{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "Bi4In4O12",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -109.85065564448125,
  "input_cartesian_polarization_e_A2": [
    -1.4428366618226837e-10,
    2.2219108403402718e-11,
    0.011490412417128277
  ],
  "input_reduced_polarization": [
    -6.953135683895109e-09,
    1.1322586893748243e-09,
    0.3963608196623807
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.9319139521006995e-15,
      "parent_symmetrization_rmsd_A": 0.24098244859993384,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -108.44465634491078,
      "reduced_polarization": [
        2.428789798074673e-15,
        6.536160708014429e-16,
        -1.5066139423492713e-15
      ],
      "cartesian_polarization_e_A2": [
        5.039951935124521e-17,
        1.2826367744072812e-17,
        -4.367640466011411e-17
      ],
      "ranking_score": 0.2409824485999397
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006604475277688376,
      "parent_symmetrization_rmsd_A": 0.021156039548743146,
      "parent_cell_rmsd_A": 0.03822328531601882,
      "energy_eV": -109.83548111354699,
      "reduced_polarization": [
        2.4370867079229348e-11,
        -8.951848719885247e-12,
        0.5006604475277688
      ],
      "cartesian_polarization_e_A2": [
        -1.1241267209638757e-12,
        1.2225016582471114e-13,
        0.014500239904928564
      ],
      "ranking_score": 0.5320327559332856
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999917,
      "parent_symmetrization_rmsd_A": 0.24100384921233517,
      "parent_cell_rmsd_A": 0.03822328531601882,
      "energy_eV": -108.53857705326978,
      "reduced_polarization": [
        2.4022087149278053e-15,
        2.6862625864010792e-15,
        8.219842404782444e-16
      ],
      "cartesian_polarization_e_A2": [
        5.010380301219464e-17,
        5.297782612952894e-17,
        2.380649148858579e-17
      ],
      "ranking_score": 1.2505596705413382
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.5376420306936274e-05,
      "parent_symmetrization_rmsd_A": 0.08250789898910753,
      "parent_cell_rmsd_A": 0.15815664381121808,
      "energy_eV": -109.35933642220002,
      "reduced_polarization": [
        6.690692498754158e-14,
        -1.5077943516195943e-13,
        2.5376420306936274e-05
      ],
      "cartesian_polarization_e_A2": [
        1.236829375829499e-15,
        -2.9043009121322292e-15,
        7.384776443676016e-07
      ],
      "ranking_score": 0.622097812782526
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 9.431009360518545e-05,
      "parent_symmetrization_rmsd_A": 0.06839477305620317,
      "parent_cell_rmsd_A": 0.07123508966139282,
      "energy_eV": -109.64143883313503,
      "reduced_polarization": [
        -0.5000924590928137,
        7.196742374510774e-13,
        0.5000185932759856
      ],
      "cartesian_polarization_e_A2": [
        -0.010297331006041726,
        6.125195850084948e-13,
        0.014390736484318588
      ],
      "ranking_score": 0.5863921656587617
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.3957360646015613e-05,
      "parent_symmetrization_rmsd_A": 0.0676257819216866,
      "parent_cell_rmsd_A": 0.058805679417319255,
      "energy_eV": -109.64291211324074,
      "reduced_polarization": [
        -2.2203436884001391e-13,
        0.5000237578705758,
        0.5000030852414532
      ],
      "cartesian_polarization_e_A2": [
        -1.4841137872173367e-12,
        0.009759547468349223,
        0.01441376831796259
      ],
      "ranking_score": 0.5823751164973084
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.612369102973426e-05,
      "parent_symmetrization_rmsd_A": 0.10843715369235628,
      "parent_cell_rmsd_A": 0.17894983861929836,
      "energy_eV": -109.14493550828632,
      "reduced_polarization": [
        -0.5000047979792234,
        1.1412561423108822e-13,
        7.597233530280978e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.010154889104765422,
        -7.470869824981328e-13,
        -9.33425508129848e-05
      ],
      "ranking_score": 0.6533268607292403
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 7.233236417538273e-05,
      "parent_symmetrization_rmsd_A": 0.10629377552879586,
      "parent_cell_rmsd_A": 0.16924914878354724,
      "energy_eV": -109.15973951690891,
      "reduced_polarization": [
        -5.060458934839325e-13,
        0.4999682668633416,
        6.499983803841706e-05
      ],
      "cartesian_polarization_e_A2": [
        1.2643449241119023e-12,
        0.00961233681318796,
        -6.789374107716274e-05
      ],
      "ranking_score": 0.6487507274530334
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00013534309856173533,
      "parent_symmetrization_rmsd_A": 0.09480664574551213,
      "parent_cell_rmsd_A": 0.08502202115375238,
      "energy_eV": -109.42907713947763,
      "reduced_polarization": [
        -0.500096425665218,
        0.5000701163827823,
        0.5000640588657493
      ],
      "cartesian_polarization_e_A2": [
        -0.010295063912016787,
        0.009755789832461758,
        0.014322750405992212
      ],
      "ranking_score": 0.6163328372310737
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0001581637197146872,
      "parent_symmetrization_rmsd_A": 0.12836098418654027,
      "parent_cell_rmsd_A": 0.18979867615088009,
      "energy_eV": -108.92251734695506,
      "reduced_polarization": [
        -0.5000071828006728,
        0.4999370758318584,
        0.0001449300475131766
      ],
      "cartesian_polarization_e_A2": [
        -0.010150278224123762,
        0.009603032574544429,
        -0.00016345486365220362
      ],
      "ranking_score": 0.6761269806636897
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "target_residual": 0.10363918033761955,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.01628010258800175,
