{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Cl16K8Zn4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -87.60571907430932,
  "input_cartesian_polarization_e_A2": [
    1.0540616504291372e-17,
    -6.075494235112388e-18,
    -0.0013658696483694116
  ],
  "input_reduced_polarization": [
    9.944915835165607e-16,
    -4.074868812973143e-16,
    -0.1571088351257705
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.251762457853436e-16,
      "parent_symmetrization_rmsd_A": 0.09376468264994407,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -87.5932818066008,
      "reduced_polarization": [
        -1.4733208644689787e-16,
        5.804096943779684e-16,
        -1.7961954590058792e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.5615728154505735e-18,
        8.653716018955262e-18,
        -1.5615728154505735e-18
      ],
      "ranking_score": 0.09376468264994532
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcn",
      "spacegroup_number": 60,
      "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": 1.339531389632003e-15,
      "parent_symmetrization_rmsd_A": 0.8761904427100438,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -83.08223472291475,
      "reduced_polarization": [
        -2.479035009257862e-16,
        1.292284366523879e-15,
        -2.5077741939050183e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.6275292588099008e-18,
        1.926753124897088e-17,
        -2.1802037127172883e-18
      ],
      "ranking_score": 0.8761904427100464
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.092569427105168e-14,
      "parent_symmetrization_rmsd_A": 0.9381447414099591,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": 1684.671466831983,
      "reduced_polarization": [
        -4.920124332709478e-14,
        7.624750511407418e-14,
        -5.7478254688188135e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.214839884430202e-16,
        1.1368250096480176e-15,
        -4.997033009441835e-17
      ],
      "ranking_score": 0.9381447414101409
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_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": 1.4847044355022362e-15,
      "parent_symmetrization_rmsd_A": 2.242212687520563,
      "parent_cell_rmsd_A": 5.046083927983733,
      "energy_eV": -87.59281449024994,
      "reduced_polarization": [
        -1.1740525638737166e-15,
        -5.613110809393368e-18,
        9.087993898812918e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2443783373121758e-17,
        -4.879915048283042e-20,
        1.354989745073258e-17
      ],
      "ranking_score": 3.503733669516499
    },
    {
      "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": 0.0003935492835609272,
      "parent_symmetrization_rmsd_A": 0.04102983450019286,
      "parent_cell_rmsd_A": 0.020401115140704723,
      "energy_eV": -87.50775945333177,
      "reduced_polarization": [
        -3.6139490652545e-15,
        5.123966854709945e-15,
        -0.0003935492835609272
      ],
      "cartesian_polarization_e_A2": [
        -3.808841809532023e-17,
        7.612825402470255e-17,
        -3.4239645573612047e-06
      ],
      "ranking_score": 0.5469172118524909
    },
    {
      "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": 2.1201408224215155e-15,
      "parent_symmetrization_rmsd_A": 0.09377162769553954,
      "parent_cell_rmsd_A": 0.020401115140704723,
      "energy_eV": -87.58960383504694,
      "reduced_polarization": [
        6.360524565214125e-16,
        3.244628636991619e-16,
        -1.9962861091365123e-15
      ],
      "cartesian_polarization_e_A2": [
        6.704338899431367e-18,
        4.817731455509256e-18,
        -1.7368124322802274e-17
      ],
      "ranking_score": 0.09887190648071997
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.119146286792208e-15,
      "parent_symmetrization_rmsd_A": 2.2435121374898976,
      "parent_cell_rmsd_A": 5.035087445451305,
      "energy_eV": -87.55637320998532,
      "reduced_polarization": [
        -1.7038216770102679e-15,
        1.257916182872564e-15,
        7.361762453678858e-17
      ],
      "cartesian_polarization_e_A2": [
        -1.7959207341713495e-17,
        1.094414500597092e-17,
        1.0930987336029404e-18
      ],
      "ranking_score": 3.5022839988527283
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.701310421161397e-05,
      "parent_symmetrization_rmsd_A": 0.09381937630579473,
      "parent_cell_rmsd_A": 0.045296872098416506,
      "energy_eV": -87.21709530872234,
      "reduced_polarization": [
        2.5571578756986636e-15,
        -5.914466751245779e-16,
        -0.4999629868957884
      ],
      "cartesian_polarization_e_A2": [
        1.4130259437906432e-17,
        -1.4143403865290532e-16,
        -0.004339324668498252
      ],
      "ranking_score": 0.6052176205388221
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.607757750514542e-07,
      "parent_symmetrization_rmsd_A": 0.17736419052785019,
      "parent_cell_rmsd_A": 0.022276460950358526,
      "energy_eV": -86.64881709593314,
      "reduced_polarization": [
        0.49999983671400605,
        2.8285418628048104e-15,
        -7.430460713074826e-07
      ],
      "cartesian_polarization_e_A2": [
        0.005270902605290772,
        -3.8108258854723526e-17,
        -8.213247504159107e-06
      ],
      "ranking_score": 0.68293482731699
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0001292955328470232,
      "parent_symmetrization_rmsd_A": 0.3018200096840139,
      "parent_cell_rmsd_A": 0.07396868685617618,
      "energy_eV": -84.65631274673747,
      "reduced_polarization": [
        -2.686719485650921e-15,
        -0.49996121629135504,
        -0.00012334163432490387
      ],
      "cartesian_polarization_e_A2": [
        -1.4975505930314512e-15,
        -0.007416630876054548,
        5.645192680813742e-05
      ],
      "ranking_score": 0.820570772463752
