{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Be4O16P4Rb4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -180.7535891747667,
  "input_cartesian_polarization_e_A2": [
    4.504665366218056e-18,
    1.6808991807410862e-17,
    0.0005820719863747665
  ],
  "input_reduced_polarization": [
    1.9983424952240215e-16,
    7.384655843800999e-16,
    0.04411408133206383
  ],
  "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.416662852122678e-15,
      "parent_symmetrization_rmsd_A": 0.23503975217646214,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -180.00770910344073,
      "reduced_polarization": [
        3.5001028874264426e-16,
        1.0375005202676377e-15,
        -4.278784432235293e-15
      ],
      "cartesian_polarization_e_A2": [
        7.88993493000918e-18,
        2.3615640477006882e-17,
        -5.645726893853251e-17
      ],
      "ranking_score": 0.23503975217647097
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.330987142481978e-15,
      "parent_symmetrization_rmsd_A": 0.6151136377541429,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -139.64680268043247,
      "reduced_polarization": [
        -5.414346800687128e-16,
        2.8325033317092774e-15,
        -1.6671078868672497e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.2205025200654934e-17,
        6.447358726558989e-17,
        -2.1996985314177948e-17
      ],
      "ranking_score": 0.6151136377541495
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.457069252511918e-05,
      "parent_symmetrization_rmsd_A": 0.004040152451729473,
      "parent_cell_rmsd_A": 0.0028867049346287467,
      "energy_eV": -180.74532457817193,
      "reduced_polarization": [
        3.3018259776812263e-16,
        -1.3910559938467608e-15,
        3.457069252511918e-05
      ],
      "cartesian_polarization_e_A2": [
        7.44304430219844e-18,
        -3.164986455246541e-17,
        4.5634630652969187e-07
      ],
      "ranking_score": 0.5048309700704369
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5778323605759322e-15,
      "parent_symmetrization_rmsd_A": 0.23503997735929227,
      "parent_cell_rmsd_A": 0.0028867049346287467,
      "energy_eV": -180.00662245400574,
      "reduced_polarization": [
        6.287504294059061e-16,
        -2.511493341827786e-16,
        -1.4251848538144284e-15
      ],
      "cartesian_polarization_e_A2": [
        1.417292850752159e-17,
        -5.714308118000743e-18,
        -1.8812982808710186e-17
      ],
      "ranking_score": 0.23576165359295262
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 5.552616529791443e-06,
      "parent_symmetrization_rmsd_A": 0.042069227666230814,
      "parent_cell_rmsd_A": 0.03002765852730117,
      "energy_eV": -179.66982007949528,
      "reduced_polarization": [
        -2.5704383335347683e-16,
        -1.2579244899098209e-15,
        0.4999944473834702
      ],
      "cartesian_polarization_e_A2": [
        -4.457940518536456e-17,
        -7.810875124823292e-17,
        0.006567897478088397
      ],
      "ranking_score": 0.5495872475311157
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00025618395229164224,
      "parent_symmetrization_rmsd_A": 0.07676859920358835,
      "parent_cell_rmsd_A": 0.08219898797446977,
      "energy_eV": -176.37080099854322,
      "reduced_polarization": [
        -1.7479761972873446e-16,
        0.49974667420700025,
        3.8160974998227005e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.837797736815224e-16,
        0.0113744390910799,
        0.00017229456485563744
      ],
      "ranking_score": 0.5978307141017891
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.390731937755254e-05,
      "parent_symmetrization_rmsd_A": 0.08154136463468165,
      "parent_cell_rmsd_A": 0.006097056068628972,
      "energy_eV": -176.45126054583508,
      "reduced_polarization": [
        0.4999690232325439,
        2.2581377888646367e-15,
        1.3789350432168753e-05
      ],
      "cartesian_polarization_e_A2": [
        0.011270017301106858,
        -2.051553936891001e-16,
        1.140162548646047e-05
      ],
      "ranking_score": 0.583133443290594
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.1043641791353915e-05,
      "parent_symmetrization_rmsd_A": 0.09120803218539968,
      "parent_cell_rmsd_A": 0.09405204273648213,
      "energy_eV": -175.71892796748227,
      "reduced_polarization": [
        4.475849485210947e-16,
        0.49997590722376073,
        0.4999804233345854
      ],
      "cartesian_polarization_e_A2": [
        -4.377800496706332e-16,
        0.011542825992524515,
        0.0067472114828271935
      ],
      "ranking_score": 0.6147831301531029
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00019781411307640944,
      "parent_symmetrization_rmsd_A": 0.092131430523431,
      "parent_cell_rmsd_A": 0.03087259665949258,
      "energy_eV": -175.41852515942585,
      "reduced_polarization": [
        0.4998180015124478,
        -1.4552073142258043e-15,
        0.4999224953300702
      ],
      "cartesian_polarization_e_A2": [
        0.011276590122670078,
        -4.852640003446323e-16,
        0.006577874195320265
      ],
      "ranking_score": 0.6002452079144569
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0001251516674146402,
      "parent_symmetrization_rmsd_A": 0.11539957333691221,
      "parent_cell_rmsd_A": 0.08713540039552539,
      "energy_eV": -171.37226174348396,
      "reduced_polarization": [
        0.4999553064507543,
        0.4998860804711998,
        2.6225321169262725e-05
      ],
      "cartesian_polarization_e_A2": [
        0.011270020187710736,
        0.01137875308553078,
        0.0001938836875147981
      ],
      "ranking_score": 0.6374337267706228
    },
    {
      "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": 0.00041602003130075416,
      "parent_symmetrization_rmsd_A": 0.12601222069005064,
      "parent_cell_rmsd_A": 0.09971699613323465,
      "energy_eV": -170.73486887384306,
      "reduced_polarization": [
        0.4998676687129927,
        0.499695211073577,
