced_polarization": [
              -0.47629474777999736,
              -1.048264643649223,
              0.008234907099660415
            ],
            "target_residual": 0.05439879138676198,
            "energy_eV": -87.22040846957823,
            "max_atomic_step_A": 0.010274644053336165,
            "max_log_strain_component": 0.005597912098566308,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 7.029931482146273,
            "cell_principal_stretches": [
              1.0292793901535333,
              0.9956557096771468,
              0.969193962312442
            ],
            "cell_volume_ratio": 0.9932376308183513,
            "cell_rmsd_from_input_A": 0.17570256589923286
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49920466169626476,
              -1.0002462531225844,
              0.00045182634584777865
            ],
            "branch_aligned_reduced_polarization": [
              -0.49920466169626476,
              -1.0002462531225844,
              0.00045182634584777865
            ],
            "target_residual": 0.0009472859465721941,
            "energy_eV": -86.4958609680801
          }
        ],
        "iterations": 5
      },
      "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,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0009472859465721941,
        "parent_symmetrization_rmsd_A": 0.4857382231559869,
        "parent_cell_rmsd_A": 0.17570256589923286,
        "energy_eV": -86.4958609680801,
        "reduced_polarization": [
          -0.49920466169626476,
          -1.0002462531225844,
          0.00045182634584777865
        ],
        "cartesian_polarization_e_A2": [
          -0.011339684593378628,
          -0.0060766164831209234,
          5.728350255637649e-05
        ],
        "ranking_score": 1.0315584365239396
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.812723246125586e-10
            ],
            "target_residual": 0.6695799028628542,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004752141975701285,
            "step_scale": 0.4359845125993462,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0065299027124086,
              1.000167264023223,
              0.9937089146908042
            ],
            "cell_volume_ratio": 1.0003650343257364,
            "cell_rmsd_from_input_A": 0.03443184414159617
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0012962099868474902,
              -1.2302237443072779,
              -0.21619634105022334
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012962099868474902,
              -1.2302237443072779,
              -0.21619634105022334
            ],
            "target_residual": 0.36544379791764703,
            "energy_eV": -96.05190589730347,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.004527011138412916,
            "step_scale": 0.6585451899960889,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0126437816299778,
              1.0001346649123806,
              0.9876708940565833
            ],
            "cell_volume_ratio": 1.0002934754590294,
            "cell_rmsd_from_input_A": 0.06712328081451456
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00039349137337064006,
              -1.0845266235380862,
              -0.3876995637668796
            ],
            "branch_aligned_reduced_polarization": [
              -0.00039349137337064006,
              -1.0845266235380862,
              -0.3876995637668796
            ],
            "target_residual": 0.1405570805771072,
            "energy_eV": -94.33638695466308,
            "max_atomic_step_A": 0.0943016057108452,
            "max_log_strain_component": 0.003982225951952774,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0180299536898734,
              0.9999511095197071,
              0.9822325542260636
            ],
            "cell_volume_ratio": 0.9998932740388957,
            "cell_rmsd_from_input_A": 0.09617075208264346
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0014826524104552352,
              -1.0194856502204328,
              -0.4825325833629449
            ],
            "branch_aligned_reduced_polarization": [
              0.0014826524104552352,
              -1.0194856502204328,
              -0.4825325833629449
            ],
            "target_residual": 0.026210674669984186,
            "energy_eV": -92.29898351875163,
            "max_atomic_step_A": 0.018619708059356636,
            "max_log_strain_component": 0.0009816914347815064,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0193874870892075,
              0.9998867786859006,
              0.9808492960297617
            ],
            "cell_volume_ratio": 0.9997522930072672,
            "cell_rmsd_from_input_A": 0.10343420164467655
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              1.5457334483005051e-06,
              -1.0068875974968923,
              -0.49869432663898716
            ],
            "branch_aligned_reduced_polarization": [
              1.5457334483005051e-06,
              -1.0068875974968923,
              -0.49869432663898716
            ],
            "target_residual": 0.007010262804927298,
            "energy_eV": -91.85331335965569,
            "max_atomic_step_A": 0.0008566172433382592,
            "max_log_strain_component": 0.0001802588808158394,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.6592279351123365,
            "cell_principal_stretches": [
              1.0192959656413265,
              0.9997846693496906,
              0.9808569301287816
            ],
            "cell_volume_ratio": 0.9995682277178498,
            "cell_rmsd_from_input_A": 0.1030686280563759
