{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 12,
  "input_formula": "O8Si4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -90.71732746532835,
  "input_cartesian_polarization_e_A2": [
    -2.3365500670048072e-17,
    3.824140862528326e-18,
    -0.00023275926238032284
  ],
  "input_reduced_polarization": [
    -8.338363315704651e-16,
    9.852701219057511e-17,
    -0.008334749459464321
  ],
  "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.063439803625994e-16,
      "parent_symmetrization_rmsd_A": 0.30812667085425327,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -90.0139517088898,
      "reduced_polarization": [
        8.775069741404403e-16,
        2.266121280383228e-16,
        -9.373606581849255e-18
      ],
      "cartesian_polarization_e_A2": [
        2.4589225746057137e-17,
        8.79552398381515e-18,
        -2.617707664094317e-19
      ],
      "ranking_score": 0.3081266708542551
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnna",
      "spacegroup_number": 52,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.981354800862234e-16,
      "parent_symmetrization_rmsd_A": 0.4791551917046393,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -88.73815177259776,
      "reduced_polarization": [
        8.028186183953302e-17,
        7.496127748608651e-17,
        7.9054150688607e-16
      ],
      "cartesian_polarization_e_A2": [
        2.2496332020833698e-18,
        2.9094811460170263e-18,
        2.207695131314202e-17
      ],
      "ranking_score": 0.47915519170464094
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 4.708162004576804e-15,
      "parent_symmetrization_rmsd_A": 0.5242437507354379,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -78.83217608455737,
      "reduced_polarization": [
        -4.676508831590161e-15,
        3.152864390098404e-16,
        -4.445774069567559e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.3104366660565884e-16,
        1.2237250760090644e-17,
        -1.2415431299702414e-17
      ],
      "ranking_score": 0.5242437507354474
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.6880918589546174e-06,
      "parent_symmetrization_rmsd_A": 0.0018609796482196175,
      "parent_cell_rmsd_A": 0.00015376518772937254,
      "energy_eV": -90.71686372296294,
      "reduced_polarization": [
        1.7536460159236677e-15,
        1.6394516563744094e-15,
        3.6880918589546174e-06
      ],
      "cartesian_polarization_e_A2": [
        4.9140345384094324e-17,
        6.363387915885833e-17,
        1.0299245454730275e-07
      ],
      "ranking_score": 0.5019067971288699
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.222695621741417e-16,
      "parent_symmetrization_rmsd_A": 0.30812667187567594,
      "parent_cell_rmsd_A": 0.00015376518772937254,
      "energy_eV": -90.01397354864726,
      "reduced_polarization": [
        -6.536937451166018e-16,
        -3.014857459711352e-16,
        -5.885705577826368e-17
      ],
      "cartesian_polarization_e_A2": [
        -1.831768516652232e-17,
        -1.1701903258780438e-17,
        -1.6436230099076502e-18
      ],
      "ranking_score": 0.30816511317260975
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnna",
      "spacegroup_number": 52,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.150414826167894e-16,
      "parent_symmetrization_rmsd_A": 0.4791551929332506,
      "parent_cell_rmsd_A": 0.00015376518772937254,
      "energy_eV": -88.7380855494752,
      "reduced_polarization": [
        7.892377451941173e-16,
        -1.0877861031863203e-16,
        -1.719407278227794e-16
      ],
      "cartesian_polarization_e_A2": [
        2.2115874055706397e-17,
        -4.222145794896319e-18,
        -4.801560880898783e-18
      ],
      "ranking_score": 0.4791936342301846
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.693660937009735e-05,
      "parent_symmetrization_rmsd_A": 0.11371918641569408,
      "parent_cell_rmsd_A": 0.009435760934133725,
      "energy_eV": -89.42804774285834,
      "reduced_polarization": [
        2.203889677695999e-15,
        -1.5288302796882546e-15,
        -0.4999630633906299
      ],
      "cartesian_polarization_e_A2": [
        7.008465304080072e-17,
        1.9652761409149793e-17,
        -0.013983374393515886
      ],
      "ranking_score": 0.6161519998679676
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.5802556111935816e-06,
      "parent_symmetrization_rmsd_A": 0.11725367553993164,
      "parent_cell_rmsd_A": 0.005071254149249895,
      "energy_eV": -89.13493162405322,
      "reduced_polarization": [
        -0.4999978579159519,
        -1.6507247704205219e-15,
        2.868746446172039e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.014010862276247593,
        -1.5694320310935736e-16,
        1.705438733183917e-05
      ],
      "ranking_score": 0.6185286495884665
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00021055727824079832,
      "parent_symmetrization_rmsd_A": 0.15931720516852318,
      "parent_cell_rmsd_A": 0.016101270424382256,
      "energy_eV": -87.72646565759558,
      "reduced_polarization": [
        -4.57303163266694e-15,
        0.49982773692169824,
        -0.00012107765803059924
      ],
      "cartesian_polarization_e_A2": [
        1.3767049779705643e-18,
        0.019401814973747673,
        5.048023969593595e-05
      ],
      "ranking_score": 0.6637636373311003
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0006330496368161695,
      "parent_symmetrization_rmsd_A": 0.16453210655827483,
      "parent_cell_rmsd_A": 0.010950386904267818,
      "energy_eV": -87.59727891822759,
      "reduced_polarization": [
        -0.499799688415323,
        7.439815013084037e-16,
        -0.49939947763429055
      ],
      "cartesian_polarization_e_A2": [
        -0.013984305077502516,
        -6.041092432937275e-17,
        -0.013951248804351496
      ],
      "ranking_score": 0.6685358025579742
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 7.18476304364247e-06,