            "max_log_strain_component": 0.005527571562494591,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0005433021450894,
              1.0004078835823536,
              0.9944876773517688
            ],
            "cell_volume_ratio": 0.9954338402190561,
            "cell_rmsd_from_input_A": 0.03822328531601882
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.4370867079229348e-11,
              -8.951848719885247e-12,
              0.5006604475277688
            ],
            "branch_aligned_reduced_polarization": [
              2.4370867079229348e-11,
              -8.951848719885247e-12,
              0.5006604475277688
            ],
            "target_residual": 0.0006604475277688376,
            "energy_eV": -109.83548111354699
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006604475277688376,
        "parent_symmetrization_rmsd_A": 0.021156039548743146,
        "parent_cell_rmsd_A": 0.03822328531601882,
        "energy_eV": -109.83548111354699,
        "reduced_polarization": [
          2.4370867079229348e-11,
          -8.951848719885247e-12,
          0.5006604475277688
        ],
        "cartesian_polarization_e_A2": [
          -1.1241267209638757e-12,
          1.2225016582471114e-13,
          0.014500239904928564
        ],
        "ranking_score": 0.5320327559332856
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "target_residual": 0.3963608196623808,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.058905081105710994,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9460822042956737,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0202013400267558,
              0.9985255741832203,
              0.9980366740281557
            ],
            "cell_volume_ratio": 1.0166970943022264,
            "cell_rmsd_from_input_A": 0.14187084218893248
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.6214752324383113e-10,
              -1.9935806432825154e-11,
              0.03604492800682293
            ],
            "branch_aligned_reduced_polarization": [
              -4.6214752324383113e-10,
              -1.9935806432825154e-11,
              0.03604492800682293
            ],
            "target_residual": 0.036044928006822935,
            "energy_eV": -109.43711038425032,
            "max_atomic_step_A": 0.006066767298520782,
            "max_log_strain_component": 0.0021827017646490034,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0224305672760166,
              0.998364794221634,
              0.9978226397051881
            ],
            "cell_volume_ratio": 1.0185361234776882,
            "cell_rmsd_from_input_A": 0.15769885861650448
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.5593067961214264e-12,
              -4.878679340781351e-12,
              0.0010167716405075958
            ],
            "branch_aligned_reduced_polarization": [
              -1.5593067961214264e-12,
              -4.878679340781351e-12,
              0.0010167716405075958
            ],
            "target_residual": 0.0010167716405075958,
            "energy_eV": -109.36156999386647,
            "max_atomic_step_A": 0.0001727990549802727,
            "max_log_strain_component": 6.298806865234276e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0224949702310684,
              0.9983601548428047,
              0.9978164638173844
            ],
            "cell_volume_ratio": 1.018589243249939,
            "cell_rmsd_from_input_A": 0.15815664381121808
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              6.690692498754158e-14,
              -1.5077943516195943e-13,
              2.5376420306936274e-05
            ],
            "branch_aligned_reduced_polarization": [
              6.690692498754158e-14,
              -1.5077943516195943e-13,
              2.5376420306936274e-05
            ],
            "target_residual": 2.5376420306936274e-05,
            "energy_eV": -109.35933642220002
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9319139521006995e-15,
        "parent_symmetrization_rmsd_A": 0.24098244859993384,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -108.44465634491078,
        "reduced_polarization": [
          2.428789798074673e-15,
          6.536160708014429e-16,
          -1.5066139423492713e-15
        ],
        "cartesian_polarization_e_A2": [
          5.039951935124521e-17,
          1.2826367744072812e-17,
          -4.367640466011411e-17
        ],
        "ranking_score": 0.2409824485999397
      },
      "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": [
          -109.85065564448124,
          -109.7684107673474,
          -109.61230850030225,
          -109.40317121577753,
          -109.1570191090513,
          -108.89863127410985,
          -108.66625764770667,
          -108.50342342985596,
          -108.44465634491077
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4428367357292635e-10,
            2.22191269515702e-11,
            0.011490412417128289
          ],
          [
            -1.2384304505094955e-10,
            2.2033240268700083e-11,
            0.008376649805592556
          ],
          [
            -1.031777291777252e-10,
            2.0455856042980562e-11,
            0.005635406468205777
          ],
          [
            -8.3211170216774e-11,
            1.771256423956773e-11,
            0.0033698656491153948
          ],
          [
            -6.455088755048072e-11,
            1.4364547890692587e-11,
            0.0016343845612674358
          ],
          [
            -4.735628386792969e-11,
            1.0963551550386833e-11,
            0.00043533294464925853
          ],
          [
            -3.1283432980192584e-11,
            7.637328380430066e-12,
            -0.000221867142148708
          ],
          [
            -1.5660466654988843e-11,