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              6.475407573777391e-07,
              -1.0000014874148055,
              -0.49999810401149314
            ],
            "branch_aligned_reduced_polarization": [
              6.475407573777391e-07,
              -1.0000014874148055,
              -0.49999810401149314
            ],
            "target_residual": 2.4952924186098877e-06,
            "energy_eV": -91.82207177035158
          }
        ],
        "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.4952924186098877e-06,
        "parent_symmetrization_rmsd_A": 0.3556447690348753,
        "parent_cell_rmsd_A": 0.1030686280563759,
        "energy_eV": -91.82207177035158,
        "reduced_polarization": [
          6.475407573777391e-07,
          -1.0000014874148055,
          -0.49999810401149314
        ],
        "cartesian_polarization_e_A2": [
          0.00508396665427167,
          -0.005863705846128143,
          -0.00809703050708732
        ],
        "ranking_score": 0.8814169166338065
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846394508264e-10,
              -1.44535070124465,
              -7.812723246125586e-10
            ],
            "target_residual": 0.7092154427122936,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004129995517968376,
            "step_scale": 0.40707137529576576,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0051252297175333,
              0.9999927897097569,
              0.9948664763103771
            ],
            "cell_volume_ratio": 0.9999581854990057,
            "cell_rmsd_from_input_A": 0.020195488696877692
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.19937329712912133,
              -1.4408444408176846,
              -0.19955959429847317
            ],
            "branch_aligned_reduced_polarization": [
              -0.19937329712912133,
              -1.4408444408176846,
              -0.19955959429847314
            ],
            "target_residual": 0.42911563947179326,
            "energy_eV": -96.14829391107132,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037009544847271293,
            "step_scale": 0.5641468751323302,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0096060628656955,
              0.9999188369500547,
              0.9900954971709398
            ],
            "cell_volume_ratio": 0.9995252856542775,
            "cell_rmsd_from_input_A": 0.03830950441232059
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3593306384201991,
              -1.4641568308281545,
              -0.3590611416814547
            ],
            "branch_aligned_reduced_polarization": [
              -0.3593306384201991,
              -1.4641568308281545,
              -0.3590611416814547
            ],
            "target_residual": 0.20232736801452564,
            "energy_eV": -94.78531190097925,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004046774554945829,
            "step_scale": 0.9856668372635233,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0142844941611788,
              0.9997647038512931,
              0.9848061373643884
            ],
            "cell_volume_ratio": 0.9986385637735421,
            "cell_rmsd_from_input_A": 0.0581054881843721
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4778199546997059,
              -1.5010522252972287,
              -0.48033007046491055
            ],
            "branch_aligned_reduced_polarization": [
              -0.4778199546997059,
              -1.5010522252972287,
              -0.48033007046491055
            ],
            "target_residual": 0.029664249788501493,
            "energy_eV": -92.69007346115103,
            "max_atomic_step_A": 0.026212391619974754,
            "max_log_strain_component": 0.0014092729146735232,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.015727621203014,
              0.9996965144618294,
              0.983142933388727
            ],
            "cell_volume_ratio": 0.9983023707262213,
            "cell_rmsd_from_input_A": 0.06492651754684495
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4979370481321732,
              -1.5062169729463617,
              -0.4984957679235688
            ],
            "branch_aligned_reduced_polarization": [
              -0.4979370481321732,
              -1.5062169729463617,
              -0.4984957679235688
            ],
            "target_residual": 0.006720806288275819,
            "energy_eV": -92.1037858394157,
            "max_atomic_step_A": 0.0014742887149914099,
            "max_log_strain_component": 0.0002788244697187809,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.583830939611621,
            "cell_principal_stretches": [
              1.015606748412897,
              0.9995921287377643,
              0.9831758109042487
            ],
            "cell_volume_ratio": 0.9981127208226287,
            "cell_rmsd_from_input_A": 0.06483913883335778
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49999562099116557,
              -1.4999994343183884,
              -0.49999468127194835
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999562099116557,
              -1.4999994343183884,
              -0.49999468127194835
            ],
            "target_residual": 6.912639303847747e-06,
            "energy_eV": -92.05266170694428
          }
        ],
        "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,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 6.912639303847747e-06,
        "parent_symmetrization_rmsd_A": 0.3768543047722219,
        "parent_cell_rmsd_A": 0.06483913883335778,