        0.49974967060250064
      ],
      "cartesian_polarization_e_A2": [
        0.011278619017155453,
        0.011545240994502142,
        0.006765907927424104
      ],
      "ranking_score": 0.6517735097859608
    }
  ],
  "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "target_residual": 0.04411408133206383,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.005760894019980489,
            "max_log_strain_component": 0.0004352956679074494,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0004353904228152,
              0.9999786690078213,
              0.9995908277498103
            ],
            "cell_volume_ratio": 1.0000047084753079,
            "cell_rmsd_from_input_A": 0.0028867049346287467
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.3018259776812263e-16,
              -1.3910559938467608e-15,
              3.457069252511918e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.3018259776812263e-16,
              -1.3910559938467608e-15,
              3.457069252511918e-05
            ],
            "target_residual": 3.457069252511918e-05,
            "energy_eV": -180.74532457817193
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.416662852122678e-15,
        "parent_symmetrization_rmsd_A": 0.23503975217646214,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -180.00770910344073,
        "reduced_polarization": [
          3.5001028874264426e-16,
          1.0375005202676377e-15,
          -4.278784432235293e-15
        ],
        "cartesian_polarization_e_A2": [
          7.88993493000918e-18,
          2.3615640477006882e-17,
          -5.645726893853251e-17
        ],
        "ranking_score": 0.23503975217647097
      },
      "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": [
          -180.7535891747667,
          -180.70027229312151,
          -180.5965353588182,
          -180.46435382427754,
          -180.3249715907166,
          -180.19708255460526,
          -180.0953619389923,
          -180.030158573243,
          -180.00770910344073
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.749507310567253e-17,
            -1.3270256690061207e-17,
            0.0005820719863747538
          ],
          [
            1.0859944760641926e-17,
            -2.2026820628400913e-18,
            0.0004867663796068179
          ],
          [
            -1.8813071389175207e-17,
            6.2198686118722256e-18,
            0.0003983774234363564
          ],
          [
            4.974089412397092e-18,
            -1.5346555355853095e-18,
            0.0003175338669946365
          ],
          [
            3.8835812435811777e-17,
            -1.1221040180779646e-17,
            0.00024431207776952845
          ],
          [
            3.3942969492945674e-17,
            7.546894280878347e-18,
            0.00017768439809820075
          ],
          [
            1.581597940203213e-17,
            -6.7073474290581475e-18,
            0.00011587890777119791
          ],
          [
            3.385269563791124e-17,
            9.776658500228766e-18,
            5.715309680025239e-05
          ],
          [
            2.6053034562936492e-17,
            2.9158455176120885e-17,
            -6.622490005325784e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.206586602942757e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740502e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.0190538207352265e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.2065866029427565e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740507e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.019422377738891e-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": [
          [
            7.771561172376096e-16,
            -6.106226635438361e-16,
            0.04411408133206285
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.03689105842977969
          ],
          [
            -8.326672684688674e-16,
            2.220446049250313e-16,
            0.030192234757393743
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.024065261964466456
          ],
          [
            1.7763568394002505e-15,
            -4.996003610813204e-16,
            0.018515927791431852
          ],
          [
            1.5543122344752192e-15,
            3.3306690738754696e-16,
            0.013466348102339487
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.00878223257904398
          ],
          [
            1.5543122344752192e-15,
            4.440892098500626e-16,
            0.00433151984572977
          ],
          [
            1.1102230246251565e-15,
            1.3322676295501878e-15,
            -4.9960036108132044e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -180.00770910344073,
          -180.03015857324303,
          -180.09536193899223,
          -180.1970825546053,
          -180.3249715907166,
          -180.46435382427757,
          -180.59653535881822,
          -180.70027229312151,
          -180.7535891747667
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.2712901926662582e-17,
            3.0575754700161435e-17,
            -4.468555824204284e-17
          ],
          [
            -1.3902173675302217e-17,
            2.0284535226236414e-17,
            -5.715309680030897e-05
          ],
          [
            2.803905937369395e-17,
            2.2297642193504204e-18,
            -0.00011587890777120397
          ],
          [
            2.4012845439158372e-18,
            6.319169852410098e-20,
            -0.0001776843980982488
          ],
          [
            -4.477583209707727e-18,
            -5.461568229583013e-18,
            -0.0002443120777695375
          ],
          [
            8.97322119042234e-18,
            7.492729967857688e-18,
            -0.0003175338669947225
          ],
          [
            -1.539169228337031e-17,
            -1.0941191230172913e-17,
            -0.00039837742343641283
          ],
          [
            -1.7874223296817135e-18,
            3.2891279081794565e-17,
            -0.0004867663796068731
