{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 80,
  "input_formula": "Bi20Cl48Ga12",
  "input_spacegroup": "R3c",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -275.73311324240706,
  "input_cartesian_polarization_e_A2": [
    -5.161120419358536e-11,
    -4.003059363500224e-14,
    1.0009246274688673e-05
  ],
  "input_reduced_polarization": [
    0.0008417307391080476,
    -8.636912069723876e-12,
    0.002525211442736475
  ],
  "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": "R-3c",
      "spacegroup_number": 167,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.12871577209251e-15,
      "parent_symmetrization_rmsd_A": 0.03250872409813057,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -275.75205483228956,
      "reduced_polarization": [
        -1.6921015553466205e-15,
        -3.1173238884810925e-15,
        -6.183661751743799e-15
      ],
      "cartesian_polarization_e_A2": [
        2.963198423710322e-18,
        -1.4448257062371733e-17,
        -2.451034091842405e-17
      ],
      "ranking_score": 0.03250872409814483
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3c",
      "spacegroup_number": 161,
      "pointgroup": "3m",
      "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": 3.729105476978938e-08,
      "parent_symmetrization_rmsd_A": 0.000766348223848136,
      "parent_cell_rmsd_A": 0.0002933238382500101,
      "energy_eV": -275.73357784204615,
      "reduced_polarization": [
        -1.1710288015200222e-08,
        -6.6820383585717984e-15,
        -3.5404687831478545e-08
      ],
      "cartesian_polarization_e_A2": [
        7.327478246184428e-13,
        -3.097075086502142e-17,
        -1.4033823290187444e-10
      ],
      "ranking_score": 0.5008397537655201
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "R-3c",
      "spacegroup_number": 167,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.552274787765281e-15,
      "parent_symmetrization_rmsd_A": 0.03250872475723818,
      "parent_cell_rmsd_A": 0.0002933238382500101,
      "energy_eV": -275.75265557741125,
      "reduced_polarization": [
        1.959038753867109e-15,
        -4.014283707041979e-15,
        8.7800866940341e-16
      ],
      "cartesian_polarization_e_A2": [
        1.3377488327517426e-17,
        -1.860590109616069e-17,
        3.480278835804334e-18
      ],
      "ranking_score": 0.032582055716809784
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 6.493062912109365e-06,
      "parent_symmetrization_rmsd_A": 0.16817712524473205,
      "parent_cell_rmsd_A": 0.07828512087938819,
      "energy_eV": -272.0420347507919,
      "reduced_polarization": [
        1.338483187198467e-06,
        1.0547678893527886e-13,
        0.4999936463924627
      ],
      "cartesian_polarization_e_A2": [
        -0.0013367220682815933,
        -1.306585615155238e-13,
        0.0019742548835529118
      ],
      "ranking_score": 0.6877613915904033
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 4.242752445701457e-05,
      "parent_symmetrization_rmsd_A": 0.24540628838223583,
      "parent_cell_rmsd_A": 0.09227263964475836,
      "energy_eV": -268.3141174110786,
      "reduced_polarization": [
        0.49998708626151456,
        -1.1269637545018063e-12,
        4.0414479953107934e-05
      ],
      "cartesian_polarization_e_A2": [
        0.004010184265268231,
        -1.1910704155940224e-12,
        2.372874548068147e-05
      ],
      "ranking_score": 0.7685593033423395
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 5.443239946132538e-05,
      "parent_symmetrization_rmsd_A": 0.14085621538116663,
      "parent_cell_rmsd_A": 0.025057404112038082,
      "energy_eV": -273.19216990508505,
      "reduced_polarization": [
        4.441104556610573e-06,
        -0.4999782380222446,
        4.969485914668284e-05
      ],
      "cartesian_polarization_e_A2": [
        2.140154790842615e-06,
        -0.002317376779679126,
        7.997896306736474e-06
      ],
      "ranking_score": 0.6472294312080988
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 1.2791072147027137e-05,
      "parent_symmetrization_rmsd_A": 0.2199131247099535,
      "parent_cell_rmsd_A": 0.05545990387968478,
      "energy_eV": -269.6732176225786,
      "reduced_polarization": [
        0.5000126739196268,
        -3.383150511874774e-13,
        0.5000017272197209
      ],
      "cartesian_polarization_e_A2": [
        0.0026713171375911606,
        -5.257320423947195e-13,
        0.001981959956839592
      ],
      "ranking_score": 0.7338036828241687
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 1.769733753330168e-05,
      "parent_symmetrization_rmsd_A": 0.2199829011181059,
      "parent_cell_rmsd_A": 0.0830620658966263,
      "energy_eV": -269.6648029994607,
      "reduced_polarization": [
        -5.223569959750008e-06,
        -0.5000168996802634,
        0.5000005575658145
      ],
      "cartesian_polarization_e_A2": [
        -0.001334536168153169,
        -0.002312777763307772,
        0.0019819528791121337
      ],
      "ranking_score": 0.7407838122673291
    },
    {
      "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": 3.7655192415443047e-05,
      "parent_symmetrization_rmsd_A": 0.2931236101803376,
      "parent_cell_rmsd_A": 0.10218160749233585,
      "energy_eV": -264.66326550151086,
      "reduced_polarization": [
        0.5000040988644149,
        -0.49997639286020595,
        2.904850731271435e-05
      ],
      "cartesian_polarization_e_A2": [
        0.004012801260403521,
        -0.002323638981096548,
        3.3582247128948576e-05
      ],
      "ranking_score": 0.8187443224382525
    },
    {
      "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": 4.700574723579234e-06,
      "parent_symmetrization_rmsd_A": 0.2625230202565515,
      "parent_cell_rmsd_A": 0.06203325522281349,
      "energy_eV": -267.3143880192637,
      "reduced_polarization": [
        0.5000017332553668,
        -0.4999960063643122,
        0.4999982274023134
      ],
      "cartesian_polarization_e_A2": [
        0.002673583023431785,
        -0.0023185150420778327,
        0.0019899822725564743
      ],
      "ranking_score": 0.778040735211702
