{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 10,
  "input_formula": "I2O6Rb2",
  "input_spacegroup": "R3m",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -43.35684827871095,
  "input_cartesian_polarization_e_A2": [
    0.006777041303105977,
    6.416836983589254e-19,
    -0.004643339553637102
  ],
  "input_reduced_polarization": [
    0.19887875734636143,
    1.9635129146794677e-17,
    -0.19887882575539967
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "R-3m",
      "spacegroup_number": 166,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.6850989848337e-16,
      "parent_symmetrization_rmsd_A": 0.3859972172954355,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -36.848992538786966,
      "reduced_polarization": [
        -5.088636672873386e-16,
        -1.544817764427371e-16,
        4.0509089502508265e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.7268119750162572e-17,
        -5.048524860505663e-18,
        9.457892606433754e-18
      ],
      "ranking_score": 0.38599721729543685
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0008731628968384637,
      "parent_symmetrization_rmsd_A": 0.0974598243632829,
      "parent_cell_rmsd_A": 0.0805901805652099,
      "energy_eV": -42.04987634511832,
      "reduced_polarization": [
        0.0006003000607431277,
        -2.0264994826768344e-15,
        -0.0006340767157743096
      ],
      "cartesian_polarization_e_A2": [
        2.0147569538763863e-05,
        -6.476573837259074e-17,
        -1.4580630954700795e-05
      ],
      "ranking_score": 0.6193536952982623
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.057761854004424e-15,
      "parent_symmetrization_rmsd_A": 0.3859972172954355,
      "parent_cell_rmsd_A": 0.0805901805652099,
      "energy_eV": -36.233384800911494,
      "reduced_polarization": [
        -3.5423677876039865e-15,
        -1.0766953603733012e-15,
        1.6606591528997361e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.172747048857218e-16,
        -3.440700781135438e-17,
        3.8456280593367496e-17
      ],
      "ranking_score": 0.4061447624367461
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00047571708743292533,
      "parent_symmetrization_rmsd_A": 0.08660592469225978,
      "parent_cell_rmsd_A": 0.054574245980211544,
      "energy_eV": -41.43938132755645,
      "reduced_polarization": [
        0.0001476799465707957,
        8.816893551041363e-16,
        -0.49954778613394046
      ],
      "cartesian_polarization_e_A2": [
        0.0003263345797662329,
        -1.607380345338037e-18,
        -0.011513145840312135
      ],
      "ranking_score": 0.6012009203621785
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0001555973169564439,
      "parent_symmetrization_rmsd_A": 0.14231201243040095,
      "parent_cell_rmsd_A": 0.13133658590490993,
      "energy_eV": -39.59967583618036,
      "reduced_polarization": [
        0.5001521441375568,
        -4.4983308152982625e-15,
        3.259887193041349e-05
      ],
      "cartesian_polarization_e_A2": [
        0.016904936674051012,
        -8.612044627969348e-17,
        2.7639211817680858e-05
      ],
      "ranking_score": 0.6754573535405413
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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": 0.00012792291779841015,
      "parent_symmetrization_rmsd_A": 0.26146691745940337,
      "parent_cell_rmsd_A": 0.24268614181321324,
      "energy_eV": -38.2172601725479,
      "reduced_polarization": [
        0.49991555588837344,
        -8.167954330146449e-16,
        -0.4999039090799833
      ],
      "cartesian_polarization_e_A2": [
        0.01794866175286779,
        -8.881927909415219e-19,
        -0.012237859085126255
      ],
      "ranking_score": 0.8223942987483035
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.08994193156545309,
      "parent_symmetrization_rmsd_A": 0.2628220556269938,
      "parent_cell_rmsd_A": 0.44099922805258673,
      "energy_eV": -38.252427550174914,
      "reduced_polarization": [
        0.053289889793838814,
        0.4294036192175406,
        0.01630612522652637
      ],
      "cartesian_polarization_e_A2": [
        0.0009570281843523906,
        0.013493187050776463,
        0.00047274542207495756
      ],
      "ranking_score": 1.0529557257710467
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.09454338022655748,
      "parent_symmetrization_rmsd_A": 0.3030163321874219,
      "parent_cell_rmsd_A": 0.42592247613867873,
      "energy_eV": -33.0562968423764,
      "reduced_polarization": [
        0.05436724767847601,
        0.42525020216912535,
        -0.4801223530372926
      ],
      "cartesian_polarization_e_A2": [
        0.0013980493487665265,
        0.013627601499697587,
        -0.010692012480260896
      ],
      "ranking_score": 1.0985837116752066
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0003685073087148143,
      "parent_symmetrization_rmsd_A": 0.2045408362641266,
      "parent_cell_rmsd_A": 0.27513492180836663,
      "energy_eV": -26.386637366361086,
      "reduced_polarization": [
        0.49973205419954997,
        0.49992987978015835,
        0.00024307578934724435
      ],
      "cartesian_polarization_e_A2": [
        0.016279199558796066,
        0.016025076412857137,
        0.00012295941563561643
      ],
      "ranking_score": 0.774061581333648
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.6941617121180986e-06,
      "parent_symmetrization_rmsd_A": 0.31078947988733263,
      "parent_cell_rmsd_A": 0.34963930368070884,
      "energy_eV": -28.821505148343558,
      "reduced_polarization": [
        0.5000015642447223,
        0.5000021866676817,
        -0.5000025334667264
      ],
      "cartesian_polarization_e_A2": [
        0.017238342032954903,
        0.016710089973369504,
        -0.012093728082052965
      ],
      "ranking_score": 0.8982066941309341
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "target_residual": 0.28125708427963114,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011059484035025925,
            "step_scale": 0.9197989949244723,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0143124729789237,
              1.008284642629331,
              1.0064055086734376
            ],
            "cell_volume_ratio": 1.0292667035505043,
            "cell_rmsd_from_input_A": 0.0740356793279969
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.014418653363344924,
              3.2976362471471456e-15,
              -0.014949444570840121
            ],
            "branch_aligned_reduced_polarization": [
              0.014418653363344924,
              3.2976362471471456e-15,
              -0.014949444570840121
            ],
            "target_residual": 0.020769772694685877,
            "energy_eV": -42.22362507123181,
            "max_atomic_step_A": 0.010176477076488818,
            "max_log_strain_component": 0.0009623253807056157,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.015583341098694,
              1.0090097530818207,
              1.0069725026409875
            ],
            "cell_volume_ratio": 1.0318784532448173,
            "cell_rmsd_from_input_A": 0.0805901805652099
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0006003000607431277,