      "parent_symmetrization_rmsd_A": 0.1954762825928074,
      "parent_cell_rmsd_A": 0.018691986551879012,
      "energy_eV": -84.96493169213002,
      "reduced_polarization": [
        -1.7340270563133655e-15,
        0.49999854263436827,
        -0.4999929645962867
      ],
      "cartesian_polarization_e_A2": [
        1.7343308967121096e-16,
        0.019336746769002783,
        -0.013931036242612408
      ],
      "ranking_score": 0.7001636487568644
    },
    {
      "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": 1.18188038861018e-05,
      "parent_symmetrization_rmsd_A": 0.20261030088069643,
      "parent_cell_rmsd_A": 0.017540862936962925,
      "energy_eV": -85.34602740822642,
      "reduced_polarization": [
        -0.4999893453206743,
        0.49999550956902583,
        -2.449073994541734e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.014010894947204915,
        0.019408851963652378,
        7.371955428284182e-05
      ],
      "ranking_score": 0.7070191542227093
    },
    {
      "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": 3.3455585190735026e-05,
      "parent_symmetrization_rmsd_A": 0.2321623150200121,
      "parent_cell_rmsd_A": 0.019856502371726717,
      "energy_eV": -82.1853183151372,
      "reduced_polarization": [
        -0.49999240539903894,
        0.49998863322174797,
        -0.4999694648633724
      ],
      "cartesian_polarization_e_A2": [
        -0.013988849024134182,
        0.019334847320304348,
        -0.013911637250671672
      ],
      "ranking_score": 0.7371933517833252
    }
  ],
  "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "target_residual": 0.008334749459464321,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.0015059449910460386,
            "max_log_strain_component": 2.749141147523942e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0000229242414183,
              1.0000018140799487,
              0.9999725089664102
            ],
            "cell_volume_ratio": 0.9999972466492805,
            "cell_rmsd_from_input_A": 0.00015376518772937254
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.7536460159236677e-15,
              1.6394516563744094e-15,
              3.6880918589546174e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.7536460159236677e-15,
              1.6394516563744094e-15,
              3.6880918589546174e-06
            ],
            "target_residual": 3.6880918589546174e-06,
            "energy_eV": -90.71686372296294
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.063439803625994e-16,
        "parent_symmetrization_rmsd_A": 0.30812667085425327,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -90.0139517088898,
        "reduced_polarization": [
          8.775069741404403e-16,
          2.266121280383228e-16,
          -9.373606581849255e-18
        ],
        "cartesian_polarization_e_A2": [
          2.4589225746057137e-17,
          8.79552398381515e-18,
          -2.617707664094317e-19
        ],
        "ranking_score": 0.3081266708542551
      },
      "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": [
          -90.71732746532837,
          -90.67201467905902,
          -90.57878713709253,
          -90.45653739365177,
          -90.32451438771926,
          -90.20094597636458,
          -90.10110204994403,
          -90.03636681477532,
          -90.01395170888982
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.397761991907575e-18,
            9.02497243556685e-18,
            -0.00023275926238033943
          ],
          [
            3.935040947541648e-17,
            2.6271847725569602e-17,
            -0.00018221804117658904
          ],
          [
            2.894874632933943e-17,
            1.7208633881377468e-17,
            -0.00014700065224147813
          ],
          [
            1.8126427688384265e-17,
            2.936940182421755e-17,
            -0.00012069673425723837
          ],
          [
            4.5010137951958396e-17,
            3.097554098647944e-17,
            -9.79986757965265e-05
          ],
          [
            2.9866540136346225e-17,
            3.036367844847491e-17,
            -7.546108174287477e-05
          ],
          [
            -1.7055668246876336e-17,
            -9.02497243556685e-18,
            -5.1753613166118354e-05
          ],
          [
            3.4684957623131917e-17,
            2.447450152018129e-17,
            -2.651679740499679e-05
          ],
          [
            3.690295932339835e-17,
            1.4225804008605374e-17,
            7.579471201885661e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.404284100140767e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190302e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427362e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.714091497665893e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.4042841001407668e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190301e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427364e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.710505431213761e-17
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            2.220446049250313e-16,
            -0.00833474945946494
          ],
          [
            1.4432899320127035e-15,
            6.661338147750939e-16,
            -0.006524946438950463
          ],
          [
            9.992007221626409e-16,
            4.440892098500626e-16,
            -0.005263866169194997
          ],
          [
            6.661338147750939e-16,
            7.771561172376096e-16,
            -0.004321963518538252
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.0035091811246106275
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            -0.0027021447131042042
          ],
          [
            -6.106226635438361e-16,
            -2.220446049250313e-16,
            -0.0018532169029510381
          ],
          [
            1.2212453270876722e-15,
            6.661338147750939e-16,