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "target_residual": 0.0026618045509929178,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.0007066993488930089,
            "max_log_strain_component": 1.3363941493501373e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              0.9999923806338019,
              0.9999866361585783,
              0.9999866361478037
            ],
            "cell_volume_ratio": 0.9999656533224226,
            "cell_rmsd_from_input_A": 0.0002933238382500101
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1710288015200222e-08,
              -6.6820383585717984e-15,
              -3.5404687831478545e-08
            ],
            "branch_aligned_reduced_polarization": [
              -1.1710288015200222e-08,
              -6.6820383585717984e-15,
              -3.5404687831478545e-08
            ],
            "target_residual": 3.729105476978938e-08,
            "energy_eV": -275.73357784204615
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "R-3c",
        "spacegroup_number": 167,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.12871577209251e-15,
        "parent_symmetrization_rmsd_A": 0.03250872409813057,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -275.75205483228956,
        "reduced_polarization": [
          -1.6921015553466205e-15,
          -3.1173238884810925e-15,
          -6.183661751743799e-15
        ],
        "cartesian_polarization_e_A2": [
          2.963198423710322e-18,
          -1.4448257062371733e-17,
          -2.451034091842405e-17
        ],
        "ranking_score": 0.03250872409814483
      },
      "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": [
          -275.73311324240706,
          -275.7375476752547,
          -275.74139263130996,
          -275.74464819225057,
          -275.7473133513014,
          -275.7493872071632,
          -275.75086904822103,
          -275.75175836025454,
          -275.75205483228956
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.161122832553223e-11,
            -4.002975157501852e-14,
            1.0009246274678019e-05
          ],
          [
            -4.502597486099686e-11,
            -3.5087557634261564e-14,
            8.840629574760782e-06
          ],
          [
            -3.849587871300803e-11,
            -3.009135460568827e-14,
            7.640012186252156e-06
          ],
          [
            -3.200940256191313e-11,
            -2.5088116645605452e-14,
            6.410880587419956e-06
          ],
          [
            -2.5560501008602887e-11,
            -2.007043042846026e-14,
            5.157760107491229e-06
          ],
          [
            -1.914258601026241e-11,
            -1.5061793691393237e-14,
            3.885327328763031e-06
          ],
          [
            -1.2748294647689026e-11,
            -1.0029494002885071e-14,
            2.5983379724465844e-06
          ],
          [
            -6.370083992705305e-12,
            -5.012649845723597e-15,
            1.3016091691550653e-06
          ],
          [
            -1.1884770656248234e-17,
            2.2373213997726497e-17,
            2.7542822758516088e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357804883897504e-16,
            4.827195014328154e-15,
            6.948720141989988e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357843497147632e-16,
            4.827195014328084e-15,
            6.948705933568222e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0008417307391040962,
            -8.63675797546648e-12,
            0.0025252114427337657
          ],
          [
            0.0007434556168804951,
            -7.570388760314017e-12,
            0.0022303836223547258
          ],
          [
            0.000642489359177878,
            -6.492417714554222e-12,
            0.0019274824163491022
          ],
          [
            0.000539125166168275,
            -5.412947867711182e-12,
            0.0016173874208997852
          ],
          [
            0.0004337436005077411,
            -4.330369396399192e-12,
            0.0013012403216876578
          ],
          [
            0.0003267379446917351,
            -3.2496783042290645e-12,
            0.0009802209637083115
          ],
          [
            0.00021850813657531276,
            -2.1639356972968926e-12,
            0.0006555291577460265
          ],
          [
            0.00010945927831851332,
            -1.0815237594385962e-12,
            0.0003283802074320885
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            6.994405055138486e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -275.75205483228956,
          -275.75175836025454,
          -275.7508690482211,
          -275.7493872071633,
          -275.7473133513015,
          -275.7446481922506,
          -275.7413926313101,
          -275.73754767525475,
          -275.73311324240706
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3238462022475613e-17,
            2.279424398958462e-17,
            2.4771486103247442e-17
          ],
          [
            6.370068100155486e-12,
            4.9988571163700675e-15,
            -1.3016091691470444e-06
          ],
          [
            1.274825874289086e-11,
            1.004667096065417e-14,
            -2.5983379724214665e-06
          ],
          [
            1.9142470743975528e-11,
            1.5080265716099316e-14,
            -3.885327328770759e-06
          ],
          [
            2.556052143122224e-11,
            2.0082155314309474e-14,
            -5.1577601074659835e-06
          ],
          [
            3.2009383434360715e-11,
            2.5020480042736195e-14,
            -6.410880587418981e-06
          ],
          [
            3.849591373311026e-11,
            3.00641528705181e-14,
            -7.64001218622795e-06
          ],
          [
            4.5025960945689156e-11,
            3.503959752164471e-14,
            -8.840629574755678e-06
          ],
          [
            5.161120966164576e-11,
            4.0072046435972774e-14,
            -1.0009246274678814e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.340959317063851e-16,
            4.9180355112628675e-15,
            6.249545514699974e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.340959317063851e-16,
            4.9180355112628675e-15,