              -2.0264994826768344e-15,
              -0.0006340767157743096
            ],
            "branch_aligned_reduced_polarization": [
              0.0006003000607431277,
              -2.0264994826768344e-15,
              -0.0006340767157743096
            ],
            "target_residual": 0.0008731628968384637,
            "energy_eV": -42.04987634511832
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "R-3m",
        "spacegroup_number": 166,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.6850989848337e-16,
        "parent_symmetrization_rmsd_A": 0.3859972172954355,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.848992538786966,
        "reduced_polarization": [
          -5.088636672873386e-16,
          -1.544817764427371e-16,
          4.0509089502508265e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.7268119750162572e-17,
          -5.048524860505663e-18,
          9.457892606433754e-18
        ],
        "ranking_score": 0.38599721729543685
      },
      "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": [
          -43.356848278710956,
          -43.04769011023859,
          -42.3649640912855,
          -41.399537437318926,
          -40.234907060701,
          -39.00100456497412,
          -37.89361786923028,
          -37.12426836345416,
          -36.848992538786966
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00677704130310598,
            -1.0560268539632244e-17,
            -0.004643339553637103
          ],
          [
            0.004320445836991562,
            -1.0664837803657448e-17,
            -0.0029601856420964803
          ],
          [
            0.0019115810190033615,
            -3.226968760286115e-17,
            -0.0013097346786870826
          ],
          [
            -5.432278208313968e-05,
            -1.3128190839416842e-17,
            3.721836043342379e-05
          ],
          [
            -0.0013145582297103527,
            -1.7002138326992063e-18,
            0.0009006776177876186
          ],
          [
            -0.0018070610930666915,
            -4.973440770812037e-17,
            0.0012381194337323345
          ],
          [
            -0.001624757663751956,
            -2.1741773564905257e-19,
            0.0011132131090491823
          ],
          [
            -0.0009424466907853751,
            2.703563098635579e-17,
            0.0006457233602596493
          ],
          [
            1.8522122505762604e-17,
            -2.2884839567181156e-18,
            -3.231606001096549e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.001594155135438057,
            -4.0171461929757624e-16,
            0.001594099189610773
          ],
          [
            -0.03857696967123021,
            -5.202550457116708e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.652849884126144e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.0015941551354380565,
            -4.017146192975763e-16,
            0.0015940991896107731
          ],
          [
            -0.03857696967123021,
            -5.2025504571167077e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.6528498841260944e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.273559366969494e-16,
            -7.00262109750428e-17,
            -1.384309333829492e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1988787573463615,
            -3.3306690738754696e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.3306690738754696e-16,
            -0.12678767893616616
          ],
          [
            0.05609717206204534,
            -9.992007221626409e-16,
            -0.05609723173149839
          ],
          [
            -0.0015941551354380357,
            -3.885780586188048e-16,
            0.0015940991896107315
          ],
          [
            -0.0385769696712302,
            -5.551115123125783e-17,
            0.03857691321959522
          ],
          [
            -0.05302993725342375,
            -1.4988010832439613e-15,
            0.053029879956281056
          ],
          [
            -0.047680068614592286,
            0.0,
            0.047680018526709333
          ],
          [
            -0.027657000126060982,
            7.771561172376096e-16,
            0.02765697019738278
          ],
          [
            5.551115123125783e-16,
            -5.551115123125783e-17,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -36.848992538786966,
          -37.12426836345417,
          -37.8936178692303,
          -39.00100456497411,
          -40.234907060701,
          -41.399537437318926,
          -42.36496409128549,
          -43.0476901102386,
          -43.356848278710956
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8522122505762604e-17,
            -2.2884839567181156e-18,
            -3.231606001096549e-17
          ],
          [
            0.000942446690785255,
            9.185646139882419e-18,
            -0.000645723360259661
          ],
          [
            0.0016247576637518494,
            -4.563841581149064e-18,
            -0.0011132131090491235
          ],
          [
            0.00180706109306681,
            7.165496452559035e-18,
            -0.0012381194337324445
          ],
          [
            0.0013145582297103906,
            -2.8691379706104017e-17,
            -0.0009006776177876498
          ],
          [
            5.432278208310846e-05,
            -7.798180518742289e-17,
            -3.721836043350014e-05
          ],
          [
            -0.0019115810190032537,
            -1.0789701098324499e-16,
            0.0013097346786872129
          ],
          [
            -0.0043204458369915395,
            -1.0658922527510575e-17,
            0.0029601856420965337
          ],
          [
            -0.00677704130310595,
            3.0865265528918293e-17,
            0.00464333955363714
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135155e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370536,
            -2.3861955974121773e-15,
            -0.001594099189614043
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001273e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135157e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370503,
            -2.3861955974121773e-15,
            -0.0015940991896140413
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001274e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.19887875734636043,
          1.8308534379151734e-16,
          0.19887882575539695
        ],
        "actual_opposite_endpoint_branch_residual": 4.45314653732767e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.001594155135438057,
            -4.0171461929757624e-16,
            0.001594099189610773
          ],
          [
            -0.03857696967123021,
            -5.202550457116708e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.652849884126144e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135155e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370536,
            -2.3861955974121773e-15,
            -0.001594099189614043
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001273e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.0015941551354380565,
            -4.017146192975763e-16,
            0.0015940991896107731
          ],