            4.036021617988925e-12,
            -0.0003197569828918777
          ],
          [
            6.532388033226673e-17,
            7.24284483392067e-17,
            -1.0680692842647991e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.148005698545224e-15,
            3.6908654704364e-15,
            -3.684296103561537e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.1480056985325614e-15,
            3.69086547043875e-15,
            -3.677613769070831e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.953136066911725e-09,
            1.1322596193963363e-09,
            0.3963608196623811
          ],
          [
            -5.968087135599376e-09,
            1.122787085527932e-09,
            0.2889518376224809
          ],
          [
            -4.972210421172463e-09,
            1.0424054952551387e-09,
            0.19439287692921348
          ],
          [
            -4.010007326193943e-09,
            9.026106528864375e-10,
            0.1162432349986352
          ],
          [
            -3.1107545983566354e-09,
            7.319999051347281e-10,
            0.05637795936565726
          ],
          [
            -2.2821340373013754e-09,
            5.586892060094328e-10,
            0.01501677368081289
          ],
          [
            -1.507571567582744e-09,
            3.8918890332695355e-10,
            -0.00765328859624953
          ],
          [
            -7.546893665555388e-10,
            2.056707026909521e-10,
            -0.011029990502592402
          ],
          [
            3.1086244689504383e-15,
            3.6637359812630166e-15,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -108.44465634491074,
          -108.50342342985596,
          -108.66625764770664,
          -108.89863127410986,
          -109.15701910905128,
          -109.40317121577753,
          -109.61230850030223,
          -109.76841076734739,
          -109.85065564448124
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.745640569370906e-17,
            5.2163740936861175e-17,
            -1.0203876197886921e-17
          ],
          [
            1.5660434612910315e-11,
            -4.03607642806224e-12,
            0.0003197569828917263
          ],
          [
            3.128331271511436e-11,
            -7.637313003093273e-12,
            0.00022186714214844118
          ],
          [
            4.735612558864446e-11,
            -1.0963565556875773e-11,
            -0.0004353329446492996
          ],
          [
            6.455095692730254e-11,
            -1.4364511962558404e-11,
            -0.0016343845612675342
          ],
          [
            8.321131578889565e-11,
            -1.7712551937698294e-11,
            -0.0033698656491154434
          ],
          [
            1.0317751775722491e-10,
            -2.0455865579313458e-11,
            -0.00563540646820595
          ],
          [
            1.238429084906625e-10,
            -2.203328666295962e-11,
            -0.008376649805592662
          ],
          [
            1.442838645618334e-10,
            -2.2219069304437848e-11,
            -0.011490412417128257
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.7688663260926972e-15,
            2.6582006745605145e-15,
            -3.519818598938254e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814341
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.056377959365660625
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.7688663260926972e-15,
            2.6582006745605145e-15,
            -3.519818598938254e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814343
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.05637795936566063
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.953142336067734e-09,
          -1.1322522528358967e-09,
          -0.3963608196623818
        ],
        "actual_opposite_endpoint_branch_residual": 5.5827550657406285e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.148005698545224e-15,
            3.6908654704364e-15,
            -3.684296103561537e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814341
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.056377959365660625
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.1480056985325614e-15,
            3.69086547043875e-15,
            -3.677613769070831e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814343
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.05637795936566063
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "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": [
          [
            -6.953136066911725e-09,
            1.1322596193963363e-09,
            0.3963608196623811
          ],
          [
            -5.968087135599376e-09,
            1.122787085527932e-09,
            0.2889518376224809
          ],
          [
            -4.972210421172463e-09,
            1.0424054952551387e-09,
            0.19439287692921348
          ],
          [
            -4.010007326193943e-09,
            9.026106528864375e-10,
            0.1162432349986352
          ],
          [
            -3.1107545983566354e-09,
            7.319999051347281e-10,
            0.05637795936565726
          ],
          [
            -2.2821340373013754e-09,
            5.586892060094328e-10,
            0.01501677368081289
          ],
          [
            -1.507571567582744e-09,
            3.8918890332695355e-10,
            -0.00765328859624953
          ],
          [
            -7.546893665555388e-10,
            2.056707026909521e-10,
            -0.011029990502592402
          ],
          [
            3.1086244689504383e-15,
            3.6637359812630166e-15,
            -3.885780586188048e-16
          ],
          [
            7.546878677544555e-10,
            -2.056735337596649e-10,
            0.011029990502587128
          ],
          [