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.4776689640072829e-05,
      "parent_symmetrization_rmsd_A": 0.2042769066248739,
      "parent_cell_rmsd_A": 0.05151512534280485,
      "energy_eV": -86.2998193374024,
      "reduced_polarization": [
        0.4999870673930821,
        -6.249334490172869e-16,
        -0.49999285169705276
      ],
      "cartesian_polarization_e_A2": [
        0.005380710543254323,
        -1.3631044562867874e-16,
        -0.004347427745174513
      ],
      "ranking_score": 0.7171852413398553
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00028945426236870345,
      "parent_symmetrization_rmsd_A": 0.33425626876673586,
      "parent_cell_rmsd_A": 0.09611175743694833,
      "energy_eV": -83.81436026198503,
      "reduced_polarization": [
        -1.2212291747457983e-15,
        -0.5000897658180384,
        -0.5002751833350974
      ],
      "cartesian_polarization_e_A2": [
        -1.518063352292162e-15,
        -0.007520344003646999,
        -0.004277838815765949
      ],
      "ranking_score": 0.8588631166507104
    },
    {
      "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": 0.00043836112193863157,
      "parent_symmetrization_rmsd_A": 0.37494106173394665,
      "parent_cell_rmsd_A": 0.0797313105329105,
      "energy_eV": -83.53980229124247,
      "reduced_polarization": [
        0.49987979947885464,
        -0.4997894781617964,
        -0.0003652298777250623
      ],
      "cartesian_polarization_e_A2": [
        0.005262491205149638,
        -0.00741443119727881,
        4.854909984765752e-05
      ],
      "ranking_score": 0.8957506116110515
    },
    {
      "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": 0.0004923223603565801,
      "parent_symmetrization_rmsd_A": 0.4054127797035002,
      "parent_cell_rmsd_A": 0.10641698399067087,
      "energy_eV": -82.52040885149133,
      "reduced_polarization": [
        0.49973365339633086,
        -0.4996168775577716,
        -0.5001570286199454
      ],
      "cartesian_polarization_e_A2": [
        0.005413456982146232,
        -0.00752377114519341,
        -0.004281554778494484
      ],
      "ranking_score": 0.9330016704218811
    }
  ],
  "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": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.1571088351257705,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.04611704025712476,
            "max_log_strain_component": 0.00519665161251185,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0052101776263467,
              1.0003339271911604,
              0.9989264506218497
            ],
            "cell_volume_ratio": 1.0044663415212753,
            "cell_rmsd_from_input_A": 0.020401115140704723
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.6139490652545e-15,
              5.123966854709945e-15,
              -0.0003935492835609272
            ],
            "branch_aligned_reduced_polarization": [
              -3.6139490652545e-15,
              5.123966854709945e-15,
              -0.0003935492835609272
            ],
            "target_residual": 0.0003935492835609272,
            "energy_eV": -87.50775945333177
          }
        ],
        "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": 6.251762457853436e-16,
        "parent_symmetrization_rmsd_A": 0.09376468264994407,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -87.5932818066008,
        "reduced_polarization": [
          -1.4733208644689787e-16,
          5.804096943779684e-16,
          -1.7961954590058792e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.5615728154505735e-18,
          8.653716018955262e-18,
          -1.5615728154505735e-18
        ],
        "ranking_score": 0.09376468264994532
      },
      "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": [
          -87.6057190743093,
          -87.6029837860686,
          -87.60053165954716,
          -87.59839265613607,
          -87.59659509253554,
          -87.59516504929374,
          -87.59412526897901,
          -87.59349367154717,
          -87.59328180660079
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3663762135192518e-18,
            1.968232402807494e-18,
            -0.001365869648369417
          ],
          [
            1.4639745144849128e-18,
            -6.270690837043709e-18,
            -0.0011967205899841792
          ],
          [
            2.895416261981272e-18,
            -4.896181431777319e-18,
            -0.0010269680705681029
          ],
          [
            -6.783081917113429e-18,
            9.751696904818946e-18,
            -0.0008566813147777593
          ],
          [
            -4.22925970851197e-19,
            9.938760315003129e-18,
            -0.0006859330224712133
          ],
          [
            5.514304004559838e-18,
            1.677064138259939e-17,
            -0.0005148014240218703
          ],
          [
            4.2780588589948005e-18,
            7.254807038447456e-18,
            -0.00034337199620328813
          ],
          [
            -7.759064926770037e-18,
            4.22925970851197e-19,
            -0.00017173811304328562
          ],
          [
            -3.5786043687408975e-18,
            -2.553822208601459e-18,
            -4.4732554609261225e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.205788292908023e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413384e-16,
            -0.09853956678766877
          ],
          [
            -3.990244007936818e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330238e-16,
            2.836588731922402e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.2057882929080235e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413383e-16,
            -0.09853956678766877
          ],
          [
            -3.9902440079368156e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330239e-16,