        "energy_eV": -92.05266170694428,
        "reduced_polarization": [
          -0.49999562099116557,
          -1.4999994343183884,
          -0.49999468127194835
        ],
        "cartesian_polarization_e_A2": [
          -0.00628794569460986,
          -0.008698041159881471,
          -0.008107656398505676
        ],
        "ranking_score": 0.8930779147591691
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.915846353326514e-10,
              -1.44535070124465,
              -7.81272327223504e-10
            ],
            "branch_aligned_reduced_polarization": [
              -8.915846394508264e-10,
              -1.44535070124465,
              -7.812723246125586e-10
            ],
            "target_residual": 0.8356657498224064,
            "energy_eV": -96.71296985473887,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004058127714763043,
            "step_scale": 0.3999877525149857,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0051925107888136,
              1.000057748419547,
              0.9951100065496414
            ],
            "cell_volume_ratio": 1.000334890417842,
            "cell_rmsd_from_input_A": 0.019883180718120022
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1981842252441126,
              -1.244631242414899,
              -0.19849855436878305
            ],
            "branch_aligned_reduced_polarization": [
              -0.1981842252441126,
              -1.244631242414899,
              -0.19849855436878305
            ],
            "target_residual": 0.4917726389040644,
            "energy_eV": -96.11024051567142,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003685499773899548,
            "step_scale": 0.5835094421321191,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0098276338940169,
              1.0000544375804543,
              0.9905294768210178
            ],
            "cell_volume_ratio": 1.0003184898344848,
            "cell_rmsd_from_input_A": 0.037926450191857516
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3668693648175299,
              -1.1044088683929725,
              -0.36565045739099317
            ],
            "branch_aligned_reduced_polarization": [
              -0.3668693648175299,
              -1.1044088683929725,
              -0.36565045739099317
            ],
            "target_residual": 0.2160434618831089,
            "energy_eV": -94.66514736099818,
            "max_atomic_step_A": 0.10862615790302871,
            "max_log_strain_component": 0.003445488797769523,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.0140973885133662,
              1.0000088249499963,
              0.9861411732060921
            ],
            "cell_volume_ratio": 1.0000520137849376,
            "cell_rmsd_from_input_A": 0.05479320219395843
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4851197605181153,
              -1.0131370711404897,
              -0.485810252648929
            ],
            "branch_aligned_reduced_polarization": [
              -0.4851197605181153,
              -1.0131370711404897,
              -0.485810252648929
            ],
            "target_residual": 0.024399858505240422,
            "energy_eV": -92.7538020003061,
            "max_atomic_step_A": 0.015971439395219843,
            "max_log_strain_component": 0.0007162855420187346,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1328386183962753,
            "cell_principal_stretches": [
              1.014900893949459,
              0.9999934677851761,
              0.9852868513451499
            ],
            "cell_volume_ratio": 0.9999619742177402,
            "cell_rmsd_from_input_A": 0.05826205808608304
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49924208330821235,
              -1.0036750827130554,
              -0.4994327108772084
            ],
            "branch_aligned_reduced_polarization": [
              -0.49924208330821235,
              -1.0036750827130554,
              -0.4994327108772084
            ],
            "target_residual": 0.003795060949224207,
            "energy_eV": -92.42034312246349,
            "max_atomic_step_A": 0.0005729293483561324,
            "max_log_strain_component": 8.693789194891507e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.42087772198535,
            "cell_principal_stretches": [
              1.0148678087464644,
              0.9999539817749843,
              0.9853006183032766
            ],
            "cell_volume_ratio": 0.9999038635354253,
            "cell_rmsd_from_input_A": 0.058157321170034255
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999994653473158,
              -1.0000004492146584,
              -0.4999992621628935
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999994653473158,
              -1.0000004492146584,
              -0.4999992621628935
            ],
            "target_residual": 1.0158990588393532e-06,
            "energy_eV": -92.40249679629885
          }
        ],
        "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.0158990588393532e-06,
        "parent_symmetrization_rmsd_A": 0.36016740788494295,
        "parent_cell_rmsd_A": 0.058157321170034255,
        "energy_eV": -92.40249679629885,
        "reduced_polarization": [
          -0.4999994653473158,
          -1.0000004492146584,
          -0.4999992621628935
        ],
        "cartesian_polarization_e_A2": [
          -0.006236912630487132,
          -0.005830493016151451,
          -0.008071764149441763
        ],
        "ranking_score": 0.8747087699755692
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19
        ],