            1.5075657389118646e-09,
            -3.8918818168198754e-10,
            0.007653288596240371
          ],
          [
            2.2821263767625055e-09,
            -5.586899276543988e-10,
            -0.015016773680814333
          ],
          [
            3.1107579845368605e-09,
            -7.319980177555863e-10,
            -0.056377959365660646
          ],
          [
            4.010014320598998e-09,
            -9.02610042263774e-10,
            -0.11624323499863687
          ],
          [
            4.972200207120636e-09,
            -1.0424059948554998e-09,
            -0.19439287692921947
          ],
          [
            5.9680805852835306e-09,
            -1.1227894169962838e-09,
            -0.2889518376224845
          ],
          [
            6.953145281762829e-09,
            -1.132256677305321e-09,
            -0.39636081966238007
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135678333666e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "target_residual": 0.5106281159003272,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.06246811886841195,
            "max_log_strain_component": 0.008847172959887526,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.006884773001943,
              1.0004078835617274,
              0.9882242847338759
            ],
            "cell_volume_ratio": 0.9954338401676576,
            "cell_rmsd_from_input_A": 0.07243633812411251
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4974604249156825,
              -8.102308115936247e-11,
              0.5084555773434648
            ],
            "branch_aligned_reduced_polarization": [
              -0.4974604249156825,
              -8.102308115936247e-11,
              0.5084555773434648
            ],
            "target_residual": 0.008828716204534022,
            "energy_eV": -109.63903173257859,
            "max_atomic_step_A": 0.0014129485753291856,
            "max_log_strain_component": 0.00045503988668395376,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.00706919549289,
              1.0003742995495108,
              0.9884488167138324
            ],
            "cell_volume_ratio": 0.9958089460130047,
            "cell_rmsd_from_input_A": 0.07123508966139282
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000924590928137,
              7.196742374510774e-13,
              0.5000185932759856
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000924590928137,
              7.196742374510774e-13,
              0.5000185932759856
            ],
            "target_residual": 9.431009360518545e-05,
            "energy_eV": -109.64143883313503
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 9.431009360518545e-05,
        "parent_symmetrization_rmsd_A": 0.06839477305620317,
        "parent_cell_rmsd_A": 0.07123508966139282,
        "energy_eV": -109.64143883313503,
        "reduced_polarization": [
          -0.5000924590928137,
          7.196742374510774e-13,
          0.5000185932759856
        ],
        "cartesian_polarization_e_A2": [
          -0.010297331006041726,
          6.125195850084948e-13,
          0.014390736484318588
        ],
        "ranking_score": 0.5863921656587617
      },
      "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,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586757067654e-09,
              0.3963608196623807
            ],
            "target_residual": 0.5106281216000496,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.06454586208318555,
            "max_log_strain_component": 0.006912675468410819,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0049752315566507,
              1.000543302135869,
              0.9899679925658379
            ],
            "cell_volume_ratio": 0.9954338402242024,
            "cell_rmsd_from_input_A": 0.05936761532540626
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.878130420755163e-11,
              0.49866307718893144,
              0.5028972603864846
            ],
            "branch_aligned_reduced_polarization": [
              -4.878130420755163e-11,
              0.49866307718893144,
              0.5028972603864846
            ],
            "target_residual": 0.00319084320358249,
            "energy_eV": -109.64234744919085,
            "max_atomic_step_A": 0.000504507434235861,
            "max_log_strain_component": 0.00015329959456260588,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0050326575749127,
              1.0005282304192087,
              0.9900519946349685
            ],
            "cell_volume_ratio": 0.9955601948425049,
            "cell_rmsd_from_input_A": 0.058805679417319255
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.2203436884001391e-13,
              0.5000237578705758,
              0.5000030852414532
            ],
            "branch_aligned_reduced_polarization": [
              -2.2203436884001391e-13,
              0.5000237578705758,
              0.5000030852414532
            ],
            "target_residual": 2.3957360646015613e-05,
            "energy_eV": -109.64291211324074
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.3957360646015613e-05,
        "parent_symmetrization_rmsd_A": 0.0676257819216866,
        "parent_cell_rmsd_A": 0.058805679417319255,
        "energy_eV": -109.64291211324074,
        "reduced_polarization": [
          -2.2203436884001391e-13,
          0.5000237578705758,
          0.5000030852414532
        ],
        "cartesian_polarization_e_A2": [
          -1.4841137872173367e-12,
          0.009759547468349223,
          0.01441376831796259
        ],
        "ranking_score": 0.5823751164973084
      },