            -0.0009495255337116926
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -90.0139517088898,
          -90.03636681477533,
          -90.10110204994402,
          -90.20094597636458,
          -90.32451438771928,
          -90.45653739365177,
          -90.57878713709252,
          -90.67201467905902,
          -90.71732746532837
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.109026521235529e-17,
            2.2485948271666556e-17,
            4.915388632075834e-18
          ],
          [
            7.648281725056652e-20,
            5.430280024790223e-17,
            2.6516797405024906e-05
          ],
          [
            -4.359520583282292e-18,
            9.942766242573647e-19,
            5.175361316615141e-05
          ],
          [
            4.3289274563820654e-17,
            7.418833273304953e-18,
            7.546108174287686e-05
          ],
          [
            4.952262416974182e-17,
            3.181685197623567e-17,
            9.799867579655277e-05
          ],
          [
            3.2046300427987374e-17,
            3.1243230846856425e-17,
            0.00012069673425727393
          ],
          [
            3.7935477356280995e-17,
            1.4264045417230658e-17,
            0.0001470006522414969
          ],
          [
            5.889176928293622e-17,
            2.2485948271666556e-17,
            0.0001822180411765616
          ],
          [
            3.082257535197831e-17,
            1.3422734427474425e-17,
            0.00023275926238034661
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1095072627934338e-15,
            5.793388316805817e-16,
            1.7601247024623046e-16
          ],
          [
            2.7294151606234536e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.561702316954953e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1095072627934338e-15,
            5.793388316805817e-16,
            1.7601247024623046e-16
          ],
          [
            2.7294151606233746e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.5617023169549592e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.4769442582657844e-15,
          5.005172219281217e-16,
          0.008334749459464968
        ],
        "actual_opposite_endpoint_branch_residual": 1.4004368421540665e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.404284100140767e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190302e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427362e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.714091497665893e-17
          ],
          [
            2.7294151606234536e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.561702316954953e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.4042841001407668e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190301e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427364e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.710505431213761e-17
          ],
          [
            2.7294151606233746e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.5617023169549592e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            2.220446049250313e-16,
            -0.00833474945946494
          ],
          [
            1.4432899320127035e-15,
            6.661338147750939e-16,
            -0.006524946438950463
          ],
          [
            9.992007221626409e-16,
            4.440892098500626e-16,
            -0.005263866169194997
          ],
          [
            6.661338147750939e-16,
            7.771561172376096e-16,
            -0.004321963518538252
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.0035091811246106275
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            -0.0027021447131042042
          ],
          [
            -6.106226635438361e-16,
            -2.220446049250313e-16,
            -0.0018532169029510381
          ],
          [
            1.2212453270876722e-15,
            6.661338147750939e-16,
            -0.0009495255337116926
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.0
          ],
          [
            0.0,
            1.4432899320127035e-15,
            0.0009495255337127473
          ],
          [
            -1.6653345369377348e-16,
            0.0,
            0.0018532169029522594
          ],
          [
            1.5543122344752192e-15,
            2.220446049250313e-16,
            0.0027021447131042597
          ],
          [
            1.7763568394002505e-15,
            7.771561172376096e-16,
            0.0035091811246115157
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            0.004321963518539529
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.005263866169195719
          ],
          [
            2.1094237467877974e-15,
            5.551115123125783e-16,
            0.006524946438949519
          ],
          [
            1.1102230246251565e-15,
            3.3306690738754696e-16,
            0.008334749459465218
          ]
        ]
      },
      "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.00833474945946433
            ],
            "target_residual": 0.49166525054053567,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.08883540230260298,
            "max_log_strain_component": 0.0016217130192603612,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0016230287069454,
              0.9998929935991021,
              0.9986486328745957
            ],
            "cell_volume_ratio": 1.0001624330381746,
            "cell_rmsd_from_input_A": 0.009065761957306444
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.113084814623076e-15,
              -1.981834043979752e-15,
              -0.4829028279166694
            ],
            "branch_aligned_reduced_polarization": [
              -2.113084814623076e-15,
              -1.981834043979752e-15,
              -0.4829028279166694
            ],
            "target_residual": 0.017097172083330614,
            "energy_eV": -89.51788039453263,