            6.249545514699974e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0008417307391024739,
          8.646384778758662e-12,
          -0.0025252114427198897
        ],
        "actual_opposite_endpoint_branch_residual": 1.4681523771612626e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357804883897504e-16,
            4.827195014328154e-15,
            6.948720141989988e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357843497147632e-16,
            4.827195014328084e-15,
            6.948705933568222e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0008417307391040962,
            -8.63675797546648e-12,
            0.0025252114427337657
          ],
          [
            0.0007434556168804951,
            -7.570388760314017e-12,
            0.0022303836223547258
          ],
          [
            0.000642489359177878,
            -6.492417714554222e-12,
            0.0019274824163491022
          ],
          [
            0.000539125166168275,
            -5.412947867711182e-12,
            0.0016173874208997852
          ],
          [
            0.0004337436005077411,
            -4.330369396399192e-12,
            0.0013012403216876578
          ],
          [
            0.0003267379446917351,
            -3.2496783042290645e-12,
            0.0009802209637083115
          ],
          [
            0.00021850813657531276,
            -2.1639356972968926e-12,
            0.0006555291577460265
          ],
          [
            0.00010945927831851332,
            -1.0815237594385962e-12,
            0.0003283802074320885
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            6.994405055138486e-15
          ],
          [
            -0.00010945927831984559,
            1.0785816684233396e-12,
            -0.0003283802074300346
          ],
          [
            -0.00021850813657769974,
            2.1675994332781556e-12,
            -0.0006555291577396427
          ],
          [
            -0.0003267379447067231,
            3.2537306182689463e-12,
            -0.0009802209637102544
          ],
          [
            -0.00043374360050302263,
            4.3328673982045984e-12,
            -0.001301240321681274
          ],
          [
            -0.000539125166170551,
            5.398348434937361e-12,
            -0.0016173874208995631
          ],
          [
            -0.0006424893591714387,
            6.48658904367494e-12,
            -0.001927482416342996
          ],
          [
            -0.0007434556168817719,
            7.560063686185003e-12,
            -0.0022303836223533935
          ],
          [
            -0.0008417307391065387,
            8.645861804268407e-12,
            -0.002525211442733988
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736486
            ],
            "target_residual": 0.4974755006638329,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001970998241178078,
            "step_scale": 0.6768812341384894,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0028996257718457,
              1.0015942626000784,
              1.000091601546352
            ],
            "cell_volume_ratio": 1.0045905247537743,
            "cell_rmsd_from_input_A": 0.05399062472821242
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.000368827249444794,
              -7.652003536667075e-12,
              0.34088678095403935
            ],
            "branch_aligned_reduced_polarization": [
              0.000368827249444794,
              -7.652003536667075e-12,
              0.34088678095403935
            ],
            "target_residual": 0.15911364651942267,
            "energy_eV": -273.9084661177982,
            "max_atomic_step_A": 0.05453106252916752,
            "max_log_strain_component": 0.000884545795951414,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0042212094129026,
              1.002305062081886,
              1.000113664584254
            ],
            "cell_volume_ratio": 1.0066504091407094,
            "cell_rmsd_from_input_A": 0.07850936427106306
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0006894564763890715,
              -1.3797508103870678e-11,
              0.5021543457875393
            ],
            "branch_aligned_reduced_polarization": [
              0.0006894564763890715,
              -1.3797508103870678e-11,
              0.5021543457875393
            ],
            "target_residual": 0.0022619805492362175,
            "energy_eV": -272.0192927221243,
            "max_atomic_step_A": 0.0006014117288761385,
            "max_log_strain_component": 1.045484528693923e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.004211698612477,
              1.0022947415837073,
              1.000106764093234
            ],
            "cell_volume_ratio": 1.006623564735399,
            "cell_rmsd_from_input_A": 0.07828512087938819
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.338483187198467e-06,
              1.0547678893527886e-13,
              0.4999936463924627
            ],
            "branch_aligned_reduced_polarization": [
              1.338483187198467e-06,
              1.0547678893527886e-13,
              0.4999936463924627
            ],
            "target_residual": 6.493062912109365e-06,
            "energy_eV": -272.0420347507919
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 6.493062912109365e-06,
        "parent_symmetrization_rmsd_A": 0.16817712524473205,
        "parent_cell_rmsd_A": 0.07828512087938819,
        "energy_eV": -272.0420347507919,
        "reduced_polarization": [
          1.338483187198467e-06,
          1.0547678893527886e-13,
          0.4999936463924627
        ],
        "cartesian_polarization_e_A2": [
          -0.0013367220682815933,
          -1.306585615155238e-13,
          0.0019742548835529118
        ],
        "ranking_score": 0.6877613915904033
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080375,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "target_residual": 0.4991646566658738,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0031305200467600983,
            "step_scale": 0.5359371136228074,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0029128675974668,
              1.0004420146542192,