        "endpoint_rmsd_A": 0.17112779756284915,
        "minimum_distance_A_by_image": [
          1.8379750539230821,
          1.8573883421839057,
          1.87680205619891,
          1.896216182891312,
          1.915630709714166,
          1.9350456246238126,
          1.9544609160549056,
          1.9738765728969139,
          1.9932925844719867
        ],
        "minimum_distance_A": 1.8379750539230821,
        "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": [
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576,
          700.5936751771576
        ],
        "cell_deformation_log_strain_norm": 4.965068306494545e-16
      },
      "parent_reduced_polarization": [
        -6.916838043619391e-16,
        2.1310800495793528e-17,
        -2.1534449419929853e-15
      ],
      "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": [
          -96.71296985473889,
          -96.68381836384405,
          -96.64490566521206,
          -96.60161766782757,
          -96.55886286897878,
          -96.52090757823352,
          -96.4912249486373,
          -96.47237474631864,
          -96.46591765836088
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2103113400347874e-11,
            -0.008216994005225166,
            -1.2533397825927942e-11
          ],
          [
            -1.015958021678854e-11,
            -0.007256475574408959,
            -1.0828388423703857e-11
          ],
          [
            -8.374558398438069e-12,
            -0.006268974562382791,
            -9.167609045734443e-12
          ],
          [
            -6.73706651668065e-12,
            -0.005258231117914438,
            -7.551751017507063e-12
          ],
          [
            -5.229080002962344e-12,
            -0.004228385525303436,
            -5.979269802170936e-12
          ],
          [
            -3.8276205685417705e-12,
            -0.003183684693087375,
            -4.4458512426485284e-12
          ],
          [
            -2.506959387571739e-12,
            -0.0021282286082586724,
            -2.944570119664908e-12
          ],
          [
            -1.2400905086549956e-12,
            -0.0010658224225606966,
            -1.466344452344158e-12
          ],
          [
            6.086195829376813e-18,
            1.211544850462179e-19,
            -3.454621814949768e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.916838043619391e-16,
            2.1310800495793528e-17,
            -2.1534449419929853e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.9168380436769045e-16,
            2.7755575615628914e-17,
            -2.1534449419980747e-15
          ]
        ],
        "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": [
          [
            -8.915843618950703e-10,
            -0.44535070124464493,
            -7.81271713989895e-10
          ],
          [
            -7.569977977794906e-10,
            -0.27639767698105144,
            -6.749896197533189e-10
          ],
          [
            -6.307414035511272e-10,
            -0.10269847757744821,
            -5.714645978649457e-10
          ],
          [
            -5.123428903353044e-10,
            0.07508901323875439,
            -4.707397804892821e-10
          ],
          [
            -4.009522713843694e-10,
            0.25623652880314385,
            -3.727188557789418e-10
          ],
          [
            -2.954205213789862e-10,
            0.43999704748846447,
            -2.7713292771736064e-10
          ],
          [
            -1.9440260512482155e-10,
            -0.37435060916431767,
            -1.8355034159256434e-10
          ],
          [
            -9.643613685383912e-11,
            -0.18747575875931977,
            -9.140482815084283e-11
          ],
          [
            -6.661338147750939e-16,
            0.0,
            -2.1649348980190553e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -96.46591765836088,
          -96.47237474631866,
          -96.49122494863732,
          -96.5209075782335,
          -96.55886286897876,
          -96.60161766782757,
          -96.64490566521204,
          -96.683818363844,
          -96.7129698547389
        ],
        "cartesian_polarizations_e_A2": [
          [
            9.161482737467132e-19,
            1.0751144242182218e-18,
            -3.5620835313838423e-17
          ],
          [
            1.2400565418387274e-12,
            0.001065822422560695,
            1.4662954805048116e-12
          ],
          [
            2.506947499928868e-12,
            0.0021282286082586837,
            2.944578399664441e-12
          ],
          [
            3.827596642215368e-12,
            0.0031836846930873752,
            4.445834043821746e-12
          ],
          [
            5.229034230213727e-12,
            0.004228385525303388,
            5.9792695446589885e-12
          ],
          [
            6.737001103693904e-12,
            0.005258231117914433,
            7.551802034585529e-12
          ],
          [
            8.374548887828556e-12,
            0.006268974562382791,
            9.167592446118153e-12
          ],
          [
            1.0159586961620696e-11,
            0.0072564755744088634,
            1.0828375142029963e-11
          ],
          [
            1.2103145299640337e-11,
            0.008216994005225096,
            1.253329789148381e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.531120820250866e-16,
            1.8911020088050538e-16,
            -2.220431403061288e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.531120820250866e-16,
            1.8911020088050538e-16,