            "max_atomic_step_A": 0.0033398201386788044,
            "max_log_strain_component": 6.622246716431976e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0016893608513897,
              0.9998886242482031,
              0.9985934887768884
            ],
            "cell_volume_ratio": 1.0001690665335337,
            "cell_rmsd_from_input_A": 0.009435760934133725
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.203889677695999e-15,
              -1.5288302796882546e-15,
              -0.4999630633906299
            ],
            "branch_aligned_reduced_polarization": [
              2.203889677695999e-15,
              -1.5288302796882546e-15,
              -0.4999630633906299
            ],
            "target_residual": 3.693660937009735e-05,
            "energy_eV": -89.42804774285834
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.693660937009735e-05,
        "parent_symmetrization_rmsd_A": 0.11371918641569408,
        "parent_cell_rmsd_A": 0.009435760934133725,
        "energy_eV": -89.42804774285834,
        "reduced_polarization": [
          2.203889677695999e-15,
          -1.5288302796882546e-15,
          -0.4999630633906299
        ],
        "cartesian_polarization_e_A2": [
          7.008465304080072e-17,
          1.9652761409149793e-17,
          -0.013983374393515886
        ],
        "ranking_score": 0.6161519998679676
      },
      "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.326672684688674e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "target_residual": 0.5000694632234118,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.09390960573908794,
            "max_log_strain_component": 0.0011981733608449683,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.001186127179931,
              1.0000229242414158,
              0.9987896314675684
            ],
            "cell_volume_ratio": 0.9999972466492751,
            "cell_rmsd_from_input_A": 0.005015083872602838
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49478099183012947,
              3.1001342742400364e-15,
              -0.0004180753514940278
            ],
            "branch_aligned_reduced_polarization": [
              -0.49478099183012947,
              3.1001342742400364e-15,
              -0.0004180753514940278
            ],
            "target_residual": 0.005235726623564509,
            "energy_eV": -89.17070616583092,
            "max_atomic_step_A": 0.0010541353517242997,
            "max_log_strain_component": 1.3355532384739556e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.00119861825041,
              1.0000245153333018,
              0.9987753904801766
            ],
            "cell_volume_ratio": 0.9999970555513991,
            "cell_rmsd_from_input_A": 0.005071254149249895
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999978579159519,
              -1.6507247704205219e-15,
              2.868746446172039e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999978579159519,
              -1.6507247704205219e-15,
              2.868746446172039e-06
            ],
            "target_residual": 3.5802556111935816e-06,
            "energy_eV": -89.13493162405322
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.5802556111935816e-06,
        "parent_symmetrization_rmsd_A": 0.11725367553993164,
        "parent_cell_rmsd_A": 0.005071254149249895,
        "energy_eV": -89.13493162405322,
        "reduced_polarization": [
          -0.4999978579159519,
          -1.6507247704205219e-15,
          2.868746446172039e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.014010862276247593,
          -1.5694320310935736e-16,
          1.705438733183917e-05
        ],
        "ranking_score": 0.6185286495884665
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.338363315704651e-16,
              1.1102230246251565e-16,
              -0.008334749459464321
            ],
            "target_residual": 0.5000694632234125,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002567858009158514,
            "step_scale": 0.9525671976519633,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.002569089350233,
              1.0000017280329814,
              0.997433154328437
            ],
            "cell_volume_ratio": 0.9999973772482548,
            "cell_rmsd_from_input_A": 0.014881770067656194
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.069271224495243e-16,
              0.4668342436183358,
              -0.01881936833174213
            ],
            "branch_aligned_reduced_polarization": [
              -6.069271224495243e-16,
              0.4668342436183358,
              -0.01881936833174213
            ],
            "target_residual": 0.038133135470004006,
            "energy_eV": -88.11778005984347,
            "max_atomic_step_A": 0.009773350905640193,
            "max_log_strain_component": 0.000208678791858801,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0027734004347444,
              1.0000068281557972,
              0.9972171260663641
            ],
            "cell_volume_ratio": 0.9999896365157422,
            "cell_rmsd_from_input_A": 0.016101270424382256
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.57303163266694e-15,
              0.49982773692169824,
              -0.00012107765803059924
            ],
            "branch_aligned_reduced_polarization": [
              -4.57303163266694e-15,
              0.49982773692169824,
              -0.00012107765803059924
            ],
            "target_residual": 0.00021055727824079832,
            "energy_eV": -87.72646565759558
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00021055727824079832,
        "parent_symmetrization_rmsd_A": 0.15931720516852318,
        "parent_cell_rmsd_A": 0.016101270424382256,
        "energy_eV": -87.72646565759558,
        "reduced_polarization": [
          -4.57303163266694e-15,
          0.49982773692169824,
          -0.00012107765803059924
        ],
        "cartesian_polarization_e_A2": [