              0.9966369742702758
            ],
            "cell_volume_ratio": 0.9999818571667961,
            "cell_rmsd_from_input_A": 0.049570315764978605
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2686395847525336,
              4.790935087894056e-11,
              0.00025096756350628894
            ],
            "branch_aligned_reduced_polarization": [
              0.2686395847525336,
              4.790935087894056e-11,
              0.00025096756350628894
            ],
            "target_residual": 0.23136055136560776,
            "energy_eV": -273.5268025320763,
            "max_atomic_step_A": 0.11076288233970892,
            "max_log_strain_component": 0.002623643469945015,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0053744274385399,
              1.0008304518078361,
              0.9938413649687082
            ],
            "cell_volume_ratio": 1.0000124663441365,
            "cell_rmsd_from_input_A": 0.09065687675738883
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49059568175579493,
              7.687262789434657e-11,
              -0.003696644404277205
            ],
            "branch_aligned_reduced_polarization": [
              0.49059568175579493,
              7.687262789434657e-11,
              -0.003696644404277205
            ],
            "target_residual": 0.010104770234397329,
            "energy_eV": -268.5790516823985,
            "max_atomic_step_A": 0.004449085903274337,
            "max_log_strain_component": 0.00012068121876246777,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0055048717028217,
              1.0008703986921785,
              0.9937305039088764
            ],
            "cell_volume_ratio": 1.000070565964315,
            "cell_rmsd_from_input_A": 0.09227263964475836
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49998708626151456,
              -1.1269637545018063e-12,
              4.0414479953107934e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49998708626151456,
              -1.1269637545018063e-12,
              4.0414479953107934e-05
            ],
            "target_residual": 4.242752445701457e-05,
            "energy_eV": -268.3141174110786
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 4.242752445701457e-05,
        "parent_symmetrization_rmsd_A": 0.24540628838223583,
        "parent_cell_rmsd_A": 0.09227263964475836,
        "energy_eV": -268.3141174110786,
        "reduced_polarization": [
          0.49998708626151456,
          -1.1269637545018063e-12,
          4.0414479953107934e-05
        ],
        "cartesian_polarization_e_A2": [
          0.004010184265268231,
          -1.1910704155940224e-12,
          2.372874548068147e-05
        ],
        "ranking_score": 0.7685593033423395
      },
      "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": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080476,
              -8.636924508920174e-12,
              0.002525211442736475
            ],
            "target_residual": 0.5000070851446315,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0031288157006545466,
            "step_scale": 0.9278014536367761,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0032503044360224,
              0.9999880055701487,
              0.9967404174561902
            ],
            "cell_volume_ratio": 0.9999681330651219,
            "cell_rmsd_from_input_A": 0.023289043694824256
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0004432379069752403,
              -0.4640298631671982,
              -1.110720827239496e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004432379069752403,
              -0.4640298631671982,
              -1.110720827239496e-05
            ],
            "target_residual": 0.035972869318178405,
            "energy_eV": -273.5258481067709,
            "max_atomic_step_A": 0.01044681905830034,
            "max_log_strain_component": 0.00023745616918581164,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.003499520201634,
              0.9999836506168336,
              0.9964955611690255
            ],
            "cell_volume_ratio": 0.9999664684139313,
            "cell_rmsd_from_input_A": 0.025057404112038082
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.441104556610573e-06,
              -0.4999782380222446,
              4.969485914668284e-05
            ],
            "branch_aligned_reduced_polarization": [
              4.441104556610573e-06,
              -0.4999782380222446,
              4.969485914668284e-05
            ],
            "target_residual": 5.443239946132538e-05,
            "energy_eV": -273.19216990508505
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 5.443239946132538e-05,
        "parent_symmetrization_rmsd_A": 0.14085621538116663,
        "parent_cell_rmsd_A": 0.025057404112038082,
        "energy_eV": -273.19216990508505,
        "reduced_polarization": [
          4.441104556610573e-06,
          -0.4999782380222446,
          4.969485914668284e-05
        ],
        "cartesian_polarization_e_A2": [
          2.140154790842615e-06,
          -0.002317376779679126,
          7.997896306736474e-06
        ],
        "ranking_score": 0.6472294312080988
      },
      "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": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080375,
              -8.636912069723876e-12,
              0.002525211442736486
            ],
            "target_residual": 0.7047269989305243,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0021183990678948993,
            "step_scale": 0.5440303837052808,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.003101520199571,
              1.0017377067434516,
              0.9988491167468068
            ],
            "cell_volume_ratio": 1.003688157634425,
            "cell_rmsd_from_input_A": 0.030292423703015343
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2732649617752378,
              2.358411817944842e-11,
              0.2737418931635165
            ],
            "branch_aligned_reduced_polarization": [
              0.2732649617752378,
              2.358411817944842e-11,
              0.2737418931635165
            ],
            "target_residual": 0.32031470223518305,