      "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,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135678333666e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "target_residual": 0.6380453686144103,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.08286264844324517,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9460822033706285,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0230884832996556,
              0.9985255741651833,
              0.9952202266099738
            ],
            "cell_volume_ratio": 1.0166970942360984,
            "cell_rmsd_from_input_A": 0.15443941882460563
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4587481318806611,
              -7.213513886416194e-11,
              0.04804062956152487
            ],
            "branch_aligned_reduced_polarization": [
              -0.4587481318806611,
              -7.213513886416194e-11,
              0.04804062956152487
            ],
            "target_residual": 0.06332155013897706,
            "energy_eV": -109.28765403052275,
            "max_atomic_step_A": 0.010080973794507887,
            "max_log_strain_component": 0.0031063736793989797,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0264770727687391,
              0.998296763414735,
              0.994717257993448
            ],
            "cell_volume_ratio": 1.0193153619071733,
            "cell_rmsd_from_input_A": 0.17791884552924145
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4996284960284984,
              2.3618196364193454e-12,
              0.0022641215415820427
            ],
            "branch_aligned_reduced_polarization": [
              -0.4996284960284984,
              2.3618196364193454e-12,
              0.0022641215415820427
            ],
            "target_residual": 0.0022943978634703496,
            "energy_eV": -109.15052195999691,
            "max_atomic_step_A": 0.000413072151303186,
            "max_log_strain_component": 0.0001462448736841624,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0266199315548448,
              0.9982859925327229,
              0.9947100067881763
            ],
            "cell_volume_ratio": 1.0194387933101814,
            "cell_rmsd_from_input_A": 0.17894983861929836
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000047979792234,
              1.1412561423108822e-13,
              7.597233530280978e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000047979792234,
              1.1412561423108822e-13,
              7.597233530280978e-05
            ],
            "target_residual": 7.612369102973426e-05,
            "energy_eV": -109.14493550828632
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.612369102973426e-05,
        "parent_symmetrization_rmsd_A": 0.10843715369235628,
        "parent_cell_rmsd_A": 0.17894983861929836,
        "energy_eV": -109.14493550828632,
        "reduced_polarization": [
          -0.5000047979792234,
          1.1412561423108822e-13,
          7.597233530280978e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.010154889104765422,
          -7.470869824981328e-13,
          -9.33425508129848e-05
        ],
        "ranking_score": 0.6533268607292403
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586757067654e-09,
              0.3963608196623807
            ],
            "target_residual": 0.6380453731759017,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.08952752669258765,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9460822042163726,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0220749767237292,
              0.9980366740196186,
              0.9966951075452724
            ],
            "cell_volume_ratio": 1.0166970943057876,
            "cell_rmsd_from_input_A": 0.14890332023727715
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.402494556788315e-10,
              0.46068112898270797,
              0.04148605824281132
            ],
            "branch_aligned_reduced_polarization": [
              -5.402494556788315e-10,
              0.46068112898270797,
              0.04148605824281132
            ],
            "target_residual": 0.05715825965335527,
            "energy_eV": -109.28310539732115,
            "max_atomic_step_A": 0.008724747334748371,
            "max_log_strain_component": 0.002622035642628152,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.024876110312216,
              0.9977795644495749,
              0.9963878814633619
            ],
            "cell_volume_ratio": 1.018906684960948,
            "cell_rmsd_from_input_A": 0.1683988208044557
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.738921212627991e-11,
              0.4990543601358926,
              0.0018126623827176337
            ],
            "branch_aligned_reduced_polarization": [
              -1.738921212627991e-11,
              0.4990543601358926,
              0.0018126623827176337
            ],
            "target_residual": 0.0020444998572532653,
            "energy_eV": -109.16462842423098,
            "max_atomic_step_A": 0.00033929185826741994,
            "max_log_strain_component": 0.00011705140852268443,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0249956285415613,
              0.9977680882564463,
              0.9963797165098426
            ],
            "cell_volume_ratio": 1.0190054361313814,
            "cell_rmsd_from_input_A": 0.16924914878354724
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.060458934839325e-13,
              0.4999682668633416,
              6.499983803841706e-05
            ],
            "branch_aligned_reduced_polarization": [
              -5.060458934839325e-13,
              0.4999682668633416,
              6.499983803841706e-05
            ],
            "target_residual": 7.233236417538273e-05,
            "energy_eV": -109.15973951690891
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 7.233236417538273e-05,
        "parent_symmetrization_rmsd_A": 0.10629377552879586,
        "parent_cell_rmsd_A": 0.16924914878354724,