          1.3767049779705643e-18,
          0.019401814973747673,
          5.048023969593595e-05
        ],
        "ranking_score": 0.6637636373311003
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.326672684688674e-16,
              9.852701219057511e-17,
              -0.00833474945946433
            ],
            "target_residual": 0.7012379899785001,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0015020227178119483,
            "step_scale": 0.9261951405546496,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0020719683809525,
              0.9993333061305696,
              0.9987483078879479
            ],
            "cell_volume_ratio": 1.0001504437888793,
            "cell_rmsd_from_input_A": 0.009599843086277714
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.46187746821881853,
              2.28401281148603e-15,
              -0.44199360562793943
            ],
            "branch_aligned_reduced_polarization": [
              -0.46187746821881853,
              2.28401281148603e-15,
              -0.44199360562793943
            ],
            "target_residual": 0.06941231315447001,
            "energy_eV": -88.20133093668382,
            "max_atomic_step_A": 0.013787985081296306,
            "max_log_strain_component": 0.00023347755740623976,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0023370191237277,
              0.9992869414639746,
              0.9985538829898879
            ],
            "cell_volume_ratio": 1.0001738311189803,
            "cell_rmsd_from_input_A": 0.010950386904267818
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.499799688415323,
              7.439815013084037e-16,
              -0.49939947763429055
            ],
            "branch_aligned_reduced_polarization": [
              -0.499799688415323,
              7.439815013084037e-16,
              -0.49939947763429055
            ],
            "target_residual": 0.0006330496368161695,
            "energy_eV": -87.59727891822759
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0006330496368161695,
        "parent_symmetrization_rmsd_A": 0.16453210655827483,
        "parent_cell_rmsd_A": 0.010950386904267818,
        "energy_eV": -87.59727891822759,
        "reduced_polarization": [
          -0.499799688415323,
          7.439815013084037e-16,
          -0.49939947763429055
        ],
        "cartesian_polarization_e_A2": [
          -0.013984305077502516,
          -6.041092432937275e-17,
          -0.013951248804351496
        ],
        "ranking_score": 0.6685358025579742
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.338363315704651e-16,
              1.1102230246251565e-16,
              -0.00833474945946433
            ],
            "target_residual": 0.7012379899785005,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0020974421068673537,
            "step_scale": 0.7780627055133371,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0025033284466354,
              0.999916741321538,
              0.9977120559742014
            ],
            "cell_volume_ratio": 1.00012638081125,
            "cell_rmsd_from_input_A": 0.014048643476871457
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.146944945015449e-15,
              0.3863821242163684,
              -0.3854412853803358
            ],
            "branch_aligned_reduced_polarization": [
              -7.146944945015449e-15,
              0.3863821242163684,
              -0.3854412853803358
            ],
            "target_residual": 0.16134658593504358,
            "energy_eV": -87.71762029798073,
            "max_atomic_step_A": 0.03887264063222166,
            "max_log_strain_component": 0.0006555815902551641,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0033131319320534,
              0.9998874898202988,
              0.9969802039281658
            ],
            "cell_volume_ratio": 1.0001707888201163,
            "cell_rmsd_from_input_A": 0.018575727348890642
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.874865502603208e-15,
              0.4979801779410674,
              -0.4958561587482205
            ],
            "branch_aligned_reduced_polarization": [
              4.874865502603208e-15,
              0.4979801779410674,
              -0.4958561587482205
            ],
            "target_residual": 0.004609891698261506,
            "energy_eV": -85.04815339502002,
            "max_atomic_step_A": 0.0010913174932634855,
            "max_log_strain_component": 1.8386155053691027e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0033341866966197,
              0.9998862767086294,
              0.9969623278991605
            ],
            "cell_volume_ratio": 1.000172630569695,
            "cell_rmsd_from_input_A": 0.018691986551879012
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.7340270563133655e-15,
              0.49999854263436827,
              -0.4999929645962867
            ],
            "branch_aligned_reduced_polarization": [
              -1.7340270563133655e-15,
              0.49999854263436827,
              -0.4999929645962867
            ],
            "target_residual": 7.18476304364247e-06,
            "energy_eV": -84.96493169213002
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 7.18476304364247e-06,
        "parent_symmetrization_rmsd_A": 0.1954762825928074,
        "parent_cell_rmsd_A": 0.018691986551879012,
        "energy_eV": -84.96493169213002,
        "reduced_polarization": [
          -1.7340270563133655e-15,
          0.49999854263436827,
          -0.4999929645962867
        ],
        "cartesian_polarization_e_A2": [
          1.7343308967121096e-16,
          0.019336746769002783,
          -0.013931036242612408
        ],
        "ranking_score": 0.7001636487568644
      },
      "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.326672684688674e-16,
              1.1102230246251565e-16,
              -0.008334749459464321
            ],