          ],
          [
            -3.642550050639249e-17,
            1.9837679643815987e-17,
            -0.0005820719863748215
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.007581105808344e-15,
            1.3432776231446824e-15,
            -3.386629827240917e-15
          ],
          [
            -6.167229343977941e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695204e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689171e-16,
            2.7761864074439846e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.980666212931217e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547006e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.4450050250745942e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.007581105808344e-15,
            1.3432776231446824e-15,
            -3.386629827240917e-15
          ],
          [
            -6.16722934397794e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.2438580741815249e-15,
            9.795972037695203e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689177e-16,
            2.7761864074439795e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.9806662129312165e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547005e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.445005025074594e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.5353998249877552e-15,
          3.1450226015758292e-15,
          -0.04411408133207291
        ],
        "actual_opposite_endpoint_branch_residual": 6.258298704134615e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.206586602942757e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740502e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.0190538207352265e-15
          ],
          [
            -6.167229343977941e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695204e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689171e-16,
            2.7761864074439846e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.980666212931217e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547006e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.4450050250745942e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.2065866029427565e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740507e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.019422377738891e-15
          ],
          [
            -6.167229343977942e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695203e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689177e-16,
            2.7761864074439795e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.9806662129312165e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547005e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.445005025074594e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "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": [
          [
            7.771561172376096e-16,
            -6.106226635438361e-16,
            0.04411408133206285
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.03689105842977969
          ],
          [
            -8.326672684688674e-16,
            2.220446049250313e-16,
            0.030192234757393743
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.024065261964466456
          ],
          [
            1.7763568394002505e-15,
            -4.996003610813204e-16,
            0.018515927791431852
          ],
          [
            1.5543122344752192e-15,
            3.3306690738754696e-16,
            0.013466348102339487
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.00878223257904398
          ],
          [
            1.5543122344752192e-15,
            4.440892098500626e-16,
            0.00433151984572977
          ],
          [
            1.1102230246251565e-15,
            1.3322676295501878e-15,
            -4.9960036108132044e-15
          ],
          [
            -6.106226635438361e-16,
            8.881784197001252e-16,
            -0.004331519845734044
          ],
          [
            1.2212453270876722e-15,
            1.1102230246251565e-16,
            -0.00878223257904448
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.01346634810234315
          ],
          [
            -2.220446049250313e-16,
            -2.220446049250313e-16,
            -0.018515927791432518
          ],
          [
            4.440892098500626e-16,
            3.3306690738754696e-16,
            -0.024065261964473006
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.030192234757398073
          ],
          [
            -5.551115123125783e-17,
            1.4432899320127035e-15,
            -0.03689105842978385
          ],
          [
            -1.609823385706477e-15,
            8.881784197001252e-16,
            -0.04411408133206801
          ]
        ]
      },
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206385
            ],
            "target_residual": 0.45588591866793615,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.0595345155864896,
            "max_log_strain_component": 0.00449845399618291,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0042383097454555,
              1.000220466443478,
              0.9955116488931899
            ],
            "cell_volume_ratio": 0.9999513427402185,
            "cell_rmsd_from_input_A": 0.029938236217100858
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.286022011341878e-16,
              -4.242833329752677e-16,
              0.4986786780269577
            ],
            "branch_aligned_reduced_polarization": [
              -5.286022011341878e-16,
              -4.242833329752677e-16,
              0.4986786780269577
            ],
            "target_residual": 0.0013213219730422998,
            "energy_eV": -179.67640888718742,
            "max_atomic_step_A": 0.00017342369294968377,
            "max_log_strain_component": 1.3392677482272757e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0042509547101959,
              1.000221122882868,
              0.9954983164160254
            ],