          [
            -0.03857696967123021,
            -5.2025504571167077e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.6528498841260944e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.273559366969494e-16,
            -7.00262109750428e-17,
            -1.384309333829492e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135157e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370503,
            -2.3861955974121773e-15,
            -0.0015940991896140413
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001274e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "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": [
          [
            0.1988787573463615,
            -3.3306690738754696e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.3306690738754696e-16,
            -0.12678767893616616
          ],
          [
            0.05609717206204534,
            -9.992007221626409e-16,
            -0.05609723173149839
          ],
          [
            -0.0015941551354380357,
            -3.885780586188048e-16,
            0.0015940991896107315
          ],
          [
            -0.0385769696712302,
            -5.551115123125783e-17,
            0.03857691321959522
          ],
          [
            -0.05302993725342375,
            -1.4988010832439613e-15,
            0.053029879956281056
          ],
          [
            -0.047680068614592286,
            0.0,
            0.047680018526709333
          ],
          [
            -0.027657000126060982,
            7.771561172376096e-16,
            0.02765697019738278
          ],
          [
            5.551115123125783e-16,
            -5.551115123125783e-17,
            -1.3877787807814457e-15
          ],
          [
            0.02765700012605732,
            3.3306690738754696e-16,
            -0.02765697019738328
          ],
          [
            0.047680068614589066,
            -1.6653345369377348e-16,
            -0.04768001852670678
          ],
          [
            0.053029937253427195,
            2.220446049250313e-16,
            -0.05302987995628572
          ],
          [
            0.038576969671231365,
            -8.881784197001252e-16,
            -0.0385769132195965
          ],
          [
            0.0015941551354370365,
            -2.3869795029440866e-15,
            -0.0015940991896140622
          ],
          [
            -0.05609717206204201,
            -3.2751579226442118e-15,
            0.05609723173150394
          ],
          [
            -0.12678761392447674,
            -3.3306690738754696e-16,
            0.12678767893616838
          ],
          [
            -0.19887875734636057,
            9.992007221626409e-16,
            0.19887882575540128
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        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": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "target_residual": 0.36086939701515264,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009512971280429066,
            "step_scale": 0.9760774288909542,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0089143694326526,
              1.0058066488487911,
              0.990390302545372
            ],
            "cell_volume_ratio": 1.0050211214848601,
            "cell_rmsd_from_input_A": 0.056133113856237975
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.013212571097882176,
              -2.7997251833314435e-15,
              -0.46280988161277925
            ],
            "branch_aligned_reduced_polarization": [
              -0.013212571097882176,
              -2.7997251833314435e-15,
              -0.46280988161277925
            ],
            "target_residual": 0.039467416189460466,
            "energy_eV": -41.71807893951468,
            "max_atomic_step_A": 0.016584179982761797,
            "max_log_strain_component": 0.0024843361631892804,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.008153625169606,
              1.005060253949194,
              0.9877912385879813
            ],
            "cell_volume_ratio": 1.0008845482969162,
            "cell_rmsd_from_input_A": 0.054574245980211544
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0001476799465707957,
              8.816893551041363e-16,
              -0.49954778613394046
            ],
            "branch_aligned_reduced_polarization": [
              0.0001476799465707957,
              8.816893551041363e-16,
              -0.49954778613394046
            ],
            "target_residual": 0.00047571708743292533,
            "energy_eV": -41.43938132755645
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00047571708743292533,
        "parent_symmetrization_rmsd_A": 0.08660592469225978,
        "parent_cell_rmsd_A": 0.054574245980211544,
        "energy_eV": -41.43938132755645,
        "reduced_polarization": [
          0.0001476799465707957,
          8.816893551041363e-16,
          -0.49954778613394046
        ],
        "cartesian_polarization_e_A2": [
          0.0003263345797662329,
          -1.607380345338037e-18,
          -0.011513145840312135
        ],
        "ranking_score": 0.6012009203621785
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.1988787573463614,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "target_residual": 0.36086949179879163,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012099628391474482,
            "step_scale": 0.7998670690530366,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0035479631429847,
              0.9916023496516203,
              0.9879638588101204
            ],
            "cell_volume_ratio": 0.9831431071821903,
            "cell_rmsd_from_input_A": 0.0708444378955037
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.40106466617687553,
              1.7548984609721714e-16,
              -0.025985624282839022
            ],
            "branch_aligned_reduced_polarization": [
              0.40106466617687553,
              1.7548984609721714e-16,
              -0.025985624282839022
            ],
            "target_residual": 0.1022910208574631,
            "energy_eV": -41.77758563253761,
            "max_atomic_step_A": 0.054499581426844086,
            "max_log_strain_component": 0.010108182288393455,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.003828310379204,
              0.9845261655802607,
              0.9779571106312659
            ],
            "cell_volume_ratio": 0.9665103547386901,
            "cell_rmsd_from_input_A": 0.12875593089553852
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49684368779299265,
              1.575853710792088e-15,
              0.0038624940116476813
            ],
            "branch_aligned_reduced_polarization": [
              0.49684368779299265,
              1.575853710792088e-15,
              0.0038624940116476813
            ],
            "target_residual": 0.004988102518805904,
            "energy_eV": -39.65081482951457,
            "max_atomic_step_A": 0.0022094654589096888,
            "max_log_strain_component": 0.00045161417584947087,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0035948962543424,
              0.9842005459493032,
              0.9775029531248213
            ],
            "cell_volume_ratio": 0.9655174422128439,