            "target_residual": 0.707155900808691,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0020249943165123463,
            "step_scale": 0.7511876258194421,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0022155145162581,
              1.0000039784863324,
              0.9977833497585558
            ],
            "cell_volume_ratio": 0.9999979317163015,
            "cell_rmsd_from_input_A": 0.012324925872599394
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3682356749571244,
              0.36758892082364064,
              -0.014194812756546809
            ],
            "branch_aligned_reduced_polarization": [
              -0.3682356749571244,
              0.36758892082364064,
              -0.014194812756546809
            ],
            "target_residual": 0.18733932836392392,
            "energy_eV": -88.14220019632361,
            "max_atomic_step_A": 0.04722468542990774,
            "max_log_strain_component": 0.0008231088818118399,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0031044969825524,
              1.0000230409126265,
              0.9968701567200561
            ],
            "cell_volume_ratio": 0.9999879772183357,
            "cell_rmsd_from_input_A": 0.017342962194805238
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.495244616292752,
              0.495663569153147,
              -0.002066230263413129
            ],
            "branch_aligned_reduced_polarization": [
              -0.495244616292752,
              0.495663569153147,
              -0.002066230263413129
            ],
            "target_residual": 0.00675926136453843,
            "energy_eV": -85.46524361759533,
            "max_atomic_step_A": 0.001818639637616574,
            "max_log_strain_component": 3.191798448998348e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0031388174248492,
              1.000025007246745,
              0.9968330798619424
            ],
            "cell_volume_ratio": 0.9999869631980717,
            "cell_rmsd_from_input_A": 0.017540862936962925
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999893453206743,
              0.49999550956902583,
              -2.449073994541734e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999893453206743,
              0.49999550956902583,
              -2.449073994541734e-06
            ],
            "target_residual": 1.18188038861018e-05,
            "energy_eV": -85.34602740822642
          }
        ],
        "iterations": 3
      },
      "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": 1.18188038861018e-05,
        "parent_symmetrization_rmsd_A": 0.20261030088069643,
        "parent_cell_rmsd_A": 0.017540862936962925,
        "energy_eV": -85.34602740822642,
        "reduced_polarization": [
          -0.4999893453206743,
          0.49999550956902583,
          -2.449073994541734e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.014010894947204915,
          0.019408851963652378,
          7.371955428284182e-05
        ],
        "ranking_score": 0.7070191542227093
      },
      "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": [
              -8.338363315704651e-16,
              9.852701219057511e-17,
              -0.008334749459464321
            ],
            "branch_aligned_reduced_polarization": [
              -8.326672684688674e-16,
              1.1102230246251565e-16,
              -0.00833474945946433
            ],
            "target_residual": 0.8612402211863347,
            "energy_eV": -90.71732746532835,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0017684772773215952,
            "step_scale": 0.6560306053389691,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0023067923833673,
              0.9998206859218673,
              0.9979837820288066
            ],
            "cell_volume_ratio": 1.0001065580676887,
            "cell_rmsd_from_input_A": 0.012295405489208884
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3253743055882421,
              0.3250441803688633,
              -0.3262206364166491
            ],
            "branch_aligned_reduced_polarization": [
              -0.3253743055882421,
              0.3250441803688633,
              -0.3262206364166491
            ],
            "target_residual": 0.30216376218703983,
            "energy_eV": -87.87765691428484,
            "max_atomic_step_A": 0.06852433841775453,
            "max_log_strain_component": 0.001018051535376441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0036627266037055,
              0.9997099878400152,
              0.9968110372809679
            ],
            "cell_volume_ratio": 1.0001719374162399,
            "cell_rmsd_from_input_A": 0.019491016111781227
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49311367558523483,
              0.49288996782736494,
              -0.4915712451454006
            ],
            "branch_aligned_reduced_polarization": [
              -0.49311367558523483,
              0.49288996782736494,
              -0.4915712451454006
            ],
            "target_residual": 0.013000689590949742,
            "energy_eV": -82.53292018447547,
            "max_atomic_step_A": 0.003209561807169826,
            "max_log_strain_component": 4.8920300089049536e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6734511637493392,
            "cell_principal_stretches": [
              1.0037316836581305,
              0.9997037907296885,
              0.9967525886037171
            ],
            "cell_volume_ratio": 1.0001758048231202,
            "cell_rmsd_from_input_A": 0.019856502371726717
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999240539903894,
              0.49998863322174797,
              -0.4999694648633724
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999240539903894,
              0.49998863322174797,
              -0.4999694648633724
            ],
            "target_residual": 3.3455585190735026e-05,
            "energy_eV": -82.1853183151372
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.3455585190735026e-05,