            "cell_volume_ratio": 0.9999511978826545,
            "cell_rmsd_from_input_A": 0.03002765852730117
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.5704383335347683e-16,
              -1.2579244899098209e-15,
              0.4999944473834702
            ],
            "branch_aligned_reduced_polarization": [
              -2.5704383335347683e-16,
              -1.2579244899098209e-15,
              0.4999944473834702
            ],
            "target_residual": 5.552616529791443e-06,
            "energy_eV": -179.66982007949528
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 5.552616529791443e-06,
        "parent_symmetrization_rmsd_A": 0.042069227666230814,
        "parent_cell_rmsd_A": 0.03002765852730117,
        "energy_eV": -179.66982007949528,
        "reduced_polarization": [
          -2.5704383335347683e-16,
          -1.2579244899098209e-15,
          0.4999944473834702
        ],
        "cartesian_polarization_e_A2": [
          -4.457940518536456e-17,
          -7.810875124823292e-17,
          0.006567897478088397
        ],
        "ranking_score": 0.5495872475311157
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              1.9983424952240215e-16,
              7.216449660063518e-16,
              0.04411408133206383
            ],
            "target_residual": 0.5019422797212556,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.11033537608113349,
            "max_log_strain_component": 0.014474106503234083,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0145988217885806,
              0.999978669007822,
              0.9856369025345965
            ],
            "cell_volume_ratio": 1.0000047084753099,
            "cell_rmsd_from_input_A": 0.07878386054382425
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.6706190636930407e-14,
              0.4828086800806936,
              -0.01974478293790692
            ],
            "branch_aligned_reduced_polarization": [
              1.6706190636930407e-14,
              0.4828086800806936,
              -0.01974478293790692
            ],
            "target_residual": 0.026180105687964687,
            "energy_eV": -176.64690784089,
            "max_atomic_step_A": 0.005122695568730871,
            "max_log_strain_component": 0.00063103129377527,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0152269874702817,
              0.9999903684905108,
              0.9850129773451062
            ],
            "cell_volume_ratio": 1.0000021259864724,
            "cell_rmsd_from_input_A": 0.08219898797446977
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.7479761972873446e-16,
              0.49974667420700025,
              3.8160974998227005e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.7479761972873446e-16,
              0.49974667420700025,
              3.8160974998227005e-05
            ],
            "target_residual": 0.00025618395229164224,
            "energy_eV": -176.37080099854322
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00025618395229164224,
        "parent_symmetrization_rmsd_A": 0.07676859920358835,
        "parent_cell_rmsd_A": 0.08219898797446977,
        "energy_eV": -176.37080099854322,
        "reduced_polarization": [
          -1.7479761972873446e-16,
          0.49974667420700025,
          3.8160974998227005e-05
        ],
        "cartesian_polarization_e_A2": [
          -2.837797736815224e-16,
          0.0113744390910799,
          0.00017229456485563744
        ],
        "ranking_score": 0.5978307141017891
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "target_residual": 0.5019422797212562,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.10894573636644089,
            "max_log_strain_component": 0.0009623891026151083,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.00119679832359,
              0.9995908277498163,
              0.9992181874916366
            ],
            "cell_volume_ratio": 1.0000047084753145,
            "cell_rmsd_from_input_A": 0.005936725730906165
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48547179152741066,
              5.443721960579064e-15,
              0.00017232124644643275
            ],
            "branch_aligned_reduced_polarization": [
              0.48547179152741066,
              5.443721960579064e-15,
              0.00017232124644643275
            ],
            "target_residual": 0.014529230400643856,
            "energy_eV": -176.71842375709136,
            "max_atomic_step_A": 0.0033960060390121963,
            "max_log_strain_component": 3.291642045285119e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.001229773954295,
              0.9995894331501733,
              0.9991866881868711
            ],
            "cell_volume_ratio": 1.0000047245267503,
            "cell_rmsd_from_input_A": 0.006097056068628972
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999690232325439,
              2.2581377888646367e-15,
              1.3789350432168753e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999690232325439,
              2.2581377888646367e-15,
              1.3789350432168753e-05
            ],
            "target_residual": 3.390731937755254e-05,
            "energy_eV": -176.45126054583508
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.390731937755254e-05,
        "parent_symmetrization_rmsd_A": 0.08154136463468165,
        "parent_cell_rmsd_A": 0.006097056068628972,
        "energy_eV": -176.45126054583508,
        "reduced_polarization": [
          0.4999690232325439,
          2.2581377888646367e-15,
          1.3789350432168753e-05
        ],
        "cartesian_polarization_e_A2": [
          0.011270017301106858,
          -2.051553936891001e-16,
          1.140162548646047e-05
        ],
        "ranking_score": 0.583133443290594
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              1.9983424952240215e-16,
              7.216449660063518e-16,
              0.04411408133206385
            ],
            "target_residual": 0.6766328183288979,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013805773772336086,