        "energy_eV": -109.15973951690891,
        "reduced_polarization": [
          -5.060458934839325e-13,
          0.4999682668633416,
          6.499983803841706e-05
        ],
        "cartesian_polarization_e_A2": [
          1.2643449241119023e-12,
          0.00961233681318796,
          -6.789374107716274e-05
        ],
        "ranking_score": 0.6487507274530334
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135678333666e-09,
              1.1322586757067654e-09,
              0.3963608196623807
            ],
            "target_residual": 0.7146615084189573,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.09778542427528766,
            "max_log_strain_component": 0.00884717293219956,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0091479763980187,
              1.0004590104954356,
              0.985957618204238
            ],
            "cell_volume_ratio": 0.9954338401728035,
            "cell_rmsd_from_input_A": 0.08550682468620782
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49270396383905407,
              0.4934478400569739,
              0.5106520935785169
            ],
            "branch_aligned_reduced_polarization": [
              -0.49270396383905407,
              0.4934478400569739,
              0.5106520935785169
            ],
            "target_residual": 0.014478606327485669,
            "energy_eV": -109.43489801119249,
            "max_atomic_step_A": 0.002248374625535619,
            "max_log_strain_component": 0.0005860461115059093,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0095202624989525,
              1.0004102112072877,
              0.9861204708709433
            ],
            "cell_volume_ratio": 0.9959169653925054,
            "cell_rmsd_from_input_A": 0.08502202115375238
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.500096425665218,
              0.5000701163827823,
              0.5000640588657493
            ],
            "branch_aligned_reduced_polarization": [
              -0.500096425665218,
              0.5000701163827823,
              0.5000640588657493
            ],
            "target_residual": 0.00013534309856173533,
            "energy_eV": -109.42907713947763
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00013534309856173533,
        "parent_symmetrization_rmsd_A": 0.09480664574551213,
        "parent_cell_rmsd_A": 0.08502202115375238,
        "energy_eV": -109.42907713947763,
        "reduced_polarization": [
          -0.500096425665218,
          0.5000701163827823,
          0.5000640588657493
        ],
        "cartesian_polarization_e_A2": [
          -0.010295063912016787,
          0.009755789832461758,
          0.014322750405992212
        ],
        "ranking_score": 0.6163328372310737
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.953135683895109e-09,
              1.1322586893748243e-09,
              0.3963608196623807
            ],
            "branch_aligned_reduced_polarization": [
              -6.953135678333666e-09,
              1.1322586757067654e-09,
              0.3963608196623807
            ],
            "target_residual": 0.8106182154862053,
            "energy_eV": -109.85065564448125,
            "max_atomic_step_A": 0.11484146819378198,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9460822032913274,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0246211613268932,
              0.9983507706155047,
              0.9939055226860856
            ],
            "cell_volume_ratio": 1.01669709423966,
            "cell_rmsd_from_input_A": 0.16092595078756605
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4548915021211776,
              0.4564061442420083,
              0.053291578231631505
            ],
            "branch_aligned_reduced_polarization": [
              -0.4548915021211776,
              0.4564061442420083,
              0.053291578231631505
            ],
            "target_residual": 0.08231156146708923,
            "energy_eV": -109.12504639470868,
            "max_atomic_step_A": 0.013126476860873816,
            "max_log_strain_component": 0.0035627350348363092,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0286094071696446,
              0.998061549063562,
              0.9932643568241437
            ],
            "cell_volume_ratio": 1.0197005826257277,
            "cell_rmsd_from_input_A": 0.18824954438494523
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49951127859023586,
              0.4986191232641153,
              0.003296470577273929
            ],
            "branch_aligned_reduced_polarization": [
              -0.49951127859023586,
              0.4986191232641153,
              0.003296470577273929
            ],
            "target_residual": 0.003607268695689605,
            "energy_eV": -108.93214637261646,
            "max_atomic_step_A": 0.0006375903279680446,
            "max_log_strain_component": 0.0002201867276487489,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.746829342404636,
            "cell_principal_stretches": [
              1.0288253720748544,
              0.9980432971876876,
              0.993255077334357
            ],
            "cell_volume_ratio": 1.0198864972457489,
            "cell_rmsd_from_input_A": 0.18979867615088009
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000071828006728,
              0.4999370758318584,
              0.0001449300475131766
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000071828006728,
              0.4999370758318584,
              0.0001449300475131766
            ],
            "target_residual": 0.0001581637197146872,
            "energy_eV": -108.92251734695506
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0001581637197146872,
        "parent_symmetrization_rmsd_A": 0.12836098418654027,
        "parent_cell_rmsd_A": 0.18979867615088009,