            2.8365887319224e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.134781488891349e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.15710883512577112
          ],
          [
            1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.13765250445962673
          ],
          [
            2.220446049250313e-16,
            -3.3306690738754696e-16,
            -0.1181267608303112
          ],
          [
            -6.661338147750939e-16,
            6.661338147750939e-16,
            -0.09853956678766879
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            -0.07889928461577833
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-15,
            -0.059214912744945336
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.03949628312094883
          ],
          [
            -7.216449660063518e-16,
            0.0,
            -0.019754136069382144
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -4.996003610813204e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.59328180660079,
          -87.59349367154715,
          -87.59412526897904,
          -87.5951650492937,
          -87.59659509253554,
          -87.59839265613604,
          -87.60053165954714,
          -87.60298378606865,
          -87.60571907430929
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.5786043687408975e-18,
            -2.553822208601459e-18,
            -4.4732554609261225e-18
          ],
          [
            -3.643669902718005e-18,
            6.360155946262232e-18,
            0.00017173811304329803
          ],
          [
            7.970527912195636e-18,
            1.655104520542665e-17,
            0.0003433719962032995
          ],
          [
            3.611137135729451e-18,
            1.9096734222280973e-17,
            0.0005148014240218664
          ],
          [
            4.749783980328828e-18,
            4.0543960859484945e-17,
            0.0006859330224711977
          ],
          [
            -2.9442154124641023e-18,
            1.5640127729747152e-17,
            0.000856681314777754
          ],
          [
            3.05808009692404e-18,
            2.5033964197692007e-17,
            0.001026968070568089
          ],
          [
            3.9527311891092646e-18,
            2.404171480454112e-17,
            0.0011967205899841755
          ],
          [
            -8.165724514126957e-18,
            9.564633494634763e-18,
            0.0013658696483693968
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.885253359585084e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809125e-16,
            0.15710883512576881
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.8852533595850833e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809126e-16,
            0.15710883512576881
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.04187638522651e-16,
          -4.745831147639403e-16,
          0.15710883512577012
        ],
        "actual_opposite_endpoint_branch_residual": 1.7171328917433152e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.205788292908023e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413384e-16,
            -0.09853956678766877
          ],
          [
            -3.990244007936818e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330238e-16,
            2.836588731922402e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.885253359585084e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809125e-16,
            0.15710883512576881
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.2057882929080235e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413383e-16,
            -0.09853956678766877
          ],
          [
            -3.9902440079368156e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330239e-16,
            2.8365887319224e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.134781488891349e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.8852533595850833e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809126e-16,
            0.15710883512576881
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.15710883512577112
          ],
          [
            1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.13765250445962673
          ],
          [
            2.220446049250313e-16,
            -3.3306690738754696e-16,
            -0.1181267608303112
          ],
          [
            -6.661338147750939e-16,
            6.661338147750939e-16,
            -0.09853956678766879
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            -0.07889928461577833
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-15,
            -0.059214912744945336
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.03949628312094883
          ],
          [
            -7.216449660063518e-16,
            0.0,
            -0.019754136069382144
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -4.996003610813204e-16
          ],
          [
            -3.3306690738754696e-16,
            4.440892098500626e-16,
            0.019754136069383588
          ],
          [
            7.771561172376096e-16,
            1.1102230246251565e-15,
            0.039496283120950104
          ],
          [
            3.3306690738754696e-16,
            1.3322676295501878e-15,
            0.05921491274494495
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            0.07889928461577655
          ],
          [
            -2.7755575615628914e-16,
            9.992007221626409e-16,
            0.09853956678766818
          ],
          [
            3.3306690738754696e-16,
            1.6653345369377348e-15,
            0.1181267608303096
          ],
          [
            3.3306690738754696e-16,
            1.6653345369377348e-15,
            0.1376525044596263
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.1571088351257688
          ]
        ]
      },