        "parent_symmetrization_rmsd_A": 0.2321623150200121,
        "parent_cell_rmsd_A": 0.019856502371726717,
        "energy_eV": -82.1853183151372,
        "reduced_polarization": [
          -0.49999240539903894,
          0.49998863322174797,
          -0.4999694648633724
        ],
        "cartesian_polarization_e_A2": [
          -0.013988849024134182,
          0.019334847320304348,
          -0.013911637250671672
        ],
        "ranking_score": 0.7371933517833252
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11
        ],
        "endpoint_rmsd_A": 0.30812667085425327,
        "minimum_distance_A_by_image": [
          1.6254456478456307,
          1.610018786749802,
          1.5965475552358643,
          1.5850818153733375,
          1.575665348219654,
          1.5683350664282178,
          1.5631203198896588,
          1.560042323519079,
          1.5591137324598774
        ],
        "minimum_distance_A": 1.5591137324598774,
        "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": [
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918,
          181.44974657966918
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.3169428150008162e-15,
        3.665204853489395e-16,
        2.714091497665893e-17
      ],
      "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": [
          -90.71732746532837,
          -90.67201467905902,
          -90.57878713709253,
          -90.45653739365177,
          -90.32451438771926,
          -90.20094597636458,
          -90.10110204994403,
          -90.03636681477532,
          -90.01395170888982
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.397761991907575e-18,
            9.02497243556685e-18,
            -0.00023275926238033943
          ],
          [
            3.935040947541648e-17,
            2.6271847725569602e-17,
            -0.00018221804117658904
          ],
          [
            2.894874632933943e-17,
            1.7208633881377468e-17,
            -0.00014700065224147813
          ],
          [
            1.8126427688384265e-17,
            2.936940182421755e-17,
            -0.00012069673425723837
          ],
          [
            4.5010137951958396e-17,
            3.097554098647944e-17,
            -9.79986757965265e-05
          ],
          [
            2.9866540136346225e-17,
            3.036367844847491e-17,
            -7.546108174287477e-05
          ],
          [
            -1.7055668246876336e-17,
            -9.02497243556685e-18,
            -5.1753613166118354e-05
          ],
          [
            3.4684957623131917e-17,
            2.447450152018129e-17,
            -2.651679740499679e-05
          ],
          [
            3.690295932339835e-17,
            1.4225804008605374e-17,
            7.579471201885661e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.404284100140767e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190302e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427362e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.714091497665893e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.4042841001407668e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190301e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427364e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.710505431213761e-17
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            2.220446049250313e-16,
            -0.00833474945946494
          ],
          [
            1.4432899320127035e-15,
            6.661338147750939e-16,
            -0.006524946438950463
          ],
          [
            9.992007221626409e-16,
            4.440892098500626e-16,
            -0.005263866169194997
          ],
          [
            6.661338147750939e-16,
            7.771561172376096e-16,
            -0.004321963518538252
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.0035091811246106275
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            -0.0027021447131042042
          ],
          [
            -6.106226635438361e-16,
            -2.220446049250313e-16,
            -0.0018532169029510381
          ],
          [
            1.2212453270876722e-15,
            6.661338147750939e-16,
            -0.0009495255337116926
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -90.0139517088898,
          -90.03636681477533,
          -90.10110204994402,
          -90.20094597636458,
          -90.32451438771928,
          -90.45653739365177,
          -90.57878713709252,
          -90.67201467905902,
          -90.71732746532837
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.109026521235529e-17,
            2.2485948271666556e-17,
            4.915388632075834e-18
          ],
          [
            7.648281725056652e-20,
            5.430280024790223e-17,
            2.6516797405024906e-05
          ],
          [
            -4.359520583282292e-18,
            9.942766242573647e-19,
            5.175361316615141e-05
          ],
          [
            4.3289274563820654e-17,
            7.418833273304953e-18,
            7.546108174287686e-05
          ],
          [
            4.952262416974182e-17,
            3.181685197623567e-17,
            9.799867579655277e-05
          ],
          [
            3.2046300427987374e-17,
            3.1243230846856425e-17,
            0.00012069673425727393
          ],
          [
            3.7935477356280995e-17,
            1.4264045417230658e-17,
            0.0001470006522414969
          ],
          [
            5.889176928293622e-17,
            2.2485948271666556e-17,
            0.0001822180411765616
          ],
          [
            3.082257535197831e-17,
            1.3422734427474425e-17,
            0.00023275926238034661
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1095072627934338e-15,
            5.793388316805817e-16,
            1.7601247024623046e-16
          ],
          [