            "cell_rmsd_from_input_A": 0.13133658590490993
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5001521441375568,
              -4.4983308152982625e-15,
              3.259887193041349e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5001521441375568,
              -4.4983308152982625e-15,
              3.259887193041349e-05
            ],
            "target_residual": 0.0001555973169564439,
            "energy_eV": -39.59967583618036
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0001555973169564439,
        "parent_symmetrization_rmsd_A": 0.14231201243040095,
        "parent_cell_rmsd_A": 0.13133658590490993,
        "energy_eV": -39.59967583618036,
        "reduced_polarization": [
          0.5001521441375568,
          -4.4983308152982625e-15,
          3.259887193041349e-05
        ],
        "cartesian_polarization_e_A2": [
          0.016904936674051012,
          -8.612044627969348e-17,
          2.7639211817680858e-05
        ],
        "ranking_score": 0.6754573535405413
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.1988787573463614,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "target_residual": 0.4258496969069233,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011059485488762167,
            "step_scale": 0.6074912357271449,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              0.9936352610797505,
              0.9917834278054463,
              0.9858894839786809
            ],
            "cell_volume_ratio": 0.9715654810965147,
            "cell_rmsd_from_input_A": 0.07232335972017291
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3495257371001758,
              -1.5167506526328137e-15,
              -0.3499190221558147
            ],
            "branch_aligned_reduced_polarization": [
              0.3495257371001758,
              -1.5167506526328137e-15,
              -0.3499190221558147
            ],
            "target_residual": 0.21252483079845572,
            "energy_eV": -42.14733576140411,
            "max_atomic_step_A": 0.1026294034410255,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9131870561874046,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              0.98225802909466,
              0.9770994612161427,
              0.9609352276429728
            ],
            "cell_volume_ratio": 0.9222708369915485,
            "cell_rmsd_from_input_A": 0.19880233008374856
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4640812455629495,
              4.340291060820006e-15,
              -0.4646647497990461
            ],
            "branch_aligned_reduced_polarization": [
              0.4640812455629495,
              4.340291060820006e-15,
              -0.4646647497990461
            ],
            "target_residual": 0.05038587924283101,
            "energy_eV": -38.32657787253364,
            "max_atomic_step_A": 0.04247342057706734,
            "max_log_strain_component": 0.007498775419340294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              0.9780448009659334,
              0.9716524765402751,
              0.9517793523015587
            ],
            "cell_volume_ratio": 0.9044946238364238,
            "cell_rmsd_from_input_A": 0.24480903583650374
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.501635341734424,
              -5.133609847140818e-16,
              -0.5018113482211268
            ],
            "branch_aligned_reduced_polarization": [
              0.501635341734424,
              -5.133609847140818e-16,
              -0.5018113482211268
            ],
            "target_residual": 0.0024403534511476684,
            "energy_eV": -38.20901063943577,
            "max_atomic_step_A": 0.00201815666826469,
            "max_log_strain_component": 0.0003475380073309178,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              0.9782415976137089,
              0.9719044945425138,
              0.9522055163909668
            ],
            "cell_volume_ratio": 0.9053164462373477,
            "cell_rmsd_from_input_A": 0.24268614181321324
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49991555588837344,
              -8.167954330146449e-16,
              -0.4999039090799833
            ],
            "branch_aligned_reduced_polarization": [
              0.49991555588837344,
              -8.167954330146449e-16,
              -0.4999039090799833
            ],
            "target_residual": 0.00012792291779841015,
            "energy_eV": -38.2172601725479
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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": 0.00012792291779841015,
        "parent_symmetrization_rmsd_A": 0.26146691745940337,
        "parent_cell_rmsd_A": 0.24268614181321324,
        "energy_eV": -38.2172601725479,
        "reduced_polarization": [
          0.49991555588837344,
          -8.167954330146449e-16,
          -0.4999039090799833
        ],
        "cartesian_polarization_e_A2": [
          0.01794866175286779,
          -8.881927909415219e-19,
          -0.012237859085126255
        ],
        "ranking_score": 0.8223942987483035
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.19887875734636143,
              0.0,
              -0.19887882575539967
            ],
            "target_residual": 0.5736772153898737,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.016367912165694245,
            "step_scale": 0.5145023226067487,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0226236971387215,
              1.0047640310060781,
              0.9890716093160574
            ],
            "cell_volume_ratio": 1.0162666358004966,
            "cell_rmsd_from_input_A": 0.12059739293093862
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.10189381867111004,
              0.23607782545343425,
              -0.07128869704818762
            ],
            "branch_aligned_reduced_polarization": [
              0.10189381867111004,
              0.23607782545343425,
              -0.07128869704818762
            ],
            "target_residual": 0.29175219421213827,
            "energy_eV": -42.14797330912192,
            "max_atomic_step_A": 0.11002904201028957,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8324886971704548,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0506521504262127,
              1.0055980287226396,
              0.9759764461395234
            ],
            "cell_volume_ratio": 1.0311520363415019,
            "cell_rmsd_from_input_A": 0.2720831757146698
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.10073112416863812,
              0.3515763316861727,
              0.004407950485651619
            ],
            "branch_aligned_reduced_polarization": [
              0.10073112416863812,
              0.3515763316861727,
              0.004407950485651619
            ],
            "target_residual": 0.17943181077917753,
            "energy_eV": -39.795707753420885,
            "max_atomic_step_A": 0.07992761593058618,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8391775200883517,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0804577466141525,
              1.0048055142768209,
              0.9639140573504693
            ],
            "cell_volume_ratio": 1.0464732016493148,