            -2.220431403061288e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.91582995305543e-10,
          1.445350701244645,
          7.812673807209596e-10
        ],
        "actual_opposite_endpoint_branch_residual": 1.2362875153224023e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.916838043619391e-16,
            2.1310800495793528e-17,
            -2.1534449419929853e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.915843786731518e-10,
            -1.445350701244645,
            -7.812716876108435e-10
          ],
          [
            -7.569978249158383e-10,
            -1.2763976769810514,
            -6.74989602716886e-10
          ],
          [
            -6.307414310980726e-10,
            -1.1026984775774482,
            -5.714646063304551e-10
          ],
          [
            -5.12342907093176e-10,
            -0.9249109867612456,
            -4.707397924148724e-10
          ],
          [
            -4.009522768590362e-10,
            -0.7437634711968562,
            -3.727188820238935e-10
          ],
          [
            -2.9542051500603296e-10,
            -0.5600029525115355,
            -2.771329514038572e-10
          ],
          [
            -1.9440259747191253e-10,
            -0.37435060916431767,
            -1.8355031573882832e-10
          ],
          [
            -9.643613767801815e-11,
            -0.18747575875931974,
            -9.140484806441273e-11
          ],
          [
            -6.9168380436769045e-16,
            2.7755575615628914e-17,
            -2.1534449419980747e-15
          ],
          [
            9.6433250422651e-11,
            0.18747575875931943,
            9.140179539568691e-11
          ],
          [
            1.944022964034321e-10,
            0.37435060916431967,
            1.8355083187414123e-10
          ],
          [
            2.9541896395010384e-10,
            0.5600029525115356,
            2.771318793117867e-10
          ],
          [
            4.009502206537279e-10,
            0.7437634711968478,
            3.7271886597183836e-10
          ],
          [
            5.123414026880379e-10,
            0.9249109867612446,
            4.707429725739597e-10
          ],
          [
            6.307405420852224e-10,
            1.1026984775774482,
            5.714635715902823e-10
          ],
          [
            7.569977561770887e-10,
            1.2763976769810346,
            6.749887748012703e-10
          ],
          [
            8.915830176272205e-10,
            1.4453507012446327,
            7.812654581786575e-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": [
          [
            -8.915843618950703e-10,
            -0.44535070124464493,
            -7.81271713989895e-10
          ],
          [
            -7.569977977794906e-10,
            -0.27639767698105144,
            -6.749896197533189e-10
          ],
          [
            -6.307414035511272e-10,
            -0.10269847757744821,
            -5.714645978649457e-10
          ],
          [
            -5.123428903353044e-10,
            0.07508901323875439,
            -4.707397804892821e-10
          ],
          [
            -4.009522713843694e-10,
            0.25623652880314385,
            -3.727188557789418e-10
          ],
          [
            -2.954205213789862e-10,
            0.43999704748846447,
            -2.7713292771736064e-10
          ],
          [
            -1.9440260512482155e-10,
            -0.37435060916431767,
            -1.8355034159256434e-10
          ],
          [
            -9.643613685383912e-11,
            -0.18747575875931977,
            -9.140482815084283e-11
          ],
          [
            -6.661338147750939e-16,
            0.0,
            -2.1649348980190553e-15
          ],
          [
            9.643330578512632e-11,
            0.18747575875931943,
            9.140177503752511e-11
          ],
          [
            1.9440227205791416e-10,
            0.3743506091643196,
            1.8355084119292542e-10
          ],
          [
            2.954189115556005e-10,
            -0.43999704748846424,
            2.7713187300548725e-10
          ],
          [
            4.0095027298292507e-10,
            -0.2562365288031523,
            3.727188557789418e-10
          ],
          [
            5.123413915342212e-10,
            -0.07508901323875539,
            4.707430001360535e-10
          ],
          [
            6.307405708838587e-10,
            0.10269847757744821,
            5.714635431530724e-10
          ],
          [
            7.569977977794906e-10,
            0.27639767698103457,
            6.749887315748992e-10
          ],
          [
            8.915830296274407e-10,
            0.4453507012446327,
            7.812654967409571e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.5275950522564593e-15,
        "parent_symmetrization_rmsd_A": 0.17112779756284915,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -96.46591765836084,
        "reduced_polarization": [
          -1.7579352343684831e-15,
          -1.736331882002197e-15,
          -5.324960614876578e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.394453158052349e-17,
          -9.871257303301665e-18,
          -8.542463633584218e-18
        ],
        "ranking_score": 0.1711277975628542
      }
    }
  ],
  "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": 138,
      "full_response": 34,
      "energy_polarization": 104
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 163,
      "full_response": 59,
      "energy_polarization": 104
    },
    "elapsed_seconds": 327.7081814329722
  }
}