            "step_scale": 0.9538256312580766,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0143938752128103,
              1.0002102854743569,
              0.9855573681281851
            ],
            "cell_volume_ratio": 0.9999535894063393,
            "cell_rmsd_from_input_A": 0.08072987914113743
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.777556537625038e-14,
              0.4459453059002863,
              0.44378867263239197
            ],
            "branch_aligned_reduced_polarization": [
              1.777556537625038e-14,
              0.4459453059002863,
              0.44378867263239197
            ],
            "target_residual": 0.0779847631184581,
            "energy_eV": -176.87486184204087,
            "max_atomic_step_A": 0.016501526294827085,
            "max_log_strain_component": 0.002154282872534166,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0166842496114257,
              1.000248008145252,
              0.9832918454948804
            ],
            "cell_volume_ratio": 0.9999452651671406,
            "cell_rmsd_from_input_A": 0.09365360323840964
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.118860189266064e-16,
              0.4984329302959951,
              0.4984332285480182
            ],
            "branch_aligned_reduced_polarization": [
              1.118860189266064e-16,
              0.4984329302959951,
              0.4984332285480182
            ],
            "target_residual": 0.0022159603425953144,
            "energy_eV": -175.75434242083614,
            "max_atomic_step_A": 0.0004885975757283253,
            "max_log_strain_component": 6.656749553993724e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0167549700724166,
              1.0002491470389114,
              0.9832220859456564
            ],
            "cell_volume_ratio": 0.9999450138541182,
            "cell_rmsd_from_input_A": 0.09405204273648213
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.475849485210947e-16,
              0.49997590722376073,
              0.4999804233345854
            ],
            "branch_aligned_reduced_polarization": [
              4.475849485210947e-16,
              0.49997590722376073,
              0.4999804233345854
            ],
            "target_residual": 3.1043641791353915e-05,
            "energy_eV": -175.71892796748227
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.1043641791353915e-05,
        "parent_symmetrization_rmsd_A": 0.09120803218539968,
        "parent_cell_rmsd_A": 0.09405204273648213,
        "energy_eV": -175.71892796748227,
        "reduced_polarization": [
          4.475849485210947e-16,
          0.49997590722376073,
          0.4999804233345854
        ],
        "cartesian_polarization_e_A2": [
          -4.377800496706332e-16,
          0.011542825992524515,
          0.0067472114828271935
        ],
        "ranking_score": 0.6147831301531029
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              7.384655843800999e-16,
              0.04411408133206385
            ],
            "target_residual": 0.6766328183288982,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004309965883788602,
            "step_scale": 0.9580993575683178,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0040603618063655,
              1.0003921000024174,
              0.995519284932805
            ],
            "cell_volume_ratio": 0.999953381463146,
            "cell_rmsd_from_input_A": 0.029103180676999338
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4639254601601833,
              6.0267495223236305e-15,
              0.4758920603617386
            ],
            "branch_aligned_reduced_polarization": [
              0.4639254601601833,
              6.0267495223236305e-15,
              0.4758920603617386
            ],
            "target_residual": 0.04338853740628481,
            "energy_eV": -176.17027957060546,
            "max_atomic_step_A": 0.008939718241432353,
            "max_log_strain_component": 0.0002576761161100729,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0043036366986549,
              1.0004255315236183,
              0.9952421044372284
            ],
            "cell_volume_ratio": 0.9999505943907908,
            "cell_rmsd_from_input_A": 0.03087259665949258
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4998180015124478,
              -1.4552073142258043e-15,
              0.4999224953300702
            ],
            "branch_aligned_reduced_polarization": [
              0.4998180015124478,
              -1.4552073142258043e-15,
              0.4999224953300702
            ],
            "target_residual": 0.00019781411307640944,
            "energy_eV": -175.41852515942585
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00019781411307640944,
        "parent_symmetrization_rmsd_A": 0.092131430523431,
        "parent_cell_rmsd_A": 0.03087259665949258,
        "energy_eV": -175.41852515942585,
        "reduced_polarization": [
          0.4998180015124478,
          -1.4552073142258043e-15,
          0.4999224953300702
        ],
        "cartesian_polarization_e_A2": [
          0.011276590122670078,
          -4.852640003446323e-16,
          0.006577874195320265
        ],
        "ranking_score": 0.6002452079144569
      },
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              7.216449660063518e-16,
              0.04411408133206383
            ],
            "target_residual": 0.70848151152431,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010576137241571434,
            "step_scale": 0.7306936175448382,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0106706447920608,
              0.9999831669768361,
              0.9894620754725322
            ],
            "cell_volume_ratio": 1.0000034404506812,
            "cell_rmsd_from_input_A": 0.05769107611869379
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.35446246492261946,
              0.35211058983686094,
              0.0010222323129467088
            ],