            "cell_rmsd_from_input_A": 0.43329480896529793
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.08621432817091501,
              0.39093574738942277,
              0.00598202856562349
            ],
            "branch_aligned_reduced_polarization": [
              0.08621432817091501,
              0.39093574738942277,
              0.00598202856562349
            ],
            "target_residual": 0.1391535347924226,
            "energy_eV": -39.19373017332509,
            "max_atomic_step_A": 0.04640396133100707,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6744078820774062,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.1143806800435967,
              1.0037001172110571,
              0.9546962560614738
            ],
            "cell_volume_ratio": 1.0678315994984662,
            "cell_rmsd_from_input_A": 0.6142369535895965
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.08576878204633286,
              0.3912653310138486,
              0.009071057824628071
            ],
            "branch_aligned_reduced_polarization": [
              0.08576878204633286,
              0.3912653310138486,
              0.009071057824628071
            ],
            "target_residual": 0.13878687367073667,
            "energy_eV": -37.65397845611325,
            "max_atomic_step_A": 0.06585108172775049,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8385835519256734,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.3506061881825615,
            "cell_principal_stretches": [
              1.0825060343294015,
              1.0058946262434694,
              0.9652131725284576
            ],
            "cell_volume_ratio": 1.051008078505384,
            "cell_rmsd_from_input_A": 0.44099922805258673
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.053289889793838814,
              0.4294036192175406,
              0.01630612522652637
            ],
            "branch_aligned_reduced_polarization": [
              0.053289889793838814,
              0.4294036192175406,
              0.01630612522652637
            ],
            "target_residual": 0.08994193156545309,
            "energy_eV": -38.252427550174914
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.08994193156545309,
        "parent_symmetrization_rmsd_A": 0.2628220556269938,
        "parent_cell_rmsd_A": 0.44099922805258673,
        "energy_eV": -38.252427550174914,
        "reduced_polarization": [
          0.053289889793838814,
          0.4294036192175406,
          0.01630612522652637
        ],
        "cartesian_polarization_e_A2": [
          0.0009570281843523906,
          0.013493187050776463,
          0.00047274542207495756
        ],
        "ranking_score": 1.0529557257710467
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.19887875734636143,
              0.0,
              -0.19887882575539967
            ],
            "target_residual": 0.6166252684589563,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01666244693577001,
            "step_scale": 0.5237606092933479,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0208303298808916,
              0.9955096590066802,
              0.9866614444283877
            ],
            "cell_volume_ratio": 1.00269119380756,
            "cell_rmsd_from_input_A": 0.11861344038150635
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.09299166810970728,
              0.2280176817011777,
              -0.320672796392792
            ],
            "branch_aligned_reduced_polarization": [
              0.09299166810970728,
              0.2280176817011777,
              -0.320672796392792
            ],
            "target_residual": 0.3387920863281917,
            "energy_eV": -42.084827956517344,
            "max_atomic_step_A": 0.096122381336968,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6607104518770389,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0450391118725995,
              0.9890337441090151,
              0.969467735885103
            ],
            "cell_volume_ratio": 1.0020214402064127,
            "cell_rmsd_from_input_A": 0.26225258751461095
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.08073194998457811,
              0.34025320855639957,
              -0.42134036580728845
            ],
            "branch_aligned_reduced_polarization": [
              0.08073194998457811,
              0.34025320855639957,
              -0.42134036580728845
            ],
            "target_residual": 0.19550964982877134,
            "energy_eV": -39.13071290105179,
            "max_atomic_step_A": 0.04281181163145517,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5294724014643093,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0745723959403473,
              0.9860057601217543,
              0.9572197771983052
            ],
            "cell_volume_ratio": 1.014207447005977,
            "cell_rmsd_from_input_A": 0.41984242844770747
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.07464960257220235,
              0.37568663315147227,
              -0.45236823497563505
            ],
            "branch_aligned_reduced_polarization": [
              0.07464960257220235,
              0.37568663315147227,
              -0.45236823497563505
            ],
            "target_residual": 0.15262752497744536,
            "energy_eV": -37.48638514008991,
            "max_atomic_step_A": 0.04029383715871437,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6002827098616703,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.1064926397090935,
              0.9840295801379143,
              0.9465092711030827
            ],
            "cell_volume_ratio": 1.0305796326640764,
            "cell_rmsd_from_input_A": 0.5905813396698174
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.06740553104159505,
              0.3944326844958227,
              -0.46522254459217066
            ],
            "branch_aligned_reduced_polarization": [
              0.06740553104159505,
              0.3944326844958227,
              -0.46522254459217066
            ],
            "target_residual": 0.1299901347118369,
            "energy_eV": -35.51502482881584,
            "max_atomic_step_A": 0.09349053936234492,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9875831941644757,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.429090125205559,
            "cell_principal_stretches": [
              1.0753056885061008,
              0.983016784948965,
              0.9544566692725412
            ],
            "cell_volume_ratio": 1.0089022571827808,
            "cell_rmsd_from_input_A": 0.42592247613867873
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.05436724767847601,
              0.42525020216912535,
              -0.4801223530372926
            ],
            "branch_aligned_reduced_polarization": [
              0.05436724767847601,
              0.42525020216912535,
              -0.4801223530372926
            ],
            "target_residual": 0.09454338022655748,
            "energy_eV": -33.0562968423764
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.09454338022655748,
        "parent_symmetrization_rmsd_A": 0.3030163321874219,
        "parent_cell_rmsd_A": 0.42592247613867873,