            "energy_eV": -273.8101613986168,
            "max_atomic_step_A": 0.10136091833469972,
            "max_log_strain_component": 0.001735902197765049,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0056388092116404,
              1.003149713371678,
              0.9978961625208197
            ],
            "cell_volume_ratio": 1.00668391874823,
            "cell_rmsd_from_input_A": 0.05510799911167969
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4969472305325206,
              1.3469426202178309e-11,
              0.49881627462430395
            ],
            "branch_aligned_reduced_polarization": [
              0.4969472305325206,
              1.3469426202178309e-11,
              0.49881627462430395
            ],
            "target_residual": 0.0032742338320042477,
            "energy_eV": -269.73608690436663,
            "max_atomic_step_A": 0.0013754811351528843,
            "max_log_strain_component": 3.374787340290817e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.005676366872943,
              1.0031624396671641,
              0.9978663586857411
            ],
            "cell_volume_ratio": 1.006704219249457,
            "cell_rmsd_from_input_A": 0.05545990387968478
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000126739196268,
              -3.383150511874774e-13,
              0.5000017272197209
            ],
            "branch_aligned_reduced_polarization": [
              0.5000126739196268,
              -3.383150511874774e-13,
              0.5000017272197209
            ],
            "target_residual": 1.2791072147027137e-05,
            "energy_eV": -269.6732176225786
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 1.2791072147027137e-05,
        "parent_symmetrization_rmsd_A": 0.2199131247099535,
        "parent_cell_rmsd_A": 0.05545990387968478,
        "energy_eV": -269.6732176225786,
        "reduced_polarization": [
          0.5000126739196268,
          -3.383150511874774e-13,
          0.5000017272197209
        ],
        "cartesian_polarization_e_A2": [
          0.0026713171375911606,
          -5.257320423947195e-13,
          0.001981959956839592
        ],
        "ranking_score": 0.7338036828241687
      },
      "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": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080476,
              -8.636924508920174e-12,
              0.002525211442736486
            ],
            "target_residual": 0.7053239495097939,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018346528554843771,
            "step_scale": 0.5440376651616454,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0029906792348982,
              1.001959857656736,
              0.9987377949090019
            ],
            "cell_volume_ratio": 1.0036879371151957,
            "cell_rmsd_from_input_A": 0.045478748664743336
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00022286763345019745,
              -0.272991594990334,
              0.27368812853478797
            ],
            "branch_aligned_reduced_polarization": [
              0.00022286763345019745,
              -0.272991594990334,
              0.27368812853478797
            ],
            "target_residual": 0.32054629740663243,
            "energy_eV": -273.80875047178813,
            "max_atomic_step_A": 0.10138537020539666,
            "max_log_strain_component": 0.0015039341532342328,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0054375923796717,
              1.0035551473926818,
              0.9976936494260549
            ],
            "cell_volume_ratio": 1.0066849356451608,
            "cell_rmsd_from_input_A": 0.0826284552787033
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0009131116636203304,
              -0.49599193916086165,
              0.4987712265124832
            ],
            "branch_aligned_reduced_polarization": [
              0.0009131116636203304,
              -0.49599193916086165,
              0.4987712265124832
            ],
            "target_residual": 0.004290478864194316,
            "energy_eV": -269.72840086916716,
            "max_atomic_step_A": 0.001382264361400909,
            "max_log_strain_component": 2.9363849012400328e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.005473772288146,
              1.0035717037414915,
              0.9976620076151013
            ],
            "cell_volume_ratio": 1.0067058403742541,
            "cell_rmsd_from_input_A": 0.0830620658966263
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.223569959750008e-06,
              -0.5000168996802634,
              0.5000005575658145
            ],
            "branch_aligned_reduced_polarization": [
              -5.223569959750008e-06,
              -0.5000168996802634,
              0.5000005575658145
            ],
            "target_residual": 1.769733753330168e-05,
            "energy_eV": -269.6648029994607
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 1.769733753330168e-05,
        "parent_symmetrization_rmsd_A": 0.2199829011181059,
        "parent_cell_rmsd_A": 0.0830620658966263,
        "energy_eV": -269.6648029994607,
        "reduced_polarization": [
          -5.223569959750008e-06,
          -0.5000168996802634,
          0.5000005575658145
        ],
        "cartesian_polarization_e_A2": [
          -0.001334536168153169,
          -0.002312777763307772,
          0.0019819528791121337
        ],
        "ranking_score": 0.7407838122673291
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080375,
              -8.636924508920174e-12,
              0.002525211442736475
            ],
            "target_residual": 0.7065163511594921,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0027117687758955573,
            "step_scale": 0.46424795600409513,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.003277553783277,
              0.9998056938428274,
              0.9969111948158201
            ],
            "cell_volume_ratio": 0.9999842840088953,
            "cell_rmsd_from_input_A": 0.044522118535472166
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.23284101370525778,
              -0.23151022204739546,
              0.0012933710320557992
            ],
            "branch_aligned_reduced_polarization": [