            "branch_aligned_reduced_polarization": [
              0.35446246492261946,
              0.35211058983686094,
              0.0010222323129467088
            ],
            "target_residual": 0.20749336546912187,
            "energy_eV": -176.4832952496304,
            "max_atomic_step_A": 0.051177117956884656,
            "max_log_strain_component": 0.00514067639865831,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.01588112534085,
              0.9999918188345035,
              0.9843768441539554
            ],
            "cell_volume_ratio": 1.000001674952463,
            "cell_rmsd_from_input_A": 0.08571065941351752
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49552444727446776,
              0.49342326099650197,
              -0.002519868598321267
            ],
            "branch_aligned_reduced_polarization": [
              0.49552444727446776,
              0.49342326099650197,
              -0.002519868598321267
            ],
            "target_residual": 0.008344687284251995,
            "energy_eV": -171.59409307986033,
            "max_atomic_step_A": 0.0020785058268780582,
            "max_log_strain_component": 0.0002611883466714922,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0161450478049294,
              0.9999939837427978,
              0.9841186069709937
            ],
            "cell_volume_ratio": 1.000001232625447,
            "cell_rmsd_from_input_A": 0.08713540039552539
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999553064507543,
              0.4998860804711998,
              2.6225321169262725e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999553064507543,
              0.4998860804711998,
              2.6225321169262725e-05
            ],
            "target_residual": 0.0001251516674146402,
            "energy_eV": -171.37226174348396
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0001251516674146402,
        "parent_symmetrization_rmsd_A": 0.11539957333691221,
        "parent_cell_rmsd_A": 0.08713540039552539,
        "energy_eV": -171.37226174348396,
        "reduced_polarization": [
          0.4999553064507543,
          0.4998860804711998,
          2.6225321169262725e-05
        ],
        "cartesian_polarization_e_A2": [
          0.011270020187710736,
          0.01137875308553078,
          0.0001938836875147981
        ],
        "ranking_score": 0.6374337267706228
      },
      "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": [
              1.9983424952240215e-16,
              7.384655843800999e-16,
              0.04411408133206383
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              7.216449660063518e-16,
              0.04411408133206385
            ],
            "target_residual": 0.8413275051011391,
            "energy_eV": -180.7535891747667,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009875815336626693,
            "step_scale": 0.6823091521698542,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.010290921287306,
              1.0001614697361316,
              0.9896212477766139
            ],
            "cell_volume_ratio": 0.9999668004497358,
            "cell_rmsd_from_input_A": 0.05777077257111969
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.331391081994765,
              0.3226107328195852,
              0.33791403943870285
            ],
            "branch_aligned_reduced_polarization": [
              0.331391081994765,
              0.3226107328195852,
              0.33791403943870285
            ],
            "target_residual": 0.29354348562483723,
            "energy_eV": -176.91615385488623,
            "max_atomic_step_A": 0.06610586118570103,
            "max_log_strain_component": 0.006572375457031627,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0171939074606648,
              1.0002667268585224,
              0.9827803014884823
            ],
            "cell_volume_ratio": 0.9999447760549334,
            "cell_rmsd_from_input_A": 0.0964251214448911
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49363953467675675,
              0.4877343619737422,
              0.4887069363166885
            ],
            "branch_aligned_reduced_polarization": [
              0.49363953467675675,
              0.4877343619737422,
              0.4887069363166885
            ],
            "target_residual": 0.01784473823497253,
            "energy_eV": -171.156085835378,
            "max_atomic_step_A": 0.0042509268019799516,
            "max_log_strain_component": 0.0005577031980017275,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.2864316729280154,
            "cell_principal_stretches": [
              1.0177818916186923,
              1.0002753562818096,
              0.9822022000467681
            ],
            "cell_volume_ratio": 0.9999428778726344,
            "cell_rmsd_from_input_A": 0.09971699613323465
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4998676687129927,
              0.499695211073577,
              0.49974967060250064
            ],
            "branch_aligned_reduced_polarization": [
              0.4998676687129927,
              0.499695211073577,
              0.49974967060250064
            ],
            "target_residual": 0.00041602003130075416,
            "energy_eV": -170.73486887384306
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00041602003130075416,
        "parent_symmetrization_rmsd_A": 0.12601222069005064,
        "parent_cell_rmsd_A": 0.09971699613323465,
        "energy_eV": -170.73486887384306,
        "reduced_polarization": [
          0.4998676687129927,
          0.499695211073577,
          0.49974967060250064
        ],
        "cartesian_polarization_e_A2": [
          0.011278619017155453,
          0.011545240994502142,
          0.006765907927424104
        ],
        "ranking_score": 0.6517735097859608
      },
      "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
        ],
        "endpoint_rmsd_A": 0.23503975217646214,
        "minimum_distance_A_by_image": [
          1.5335709860344306,