        "energy_eV": -33.0562968423764,
        "reduced_polarization": [
          0.05436724767847601,
          0.42525020216912535,
          -0.4801223530372926
        ],
        "cartesian_polarization_e_A2": [
          0.0013980493487665265,
          0.013627601499697587,
          -0.010692012480260896
        ],
        "ranking_score": 1.0985837116752066
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.1988787573463614,
              0.0,
              -0.19887882575539967
            ],
            "target_residual": 0.6166253239294655,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015600073250149626,
            "step_scale": 0.4903663850824093,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.009680969175415,
              1.0019964154714054,
              0.9781901390270604
            ],
            "cell_volume_ratio": 0.989631747250502,
            "cell_rmsd_from_input_A": 0.11298200713359731
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.31651894605058056,
              0.23932501017502697,
              -0.07734860592721327
            ],
            "branch_aligned_reduced_polarization": [
              0.31651894605058056,
              0.23932501017502694,
              -0.07734860592721327
            ],
            "target_residual": 0.3280237099929255,
            "energy_eV": -40.870738870070966,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.019613252780180102,
            "step_scale": 0.7856342350967466,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0181599944797262,
              1.0019842586456296,
              0.9479228710266574
            ],
            "cell_volume_ratio": 0.9670522268561537,
            "cell_rmsd_from_input_A": 0.2575323462535211
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.46560458060165205,
              0.4453375712025756,
              -0.022387095654454518
            ],
            "branch_aligned_reduced_polarization": [
              0.46560458060165205,
              0.4453375712025756,
              -0.022387095654454518
            ],
            "target_residual": 0.06835355184233982,
            "energy_eV": -29.82996380214542,
            "max_atomic_step_A": 0.02576526052125539,
            "max_log_strain_component": 0.0027700206186006353,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.019696793052728,
              1.002382720416707,
              0.9440212134927687
            ],
            "cell_volume_ratio": 0.9649090473488025,
            "cell_rmsd_from_input_A": 0.2766557998876776
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5114739074498834,
              0.5118731348242321,
              -0.0005052000395236033
            ],
            "branch_aligned_reduced_polarization": [
              0.5114739074498834,
              0.5118731348242321,
              -0.0005052000395236033
            ],
            "target_residual": 0.016518992396717745,
            "energy_eV": -25.53553624619738,
            "max_atomic_step_A": 0.0050809636466458506,
            "max_log_strain_component": 0.0004299200235249372,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0199873689773817,
              1.0026440743434637,
              0.9444961334287694
            ],
            "cell_volume_ratio": 0.9659213589554182,
            "cell_rmsd_from_input_A": 0.27513492180836663
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49973205419954997,
              0.49992987978015835,
              0.00024307578934724435
            ],
            "branch_aligned_reduced_polarization": [
              0.49973205419954997,
              0.49992987978015835,
              0.00024307578934724435
            ],
            "target_residual": 0.0003685073087148143,
            "energy_eV": -26.386637366361086
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0003685073087148143,
        "parent_symmetrization_rmsd_A": 0.2045408362641266,
        "parent_cell_rmsd_A": 0.27513492180836663,
        "energy_eV": -26.386637366361086,
        "reduced_polarization": [
          0.49973205419954997,
          0.49992987978015835,
          0.00024307578934724435
        ],
        "cartesian_polarization_e_A2": [
          0.016279199558796066,
          0.016025076412857137,
          0.00012295941563561643
        ],
        "ranking_score": 0.774061581333648
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.19887875734636143,
              1.9635129146794677e-17,
              -0.19887882575539967
            ],
            "branch_aligned_reduced_polarization": [
              0.1988787573463614,
              0.0,
              -0.19887882575539967
            ],
            "target_residual": 0.6567708613783946,
            "energy_eV": -43.35684827871095,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013811714405921103,
            "step_scale": 0.4341518373932083,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.006986469492444,
              0.9939491736875332,
              0.9787210690855
            ],
            "cell_volume_ratio": 0.9795954284091375,
            "cell_rmsd_from_input_A": 0.10562613165754357
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.302307472673187,
              0.21180127822337955,
              -0.29417470639708676
            ],
            "branch_aligned_reduced_polarization": [
              0.302307472673187,
              0.21180127822337957,
              -0.29417470639708676
            ],
            "target_residual": 0.4055920241834965,
            "energy_eV": -41.37832198844889,
            "max_atomic_step_A": 0.11794924706932167,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6351436407816666,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.014226432996072,
              0.9815101911432763,
              0.9452172956082754
            ],
            "cell_volume_ratio": 0.9409388452434613,
            "cell_rmsd_from_input_A": 0.2626240328353013
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.41398084150055614,
              0.4075005164736894,
              -0.40951696347322486
            ],
            "branch_aligned_reduced_polarization": [
              0.41398084150055614,
              0.4075005164736894,
              -0.40951696347322486
            ],
            "target_residual": 0.1553789882213563,
            "energy_eV": -33.17838732937065,
            "max_atomic_step_A": 0.09380884905960087,
            "max_log_strain_component": 0.015564198312392441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0115133696345004,
              0.9682540884524617,
              0.9221166025533674
            ],
            "cell_volume_ratio": 0.9031228038992473,
            "cell_rmsd_from_input_A": 0.360132914529693
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5100274571874143,
              0.5261356340651152,
              -0.5152730844565532
            ],
            "branch_aligned_reduced_polarization": [
              0.5100274571874143,
              0.5261356340651152,
              -0.5152730844565532
            ],
            "target_residual": 0.03188868724874141,
            "energy_eV": -27.79610186407282,
            "max_atomic_step_A": 0.013132094225479425,