        "energy_eV": -108.92251734695506,
        "reduced_polarization": [
          -0.5000071828006728,
          0.4999370758318584,
          0.0001449300475131766
        ],
        "cartesian_polarization_e_A2": [
          -0.010150278224123762,
          0.009603032574544429,
          -0.00016345486365220362
        ],
        "ranking_score": 0.6761269806636897
      },
      "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": 0.24098244859993384,
        "minimum_distance_A_by_image": [
          2.167064988931984,
          2.1751324275160937,
          2.1755622838456303,
          2.174429508935573,
          2.174128146716651,
          2.1746585428381535,
          2.1760200890869417,
          2.178211226869086,
          2.181229456106055
        ],
        "minimum_distance_A": 2.167064988931984,
        "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": [
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956,
          291.0508255173956
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        3.148005698545224e-15,
        3.6908654704364e-15,
        -3.684296103561537e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -109.85065564448124,
          -109.7684107673474,
          -109.61230850030225,
          -109.40317121577753,
          -109.1570191090513,
          -108.89863127410985,
          -108.66625764770667,
          -108.50342342985596,
          -108.44465634491077
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4428367357292635e-10,
            2.22191269515702e-11,
            0.011490412417128289
          ],
          [
            -1.2384304505094955e-10,
            2.2033240268700083e-11,
            0.008376649805592556
          ],
          [
            -1.031777291777252e-10,
            2.0455856042980562e-11,
            0.005635406468205777
          ],
          [
            -8.3211170216774e-11,
            1.771256423956773e-11,
            0.0033698656491153948
          ],
          [
            -6.455088755048072e-11,
            1.4364547890692587e-11,
            0.0016343845612674358
          ],
          [
            -4.735628386792969e-11,
            1.0963551550386833e-11,
            0.00043533294464925853
          ],
          [
            -3.1283432980192584e-11,
            7.637328380430066e-12,
            -0.000221867142148708
          ],
          [
            -1.5660466654988843e-11,
            4.036021617988925e-12,
            -0.0003197569828918777
          ],
          [
            6.532388033226673e-17,
            7.24284483392067e-17,
            -1.0680692842647991e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.148005698545224e-15,
            3.6908654704364e-15,
            -3.684296103561537e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.1480056985325614e-15,
            3.69086547043875e-15,
            -3.677613769070831e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.953136066911725e-09,
            1.1322596193963363e-09,
            0.3963608196623811
          ],
          [
            -5.968087135599376e-09,
            1.122787085527932e-09,
            0.2889518376224809
          ],
          [
            -4.972210421172463e-09,
            1.0424054952551387e-09,
            0.19439287692921348
          ],
          [
            -4.010007326193943e-09,
            9.026106528864375e-10,
            0.1162432349986352
          ],
          [
            -3.1107545983566354e-09,
            7.319999051347281e-10,
            0.05637795936565726
          ],
          [
            -2.2821340373013754e-09,
            5.586892060094328e-10,
            0.01501677368081289
          ],
          [
            -1.507571567582744e-09,
            3.8918890332695355e-10,
            -0.00765328859624953
          ],
          [
            -7.546893665555388e-10,
            2.056707026909521e-10,
            -0.011029990502592402
          ],
          [
            3.1086244689504383e-15,
            3.6637359812630166e-15,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -108.44465634491074,
          -108.50342342985596,
          -108.66625764770664,
          -108.89863127410986,
          -109.15701910905128,
          -109.40317121577753,
          -109.61230850030223,
          -109.76841076734739,
          -109.85065564448124
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.745640569370906e-17,
            5.2163740936861175e-17,
            -1.0203876197886921e-17
          ],
          [
            1.5660434612910315e-11,
            -4.03607642806224e-12,
            0.0003197569828917263
          ],
          [
            3.128331271511436e-11,
            -7.637313003093273e-12,
            0.00022186714214844118
          ],
          [
            4.735612558864446e-11,
            -1.0963565556875773e-11,
            -0.0004353329446492996
          ],
          [
            6.455095692730254e-11,
            -1.4364511962558404e-11,
            -0.0016343845612675342
          ],
          [
            8.321131578889565e-11,
            -1.7712551937698294e-11,
            -0.0033698656491154434
          ],
          [
            1.0317751775722491e-10,
            -2.0455865579313458e-11,
            -0.00563540646820595
          ],
          [
            1.238429084906625e-10,
            -2.203328666295962e-11,
            -0.008376649805592662
          ],
          [
            1.442838645618334e-10,
            -2.2219069304437848e-11,
            -0.011490412417128257
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.7688663260926972e-15,
            2.6582006745605145e-15,
            -3.519818598938254e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814341
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.056377959365660625