              0.23284101370525778,
              -0.23151022204739546,
              0.0012933710320557992
            ],
            "target_residual": 0.3787642507308467,
            "energy_eV": -273.5247672817419,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002355233423226471,
            "step_scale": 0.7706797315357913,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.006136708229937,
              0.9996218482226694,
              0.9942267984999307
            ],
            "cell_volume_ratio": 0.999949802435995,
            "cell_rmsd_from_input_A": 0.08315074227855437
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4276657225052498,
              -0.42754403577341915,
              -0.0009602199726200706
            ],
            "branch_aligned_reduced_polarization": [
              0.4276657225052498,
              -0.42754403577341915,
              -0.0009602199726200706
            ],
            "target_residual": 0.10238670067487723,
            "energy_eV": -268.2562309990122,
            "max_atomic_step_A": 0.04875576869767902,
            "max_log_strain_component": 0.0011139237567913594,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0075031679649538,
              0.9995550183995611,
              0.9929748439878558
            ],
            "cell_volume_ratio": 0.9999801301756998,
            "cell_rmsd_from_input_A": 0.10114514331251916
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4965490168981492,
              -0.49633251489154984,
              3.661059074242625e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4965490168981492,
              -0.49633251489154984,
              3.661059074242625e-05
            ],
            "target_residual": 0.005035977732806029,
            "energy_eV": -264.87470228621805,
            "max_atomic_step_A": 0.002763602139655337,
            "max_log_strain_component": 6.393762778599071e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.007582420319514,
              0.9995503666028214,
              0.9929026092458006
            ],
            "cell_volume_ratio": 0.9999813868799763,
            "cell_rmsd_from_input_A": 0.10218160749233585
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000040988644149,
              -0.49997639286020595,
              2.904850731271435e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000040988644149,
              -0.49997639286020595,
              2.904850731271435e-05
            ],
            "target_residual": 3.7655192415443047e-05,
            "energy_eV": -264.66326550151086
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.7655192415443047e-05,
        "parent_symmetrization_rmsd_A": 0.2931236101803376,
        "parent_cell_rmsd_A": 0.10218160749233585,
        "energy_eV": -264.66326550151086,
        "reduced_polarization": [
          0.5000040988644149,
          -0.49997639286020595,
          2.904850731271435e-05
        ],
        "cartesian_polarization_e_A2": [
          0.004012801260403521,
          -0.002323638981096548,
          3.3582247128948576e-05
        ],
        "ranking_score": 0.8187443224382525
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.0008417307391080476,
              -8.636912069723876e-12,
              0.002525211442736475
            ],
            "branch_aligned_reduced_polarization": [
              0.0008417307391080375,
              -8.636924508920174e-12,
              0.002525211442736486
            ],
            "target_residual": 0.8640834120691047,
            "energy_eV": -275.73311324240706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017092203335705306,
            "step_scale": 0.43894835976781615,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0034301869956441,
              1.0007688626884024,
              0.9987781610268265
            ],
            "cell_volume_ratio": 1.002974714268706,
            "cell_rmsd_from_input_A": 0.026823799010864756
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2207013985301261,
              -0.22011365422091134,
              0.22162095779877933
            ],
            "branch_aligned_reduced_polarization": [
              0.2207013985301261,
              -0.22011365422091134,
              0.22162095779877933
            ],
            "target_residual": 0.4835689883289333,
            "energy_eV": -274.0005898097485,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0016625355036006748,
            "step_scale": 0.7812425236336507,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0067547364331204,
              1.0015096477173249,
              0.9975861462830174
            ],
            "cell_volume_ratio": 1.0058407540767762,
            "cell_rmsd_from_input_A": 0.05290158712414756
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4353206265407147,
              -0.4360777823998649,
              0.4385682986218068
            ],
            "branch_aligned_reduced_polarization": [
              0.4353206265407147,
              -0.4360777823998649,
              0.4385682986218068
            ],
            "target_residual": 0.10974208485455444,
            "energy_eV": -269.37655419842616,
            "max_atomic_step_A": 0.035491644431695134,
            "max_log_strain_component": 0.0005989683614498386,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.0078655061464135,
              1.001744600052467,
              0.9971354058235997
            ],
            "cell_volume_ratio": 1.0067316658222374,
            "cell_rmsd_from_input_A": 0.06173480127927341
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4980820619086477,
              -0.4980672446494187,
              0.498461388842802
            ],
            "branch_aligned_reduced_polarization": [
              0.4980820619086477,
              -0.4980672446494187,
              0.498461388842802
            ],
            "target_residual": 0.003127515637133567,
            "energy_eV": -267.3825175207835,
            "max_atomic_step_A": 0.0011502210047761316,
            "max_log_strain_component": 2.167859387553257e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.23483299248114786,
            "cell_principal_stretches": [