            "max_log_strain_component": 0.00219778870109843,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.7789079653410553,
            "cell_principal_stretches": [
              1.0114971639941717,
              0.9700774892189193,
              0.9248519290569327
            ],
            "cell_volume_ratio": 0.9074930402649272,
            "cell_rmsd_from_input_A": 0.3483733233858711
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4990593310988685,
              0.4983814142197221,
              -0.498315247165047
            ],
            "branch_aligned_reduced_polarization": [
              0.4990593310988685,
              0.4983814142197221,
              -0.498315247165047
            ],
            "target_residual": 0.002518545219875143,
            "energy_eV": -28.877247448589173,
            "max_atomic_step_A": 0.0009994683578212799,
            "max_log_strain_component": 0.00022009250610392712,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.614976806009607,
            "cell_principal_stretches": [
              1.0114340865513187,
              0.9699234603019208,
              0.9245332066381429
            ],
            "cell_volume_ratio": 0.9069796947537415,
            "cell_rmsd_from_input_A": 0.34963930368070884
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000015642447223,
              0.5000021866676817,
              -0.5000025334667264
            ],
            "branch_aligned_reduced_polarization": [
              0.5000015642447223,
              0.5000021866676817,
              -0.5000025334667264
            ],
            "target_residual": 3.6941617121180986e-06,
            "energy_eV": -28.821505148343558
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.6941617121180986e-06,
        "parent_symmetrization_rmsd_A": 0.31078947988733263,
        "parent_cell_rmsd_A": 0.34963930368070884,
        "energy_eV": -28.821505148343558,
        "reduced_polarization": [
          0.5000015642447223,
          0.5000021866676817,
          -0.5000025334667264
        ],
        "cartesian_polarization_e_A2": [
          0.017238342032954903,
          0.016710089973369504,
          -0.012093728082052965
        ],
        "ranking_score": 0.8982066941309341
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9
        ],
        "endpoint_rmsd_A": 0.3859972172954355,
        "minimum_distance_A_by_image": [
          1.837452495221092,
          1.8942848791326654,
          1.9520442208359015,
          2.0106506366245647,
          2.070032181076042,
          2.1301240303075915,
          2.1908677376713133,
          2.2522105605639813,
          2.3141048549999996
        ],
        "minimum_distance_A": 1.837452495221092,
        "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": [
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099,
          198.1432227935099
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.260680033796644e-16,
        -7.002621097504286e-17,
        -1.384128813708579e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -43.356848278710956,
          -43.04769011023859,
          -42.3649640912855,
          -41.399537437318926,
          -40.234907060701,
          -39.00100456497412,
          -37.89361786923028,
          -37.12426836345416,
          -36.848992538786966
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00677704130310598,
            -1.0560268539632244e-17,
            -0.004643339553637103
          ],
          [
            0.004320445836991562,
            -1.0664837803657448e-17,
            -0.0029601856420964803
          ],
          [
            0.0019115810190033615,
            -3.226968760286115e-17,
            -0.0013097346786870826
          ],
          [
            -5.432278208313968e-05,
            -1.3128190839416842e-17,
            3.721836043342379e-05
          ],
          [
            -0.0013145582297103527,
            -1.7002138326992063e-18,
            0.0009006776177876186
          ],
          [
            -0.0018070610930666915,
            -4.973440770812037e-17,
            0.0012381194337323345
          ],
          [
            -0.001624757663751956,
            -2.1741773564905257e-19,
            0.0011132131090491823
          ],
          [
            -0.0009424466907853751,
            2.703563098635579e-17,
            0.0006457233602596493
          ],
          [
            1.8522122505762604e-17,
            -2.2884839567181156e-18,
            -3.231606001096549e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.001594155135438057,
            -4.0171461929757624e-16,
            0.001594099189610773
          ],
          [
            -0.03857696967123021,
            -5.202550457116708e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.652849884126144e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.0015941551354380565,
            -4.017146192975763e-16,
            0.0015940991896107731
          ],
          [
            -0.03857696967123021,
            -5.2025504571167077e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.6528498841260944e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.273559366969494e-16,
            -7.00262109750428e-17,
            -1.384309333829492e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1988787573463615,
            -3.3306690738754696e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.3306690738754696e-16,
            -0.12678767893616616
          ],
          [
            0.05609717206204534,
            -9.992007221626409e-16,
            -0.05609723173149839
          ],
          [
            -0.0015941551354380357,
            -3.885780586188048e-16,
            0.0015940991896107315
          ],
          [
            -0.0385769696712302,
            -5.551115123125783e-17,
            0.03857691321959522
          ],
          [
            -0.05302993725342375,
            -1.4988010832439613e-15,
            0.053029879956281056
          ],
          [
            -0.047680068614592286,
            0.0,
            0.047680018526709333
          ],
          [
            -0.027657000126060982,
            7.771561172376096e-16,
            0.02765697019738278
          ],
          [
            5.551115123125783e-16,
            -5.551115123125783e-17,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -36.848992538786966,
          -37.12426836345417,
          -37.8936178692303,
          -39.00100456497411,
          -40.234907060701,
          -41.399537437318926,
          -42.36496409128549,
          -43.0476901102386,
          -43.356848278710956
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8522122505762604e-17,
            -2.2884839567181156e-18,
            -3.231606001096549e-17
          ],
          [
            0.000942446690785255,
            9.185646139882419e-18,
            -0.000645723360259661
          ],
          [
            0.0016247576637518494,
            -4.563841581149064e-18,
            -0.0011132131090491235
          ],
          [
            0.00180706109306681,
            7.165496452559035e-18,
            -0.0012381194337324445
          ],
          [
            0.0013145582297103906,
            -2.8691379706104017e-17,
            -0.0009006776177876498