          1.5335438073326797,
          1.5251975690376114,
          1.5178112141586986,
          1.511740989573818,
          1.5070027995307147,
          1.5036092366480256,
          1.5015694175685537,
          1.500888861816602
        ],
        "minimum_distance_A": 1.500888861816602,
        "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": [
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334,
          384.32466970978334
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.155754797838983e-15,
        1.281011728006296e-15,
        -5.0190538207352265e-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": [
          -180.7535891747667,
          -180.70027229312151,
          -180.5965353588182,
          -180.46435382427754,
          -180.3249715907166,
          -180.19708255460526,
          -180.0953619389923,
          -180.030158573243,
          -180.00770910344073
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.749507310567253e-17,
            -1.3270256690061207e-17,
            0.0005820719863747538
          ],
          [
            1.0859944760641926e-17,
            -2.2026820628400913e-18,
            0.0004867663796068179
          ],
          [
            -1.8813071389175207e-17,
            6.2198686118722256e-18,
            0.0003983774234363564
          ],
          [
            4.974089412397092e-18,
            -1.5346555355853095e-18,
            0.0003175338669946365
          ],
          [
            3.8835812435811777e-17,
            -1.1221040180779646e-17,
            0.00024431207776952845
          ],
          [
            3.3942969492945674e-17,
            7.546894280878347e-18,
            0.00017768439809820075
          ],
          [
            1.581597940203213e-17,
            -6.7073474290581475e-18,
            0.00011587890777119791
          ],
          [
            3.385269563791124e-17,
            9.776658500228766e-18,
            5.715309680025239e-05
          ],
          [
            2.6053034562936492e-17,
            2.9158455176120885e-17,
            -6.622490005325784e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.206586602942757e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740502e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.0190538207352265e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.2065866029427565e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740507e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.019422377738891e-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": [
          [
            7.771561172376096e-16,
            -6.106226635438361e-16,
            0.04411408133206285
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.03689105842977969
          ],
          [
            -8.326672684688674e-16,
            2.220446049250313e-16,
            0.030192234757393743
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.024065261964466456
          ],
          [
            1.7763568394002505e-15,
            -4.996003610813204e-16,
            0.018515927791431852
          ],
          [
            1.5543122344752192e-15,
            3.3306690738754696e-16,
            0.013466348102339487
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.00878223257904398
          ],
          [
            1.5543122344752192e-15,
            4.440892098500626e-16,
            0.00433151984572977
          ],
          [
            1.1102230246251565e-15,
            1.3322676295501878e-15,
            -4.9960036108132044e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -180.00770910344073,
          -180.03015857324303,
          -180.09536193899223,
          -180.1970825546053,
          -180.3249715907166,
          -180.46435382427757,
          -180.59653535881822,
          -180.70027229312151,
          -180.7535891747667
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.2712901926662582e-17,
            3.0575754700161435e-17,
            -4.468555824204284e-17
          ],
          [
            -1.3902173675302217e-17,
            2.0284535226236414e-17,
            -5.715309680030897e-05
          ],
          [
            2.803905937369395e-17,
            2.2297642193504204e-18,
            -0.00011587890777120397
          ],
          [
            2.4012845439158372e-18,
            6.319169852410098e-20,
            -0.0001776843980982488
          ],
          [
            -4.477583209707727e-18,
            -5.461568229583013e-18,
            -0.0002443120777695375
          ],
          [
            8.97322119042234e-18,
            7.492729967857688e-18,
            -0.0003175338669947225
          ],
          [
            -1.539169228337031e-17,
            -1.0941191230172913e-17,
            -0.00039837742343641283
          ],
          [
            -1.7874223296817135e-18,
            3.2891279081794565e-17,
            -0.0004867663796068731
          ],
          [
            -3.642550050639249e-17,
            1.9837679643815987e-17,
            -0.0005820719863748215
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.007581105808344e-15,
            1.3432776231446824e-15,
            -3.386629827240917e-15
          ],
          [
            -6.167229343977941e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695204e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689171e-16,
            2.7761864074439846e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.980666212931217e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547006e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.4450050250745942e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.007581105808344e-15,
            1.3432776231446824e-15,
            -3.386629827240917e-15
          ],
          [
            -6.16722934397794e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.2438580741815249e-15,
            9.795972037695203e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689177e-16,