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.7688663260926972e-15,
            2.6582006745605145e-15,
            -3.519818598938254e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814343
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.05637795936566063
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.953142336067734e-09,
          -1.1322522528358967e-09,
          -0.3963608196623818
        ],
        "actual_opposite_endpoint_branch_residual": 5.5827550657406285e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.148005698545224e-15,
            3.6908654704364e-15,
            -3.684296103561537e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814341
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.056377959365660625
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.953136040056337e-09,
            1.1322596345668375e-09,
            0.3963608196623811
          ],
          [
            -5.968087161426806e-09,
            1.122787075718053e-09,
            0.28895183762248083
          ],
          [
            -4.972210434565961e-09,
            1.0424054976804668e-09,
            0.1943928769292135
          ],
          [
            -4.010007315741642e-09,
            9.026106901881359e-10,
            0.11624323499863523
          ],
          [
            -3.1107546095159235e-09,
            7.319998567398274e-10,
            0.05637795936565723
          ],
          [
            -2.282134048373898e-09,
            5.586892274864304e-10,
            0.015016773680812924
          ],
          [
            -1.5075715770524957e-09,
            3.891889478799517e-10,
            -0.00765328859624953
          ],
          [
            -7.546893727228722e-10,
            2.0567074360070895e-10,
            -0.011029990502592383
          ],
          [
            3.1480056985325614e-15,
            3.69086547043875e-15,
            -3.677613769070831e-16
          ],
          [
            7.546878285916098e-10,
            -2.0567353665525688e-10,
            0.011029990502587163
          ],
          [
            1.5075657813901794e-09,
            -3.8918816426960657e-10,
            0.0076532885962403265
          ],
          [
            2.282126420779069e-09,
            -5.586899412400393e-10,
            -0.015016773680814343
          ],
          [
            3.110757952835844e-09,
            -7.319980258858894e-10,
            -0.05637795936566063
          ],
          [
            4.01001433096894e-09,
            -9.026100632998598e-10,
            -0.1162432349986369
          ],
          [
            4.972200246057006e-09,
            -1.0424059836403708e-09,
            -0.19439287692921947
          ],
          [
            5.9680805804864265e-09,
            -1.1227894399129858e-09,
            -0.2889518376224845
          ],
          [
            6.953145243951829e-09,
            -1.132256696939218e-09,
            -0.39636081966238007
          ]
        ],
        "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": [
          [
            -6.953136066911725e-09,
            1.1322596193963363e-09,
            0.3963608196623811
          ],
          [
            -5.968087135599376e-09,
            1.122787085527932e-09,
            0.2889518376224809
          ],
          [
            -4.972210421172463e-09,
            1.0424054952551387e-09,
            0.19439287692921348
          ],
          [
            -4.010007326193943e-09,
            9.026106528864375e-10,
            0.1162432349986352
          ],
          [
            -3.1107545983566354e-09,
            7.319999051347281e-10,
            0.05637795936565726
          ],
          [
            -2.2821340373013754e-09,
            5.586892060094328e-10,
            0.01501677368081289
          ],
          [
            -1.507571567582744e-09,
            3.8918890332695355e-10,
            -0.00765328859624953
          ],
          [
            -7.546893665555388e-10,
            2.056707026909521e-10,
            -0.011029990502592402
          ],
          [
            3.1086244689504383e-15,
            3.6637359812630166e-15,
            -3.885780586188048e-16
          ],
          [
            7.546878677544555e-10,
            -2.056735337596649e-10,
            0.011029990502587128
          ],
          [
            1.5075657389118646e-09,
            -3.8918818168198754e-10,
            0.007653288596240371
          ],
          [
            2.2821263767625055e-09,
            -5.586899276543988e-10,
            -0.015016773680814333
          ],
          [
            3.1107579845368605e-09,
            -7.319980177555863e-10,
            -0.056377959365660646
          ],
          [
            4.010014320598998e-09,
            -9.02610042263774e-10,
            -0.11624323499863687
          ],
          [
            4.972200207120636e-09,
            -1.0424059948554998e-09,
            -0.19439287692921947
          ],
          [
            5.9680805852835306e-09,
            -1.1227894169962838e-09,
            -0.2889518376224845
          ],
          [
            6.953145281762829e-09,
            -1.132256677305321e-09,
            -0.39636081966238007
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9319139521006995e-15,
        "parent_symmetrization_rmsd_A": 0.24098244859993384,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -108.44465634491078,
        "reduced_polarization": [
          2.428789798074673e-15,
          6.536160708014429e-16,
          -1.5066139423492713e-15
        ],
        "cartesian_polarization_e_A2": [
          5.039951935124521e-17,
          1.2826367744072812e-17,
          -4.367640466011411e-17
        ],
        "ranking_score": 0.2409824485999397
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 278.231386053958
  }
}