          ],
          [
            5.432278208310846e-05,
            -7.798180518742289e-17,
            -3.721836043350014e-05
          ],
          [
            -0.0019115810190032537,
            -1.0789701098324499e-16,
            0.0013097346786872129
          ],
          [
            -0.0043204458369915395,
            -1.0658922527510575e-17,
            0.0029601856420965337
          ],
          [
            -0.00677704130310595,
            3.0865265528918293e-17,
            0.00464333955363714
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135155e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370536,
            -2.3861955974121773e-15,
            -0.001594099189614043
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001273e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135157e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370503,
            -2.3861955974121773e-15,
            -0.0015940991896140413
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001274e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.19887875734636043,
          1.8308534379151734e-16,
          0.19887882575539695
        ],
        "actual_opposite_endpoint_branch_residual": 4.45314653732767e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.001594155135438057,
            -4.0171461929757624e-16,
            0.001594099189610773
          ],
          [
            -0.03857696967123021,
            -5.202550457116708e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.652849884126144e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.260680033796644e-16,
            -7.002621097504286e-17,
            -1.384128813708579e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135155e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370536,
            -2.3861955974121773e-15,
            -0.001594099189614043
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001273e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.1988787573463615,
            -3.231377657416031e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.2633752133640965e-16,
            -0.12678767893616613
          ],
          [
            0.05609717206204537,
            -9.874327261692148e-16,
            -0.05609723173149836
          ],
          [
            -0.0015941551354380565,
            -4.017146192975763e-16,
            0.0015940991896107731
          ],
          [
            -0.03857696967123021,
            -5.2025504571167077e-17,
            0.03857691321959517
          ],
          [
            -0.05302993725342374,
            -1.5218424916913756e-15,
            0.053029879956281036
          ],
          [
            -0.04768006861459226,
            -6.6528498841260944e-18,
            0.04768001852670929
          ],
          [
            -0.02765700012606097,
            8.272737913395617e-16,
            0.027656970197382776
          ],
          [
            5.273559366969494e-16,
            -7.00262109750428e-17,
            -1.384309333829492e-15
          ],
          [
            0.02765700012605736,
            2.810751601055358e-16,
            -0.02765697019738328
          ],
          [
            0.04768006861458911,
            -1.3965076420135157e-16,
            -0.04768001852670677
          ],
          [
            0.05302993725342719,
            2.1925981384086501e-16,
            -0.05302987995628574
          ],
          [
            0.03857696967123132,
            -8.779386906194425e-16,
            -0.03857691321959651
          ],
          [
            0.0015941551354370503,
            -2.3861955974121773e-15,
            -0.0015940991896140413
          ],
          [
            -0.05609717206204203,
            -3.3015826187065093e-15,
            0.056097231731503945
          ],
          [
            -0.12678761392447674,
            -3.261565175001274e-16,
            0.1267876789361684
          ],
          [
            -0.19887875734636057,
            9.444582687083169e-16,
            0.19887882575540133
          ]
        ],
        "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": [
          [
            0.1988787573463615,
            -3.3306690738754696e-16,
            -0.19887882575539972
          ],
          [
            0.12678761392447746,
            -3.3306690738754696e-16,
            -0.12678767893616616
          ],
          [
            0.05609717206204534,
            -9.992007221626409e-16,
            -0.05609723173149839
          ],
          [
            -0.0015941551354380357,
            -3.885780586188048e-16,
            0.0015940991896107315
          ],
          [
            -0.0385769696712302,
            -5.551115123125783e-17,
            0.03857691321959522
          ],
          [
            -0.05302993725342375,
            -1.4988010832439613e-15,
            0.053029879956281056
          ],
          [
            -0.047680068614592286,
            0.0,
            0.047680018526709333
          ],
          [
            -0.027657000126060982,
            7.771561172376096e-16,
            0.02765697019738278
          ],
          [
            5.551115123125783e-16,
            -5.551115123125783e-17,
            -1.3877787807814457e-15
          ],
          [
            0.02765700012605732,
            3.3306690738754696e-16,
            -0.02765697019738328
          ],
          [
            0.047680068614589066,
            -1.6653345369377348e-16,
            -0.04768001852670678
          ],
          [
            0.053029937253427195,
            2.220446049250313e-16,
            -0.05302987995628572
          ],
          [
            0.038576969671231365,
            -8.881784197001252e-16,
            -0.0385769132195965
          ],
          [
            0.0015941551354370365,
            -2.3869795029440866e-15,
            -0.0015940991896140622
          ],
          [
            -0.05609717206204201,
            -3.2751579226442118e-15,
            0.05609723173150394
          ],
          [
            -0.12678761392447674,
            -3.3306690738754696e-16,
            0.12678767893616838
          ],
          [
            -0.19887875734636057,
            9.992007221626409e-16,
            0.19887882575540128
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "R-3m",
        "spacegroup_number": 166,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.6850989848337e-16,
        "parent_symmetrization_rmsd_A": 0.3859972172954355,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.848992538786966,
        "reduced_polarization": [
          -5.088636672873386e-16,
          -1.544817764427371e-16,
          4.0509089502508265e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.7268119750162572e-17,
          -5.048524860505663e-18,
          9.457892606433754e-18
        ],
        "ranking_score": 0.38599721729543685
      }
    }
  ],
  "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": 99,
      "full_response": 31,
      "energy_polarization": 68
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 124,
      "full_response": 56,
      "energy_polarization": 68
    },
    "elapsed_seconds": 176.07468127500033
  }
}