              1.00790291703611,
              1.0017510845533648,
              0.9971176057657848
            ],
            "cell_volume_ratio": 1.0067575795041697,
            "cell_rmsd_from_input_A": 0.06203325522281349
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000017332553668,
              -0.4999960063643122,
              0.4999982274023134
            ],
            "branch_aligned_reduced_polarization": [
              0.5000017332553668,
              -0.4999960063643122,
              0.4999982274023134
            ],
            "target_residual": 4.700574723579234e-06,
            "energy_eV": -267.3143880192637
          }
        ],
        "iterations": 4
      },
      "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": 4.700574723579234e-06,
        "parent_symmetrization_rmsd_A": 0.2625230202565515,
        "parent_cell_rmsd_A": 0.06203325522281349,
        "energy_eV": -267.3143880192637,
        "reduced_polarization": [
          0.5000017332553668,
          -0.4999960063643122,
          0.4999982274023134
        ],
        "cartesian_polarization_e_A2": [
          0.002673583023431785,
          -0.0023185150420778327,
          0.0019899822725564743
        ],
        "ranking_score": 0.778040735211702
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79
        ],
        "endpoint_rmsd_A": 0.03250872409813057,
        "minimum_distance_A_by_image": [
          2.198178134243066,
          2.198139069290794,
          2.19810661217206,
          2.198080763179583,
          2.1980615225464923,
          2.198048890446326,
          2.198042866993024,
          2.198043452240918,
          2.1980506461847233
        ],
        "minimum_distance_A": 2.198042866993024,
        "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": [
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121,
          2603.95995064121
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        8.357804883897504e-16,
        4.827195014328154e-15,
        6.948720141989988e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -275.73311324240706,
          -275.7375476752547,
          -275.74139263130996,
          -275.74464819225057,
          -275.7473133513014,
          -275.7493872071632,
          -275.75086904822103,
          -275.75175836025454,
          -275.75205483228956
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.161122832553223e-11,
            -4.002975157501852e-14,
            1.0009246274678019e-05
          ],
          [
            -4.502597486099686e-11,
            -3.5087557634261564e-14,
            8.840629574760782e-06
          ],
          [
            -3.849587871300803e-11,
            -3.009135460568827e-14,
            7.640012186252156e-06
          ],
          [
            -3.200940256191313e-11,
            -2.5088116645605452e-14,
            6.410880587419956e-06
          ],
          [
            -2.5560501008602887e-11,
            -2.007043042846026e-14,
            5.157760107491229e-06
          ],
          [
            -1.914258601026241e-11,
            -1.5061793691393237e-14,
            3.885327328763031e-06
          ],
          [
            -1.2748294647689026e-11,
            -1.0029494002885071e-14,
            2.5983379724465844e-06
          ],
          [
            -6.370083992705305e-12,
            -5.012649845723597e-15,
            1.3016091691550653e-06
          ],
          [
            -1.1884770656248234e-17,
            2.2373213997726497e-17,
            2.7542822758516088e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357804883897504e-16,
            4.827195014328154e-15,
            6.948720141989988e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357843497147632e-16,
            4.827195014328084e-15,
            6.948705933568222e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0008417307391040962,
            -8.63675797546648e-12,
            0.0025252114427337657
          ],
          [
            0.0007434556168804951,
            -7.570388760314017e-12,
            0.0022303836223547258
          ],
          [
            0.000642489359177878,
            -6.492417714554222e-12,
            0.0019274824163491022
          ],
          [
            0.000539125166168275,
            -5.412947867711182e-12,
            0.0016173874208997852
          ],
          [
            0.0004337436005077411,
            -4.330369396399192e-12,
            0.0013012403216876578
          ],
          [
            0.0003267379446917351,
            -3.2496783042290645e-12,
            0.0009802209637083115
          ],
          [
            0.00021850813657531276,
            -2.1639356972968926e-12,
            0.0006555291577460265
          ],
          [
            0.00010945927831851332,
            -1.0815237594385962e-12,
            0.0003283802074320885
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            6.994405055138486e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -275.75205483228956,
          -275.75175836025454,
          -275.7508690482211,
          -275.7493872071633,
          -275.7473133513015,
          -275.7446481922506,
          -275.7413926313101,
          -275.73754767525475,
          -275.73311324240706
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3238462022475613e-17,
            2.279424398958462e-17,
            2.4771486103247442e-17
          ],
          [
            6.370068100155486e-12,
            4.9988571163700675e-15,
            -1.3016091691470444e-06
          ],
          [
            1.274825874289086e-11,
            1.004667096065417e-14,
            -2.5983379724214665e-06
          ],
          [
            1.9142470743975528e-11,
            1.5080265716099316e-14,
            -3.885327328770759e-06
          ],
          [
            2.556052143122224e-11,
            2.0082155314309474e-14,
            -5.1577601074659835e-06
          ],
          [
            3.2009383434360715e-11,
            2.5020480042736195e-14,
            -6.410880587418981e-06
          ],
          [
            3.849591373311026e-11,
            3.00641528705181e-14,
            -7.64001218622795e-06
          ],
          [