            2.7761864074439795e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.9806662129312165e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547005e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.445005025074594e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.5353998249877552e-15,
          3.1450226015758292e-15,
          -0.04411408133207291
        ],
        "actual_opposite_endpoint_branch_residual": 6.258298704134615e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.206586602942757e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740502e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.0190538207352265e-15
          ],
          [
            -6.167229343977941e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695204e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689171e-16,
            2.7761864074439846e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.980666212931217e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547006e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.4450050250745942e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.761097706902111e-16,
            -5.829991455632369e-16,
            0.04411408133206287
          ],
          [
            4.817647338185365e-16,
            -9.676992620233318e-17,
            0.03689105842977966
          ],
          [
            -8.345783086266253e-16,
            2.732560621041294e-16,
            0.03019223475739377
          ],
          [
            2.2065866029427565e-16,
            -6.74216698950682e-17,
            0.024065261964466508
          ],
          [
            1.722819521934617e-15,
            -4.929713863504105e-16,
            0.018515927791431852
          ],
          [
            1.5057650865816272e-15,
            3.3155597666045305e-16,
            0.013466348102339527
          ],
          [
            7.01622455236971e-16,
            -2.9467235724726867e-16,
            0.008782232579044032
          ],
          [
            1.5017603922024209e-15,
            4.2951569703740507e-16,
            0.004331519845729773
          ],
          [
            1.155754797838983e-15,
            1.281011728006296e-15,
            -5.019422377738891e-15
          ],
          [
            -6.167229343977942e-16,
            8.911558367895192e-16,
            -0.004331519845734062
          ],
          [
            1.243858074181525e-15,
            9.795972037695203e-17,
            -0.008782232579044492
          ],
          [
            1.0652487048689177e-16,
            2.7761864074439795e-18,
            -0.013466348102343168
          ],
          [
            -1.9863284120864019e-16,
            -2.3994182521480153e-16,
            -0.01851592779143254
          ],
          [
            3.9806662129312165e-16,
            3.291763883112153e-16,
            -0.024065261964473023
          ],
          [
            -6.828003916547005e-16,
            -4.806768465460156e-16,
            -0.030192234757398045
          ],
          [
            -7.929294870828781e-17,
            1.445005025074594e-15,
            -0.036891058429783845
          ],
          [
            -1.6158941820098045e-15,
            8.715242329083081e-16,
            -0.044114081332068004
          ]
        ],
        "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": [
          [
            7.771561172376096e-16,
            -6.106226635438361e-16,
            0.04411408133206285
          ],
          [
            4.440892098500626e-16,
            -1.1102230246251565e-16,
            0.03689105842977969
          ],
          [
            -8.326672684688674e-16,
            2.220446049250313e-16,
            0.030192234757393743
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.024065261964466456
          ],
          [
            1.7763568394002505e-15,
            -4.996003610813204e-16,
            0.018515927791431852
          ],
          [
            1.5543122344752192e-15,
            3.3306690738754696e-16,
            0.013466348102339487
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.00878223257904398
          ],
          [
            1.5543122344752192e-15,
            4.440892098500626e-16,
            0.00433151984572977
          ],
          [
            1.1102230246251565e-15,
            1.3322676295501878e-15,
            -4.9960036108132044e-15
          ],
          [
            -6.106226635438361e-16,
            8.881784197001252e-16,
            -0.004331519845734044
          ],
          [
            1.2212453270876722e-15,
            1.1102230246251565e-16,
            -0.00878223257904448
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.01346634810234315
          ],
          [
            -2.220446049250313e-16,
            -2.220446049250313e-16,
            -0.018515927791432518
          ],
          [
            4.440892098500626e-16,
            3.3306690738754696e-16,
            -0.024065261964473006
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.030192234757398073
          ],
          [
            -5.551115123125783e-17,
            1.4432899320127035e-15,
            -0.03689105842978385
          ],
          [
            -1.609823385706477e-15,
            8.881784197001252e-16,
            -0.04411408133206801
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.416662852122678e-15,
        "parent_symmetrization_rmsd_A": 0.23503975217646214,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -180.00770910344073,
        "reduced_polarization": [
          3.5001028874264426e-16,
          1.0375005202676377e-15,
          -4.278784432235293e-15
        ],
        "cartesian_polarization_e_A2": [
          7.88993493000918e-18,
          2.3615640477006882e-17,
          -5.645726893853251e-17
        ],
        "ranking_score": 0.23503975217647097
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 52,
      "full_response": 19,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 44,
      "energy_polarization": 33
    },
    "elapsed_seconds": 636.2273715120391
  }
}