            2.7294151606234536e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.561702316954953e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1095072627934338e-15,
            5.793388316805817e-16,
            1.7601247024623046e-16
          ],
          [
            2.7294151606233746e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.5617023169549592e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.4769442582657844e-15,
          5.005172219281217e-16,
          0.008334749459464968
        ],
        "actual_opposite_endpoint_branch_residual": 1.4004368421540665e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.404284100140767e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190302e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427362e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.714091497665893e-17
          ],
          [
            2.7294151606234536e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.561702316954953e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5694137173584858e-16,
            2.325237487697573e-16,
            -0.008334749459464915
          ],
          [
            1.4042841001407668e-15,
            6.76880573749251e-16,
            -0.006524946438950458
          ],
          [
            1.0330836382959772e-15,
            4.433715548575881e-16,
            -0.005263866169194994
          ],
          [
            6.468713930677585e-16,
            7.566874536236171e-16,
            -0.004321963518538243
          ],
          [
            1.6062608220269022e-15,
            7.980687987436584e-16,
            -0.0035091811246106145
          ],
          [
            1.0658366202234585e-15,
            7.823044767931664e-16,
            -0.0027021447131041817
          ],
          [
            -6.086595808190301e-16,
            -2.325237487697573e-16,
            -0.0018532169029510405
          ],
          [
            1.2377897753427364e-15,
            6.305728780196808e-16,
            -0.0009495255337117183
          ],
          [
            1.3169428150008162e-15,
            3.665204853489395e-16,
            2.710505431213761e-17
          ],
          [
            2.7294151606233746e-18,
            1.3990835731061666e-15,
            0.000949525533712725
          ],
          [
            -1.5557666415553684e-16,
            2.5617023169549592e-17,
            0.0018532169029522238
          ],
          [
            1.5448489809128748e-15,
            1.9114240364971576e-16,
            0.0027021447131042563
          ],
          [
            1.7672963165036862e-15,
            8.19744741425585e-16,
            0.003509181124611555
          ],
          [
            1.143624952301227e-15,
            8.049656895969989e-16,
            0.004321963518539517
          ],
          [
            1.3537899196692329e-15,
            3.675057554708453e-16,
            0.005263866169195665
          ],
          [
            2.1016496736800592e-15,
            5.793388316805817e-16,
            0.006524946438949474
          ],
          [
            1.099954309731252e-15,
            3.4582981278891865e-16,
            0.008334749459465171
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            2.220446049250313e-16,
            -0.00833474945946494
          ],
          [
            1.4432899320127035e-15,
            6.661338147750939e-16,
            -0.006524946438950463
          ],
          [
            9.992007221626409e-16,
            4.440892098500626e-16,
            -0.005263866169194997
          ],
          [
            6.661338147750939e-16,
            7.771561172376096e-16,
            -0.004321963518538252
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.0035091811246106275
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            -0.0027021447131042042
          ],
          [
            -6.106226635438361e-16,
            -2.220446049250313e-16,
            -0.0018532169029510381
          ],
          [
            1.2212453270876722e-15,
            6.661338147750939e-16,
            -0.0009495255337116926
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.0
          ],
          [
            0.0,
            1.4432899320127035e-15,
            0.0009495255337127473
          ],
          [
            -1.6653345369377348e-16,
            0.0,
            0.0018532169029522594
          ],
          [
            1.5543122344752192e-15,
            2.220446049250313e-16,
            0.0027021447131042597
          ],
          [
            1.7763568394002505e-15,
            7.771561172376096e-16,
            0.0035091811246115157
          ],
          [
            1.1102230246251565e-15,
            7.771561172376096e-16,
            0.004321963518539529
          ],
          [
            1.3322676295501878e-15,
            3.3306690738754696e-16,
            0.005263866169195719
          ],
          [
            2.1094237467877974e-15,
            5.551115123125783e-16,
            0.006524946438949519
          ],
          [
            1.1102230246251565e-15,
            3.3306690738754696e-16,
            0.008334749459465218
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.063439803625994e-16,
        "parent_symmetrization_rmsd_A": 0.30812667085425327,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -90.0139517088898,
        "reduced_polarization": [
          8.775069741404403e-16,
          2.266121280383228e-16,
          -9.373606581849255e-18
        ],
        "cartesian_polarization_e_A2": [
          2.4589225746057137e-17,
          8.79552398381515e-18,
          -2.617707664094317e-19
        ],
        "ranking_score": 0.3081266708542551
      }
    }
  ],
  "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": 54,
      "full_response": 19,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 79,
      "full_response": 44,
      "energy_polarization": 35
    },
    "elapsed_seconds": 170.5193622239749
  }
}