            4.5025960945689156e-11,
            3.503959752164471e-14,
            -8.840629574755678e-06
          ],
          [
            5.161120966164576e-11,
            4.0072046435972774e-14,
            -1.0009246274678814e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.340959317063851e-16,
            4.9180355112628675e-15,
            6.249545514699974e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.340959317063851e-16,
            4.9180355112628675e-15,
            6.249545514699974e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0008417307391024739,
          8.646384778758662e-12,
          -0.0025252114427198897
        ],
        "actual_opposite_endpoint_branch_residual": 1.4681523771612626e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357804883897504e-16,
            4.827195014328154e-15,
            6.948720141989988e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0008417307391041457,
            -8.636730388730007e-12,
            0.0025252114427337874
          ],
          [
            0.0007434556168804578,
            -7.570413588958232e-12,
            0.0022303836223547015
          ],
          [
            0.0006424893591778364,
            -6.4924439082252356e-12,
            0.001927482416349091
          ],
          [
            0.0005391251661682704,
            -5.4129563862776346e-12,
            0.0016173874208998365
          ],
          [
            0.00043374360050770834,
            -4.330351540441553e-12,
            0.0013012403216876264
          ],
          [
            0.0003267379446917268,
            -3.2496991903497137e-12,
            0.0009802209637083106
          ],
          [
            0.00021850813657533938,
            -2.163941374354202e-12,
            0.0006555291577459853
          ],
          [
            0.00010945927831855491,
            -1.0815182095119894e-12,
            0.00032838020743208466
          ],
          [
            8.357843497147632e-16,
            4.827195014328084e-15,
            6.948705933568222e-15
          ],
          [
            -0.00010945927831986008,
            1.0785423208275965e-12,
            -0.00032838020743006105
          ],
          [
            -0.00021850813657769963,
            2.1676474366531966e-12,
            -0.0006555291577396485
          ],
          [
            -0.00032673794470673527,
            3.253684673417761e-12,
            -0.0009802209637102604
          ],
          [
            -0.0004337436005030412,
            4.332881275799229e-12,
            -0.0013012403216812573
          ],
          [
            -0.0005391251661705711,
            5.398363262902971e-12,
            -0.0016173874208995904
          ],
          [
            -0.0006424893591714385,
            6.486574922195429e-12,
            -0.001927482416342984
          ],
          [
            -0.0007434556168817622,
            7.56006582146563e-12,
            -0.002230383622353414
          ],
          [
            -0.0008417307391065373,
            8.645855834092967e-12,
            -0.002525211442733988
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.0008417307391040962,
            -8.63675797546648e-12,
            0.0025252114427337657
          ],
          [
            0.0007434556168804951,
            -7.570388760314017e-12,
            0.0022303836223547258
          ],
          [
            0.000642489359177878,
            -6.492417714554222e-12,
            0.0019274824163491022
          ],
          [
            0.000539125166168275,
            -5.412947867711182e-12,
            0.0016173874208997852
          ],
          [
            0.0004337436005077411,
            -4.330369396399192e-12,
            0.0013012403216876578
          ],
          [
            0.0003267379446917351,
            -3.2496783042290645e-12,
            0.0009802209637083115
          ],
          [
            0.00021850813657531276,
            -2.1639356972968926e-12,
            0.0006555291577460265
          ],
          [
            0.00010945927831851332,
            -1.0815237594385962e-12,
            0.0003283802074320885
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            6.994405055138486e-15
          ],
          [
            -0.00010945927831984559,
            1.0785816684233396e-12,
            -0.0003283802074300346
          ],
          [
            -0.00021850813657769974,
            2.1675994332781556e-12,
            -0.0006555291577396427
          ],
          [
            -0.0003267379447067231,
            3.2537306182689463e-12,
            -0.0009802209637102544
          ],
          [
            -0.00043374360050302263,
            4.3328673982045984e-12,
            -0.001301240321681274
          ],
          [
            -0.000539125166170551,
            5.398348434937361e-12,
            -0.0016173874208995631
          ],
          [
            -0.0006424893591714387,
            6.48658904367494e-12,
            -0.001927482416342996
          ],
          [
            -0.0007434556168817719,
            7.560063686185003e-12,
            -0.0022303836223533935
          ],
          [
            -0.0008417307391065387,
            8.645861804268407e-12,
            -0.002525211442733988
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "R-3c",
        "spacegroup_number": 167,
        "pointgroup": "-3m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.12871577209251e-15,
        "parent_symmetrization_rmsd_A": 0.03250872409813057,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -275.75205483228956,
        "reduced_polarization": [
          -1.6921015553466205e-15,
          -3.1173238884810925e-15,
          -6.183661751743799e-15
        ],
        "cartesian_polarization_e_A2": [
          2.963198423710322e-18,
          -1.4448257062371733e-17,
          -2.451034091842405e-17
        ],
        "ranking_score": 0.03250872409814483
      }
    }
  ],
  "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": 56,
      "full_response": 24,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 81,
      "full_response": 49,
      "energy_polarization": 32
    },
    "elapsed_seconds": 554.9397060009651
  }
}