      "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": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.3428911648742295,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.10065077270580192,
            "max_log_strain_component": 0.011341729594222225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0023470378252703,
              0.9992715885750668,
              0.988722345351856
            ],
            "cell_volume_ratio": 0.9903210271138607,
            "cell_rmsd_from_input_A": 0.04389102115181685
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.236623962722692e-15,
              -6.022037754653346e-15,
              -0.49049318668105224
            ],
            "branch_aligned_reduced_polarization": [
              6.236623962722692e-15,
              -6.022037754653346e-15,
              -0.49049318668105224
            ],
            "target_residual": 0.00950681331894776,
            "energy_eV": -87.23875697148311,
            "max_atomic_step_A": 0.002783812088684566,
            "max_log_strain_component": 0.000366989618095826,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.002423073955633,
              0.9992480278919054,
              0.9883595610890333
            ],
            "cell_volume_ratio": 0.990009409703429,
            "cell_rmsd_from_input_A": 0.045296872098416506
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.5571578756986636e-15,
              -5.914466751245779e-16,
              -0.4999629868957884
            ],
            "branch_aligned_reduced_polarization": [
              2.5571578756986636e-15,
              -5.914466751245779e-16,
              -0.4999629868957884
            ],
            "target_residual": 3.701310421161397e-05,
            "energy_eV": -87.21709530872234
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.701310421161397e-05,
        "parent_symmetrization_rmsd_A": 0.09381937630579473,
        "parent_cell_rmsd_A": 0.045296872098416506,
        "energy_eV": -87.21709530872234,
        "reduced_polarization": [
          2.5571578756986636e-15,
          -5.914466751245779e-16,
          -0.4999629868957884
        ],
        "cartesian_polarization_e_A2": [
          1.4130259437906432e-17,
          -1.4143403865290532e-16,
          -0.004339324668498252
        ],
        "ranking_score": 0.6052176205388221
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.5241022668092321,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004215890545628993,
            "step_scale": 0.8112705757447759,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0045010971213089,
              1.0002708967692602,
              0.9988541432077794
            ],
            "cell_volume_ratio": 1.0036218870122247,
            "cell_rmsd_from_input_A": 0.018254335844621015
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.39885395768168797,
              7.259769371409107e-15,
              -0.026196501461654316
            ],
            "branch_aligned_reduced_polarization": [
              0.39885395768168797,
              7.259769371409107e-15,
              -0.026196501461654316
            ],
            "target_residual": 0.10448338894526835,
            "energy_eV": -86.98778414077748,
            "max_atomic_step_A": 0.03306331207320741,
            "max_log_strain_component": 0.0008661770439441273,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0054653092421553,
              1.0003265630323128,
              0.9985822029725155
            ],
            "cell_volume_ratio": 1.004367645785209,
            "cell_rmsd_from_input_A": 0.022251815045201007
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49857589195795876,
              1.6508502521504415e-15,
              -9.836625887283148e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49857589195795876,
              1.6508502521504415e-15,
              -9.836625887283148e-05
            ],
            "target_residual": 0.0014275011860909847,
            "energy_eV": -86.65376337400099,
            "max_atomic_step_A": 0.0004800834699810654,
            "max_log_strain_component": 4.979816199269063e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0054703786767007,
              1.0003267551784785,
              0.9985795366728704
            ],
            "cell_volume_ratio": 1.0043702208475251,
            "cell_rmsd_from_input_A": 0.022276460950358526
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999983671400605,
              2.8285418628048104e-15,
              -7.430460713074826e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999983671400605,
              2.8285418628048104e-15,
              -7.430460713074826e-07
            ],
            "target_residual": 7.607757750514542e-07,
            "energy_eV": -86.64881709593314
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.607757750514542e-07,
        "parent_symmetrization_rmsd_A": 0.17736419052785019,
        "parent_cell_rmsd_A": 0.022276460950358526,
        "energy_eV": -86.64881709593314,
        "reduced_polarization": [
          0.49999983671400605,
          2.8285418628048104e-15,
          -7.430460713074826e-07
        ],
        "cartesian_polarization_e_A2": [
          0.005270902605290772,
          -3.8108258854723526e-17,
          -8.213247504159107e-06
        ],
        "ranking_score": 0.68293482731699
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.944915835165607e-16,
              -3.885780586188048e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.5241022668092327,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0028590749767640027,
            "step_scale": 0.4487687864624397,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0043104353109562,
              0.999518081918112,
              0.9981824079535682
            ],
            "cell_volume_ratio": 1.0020018929990953,
            "cell_rmsd_from_input_A": 0.027153516801856785
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1949549646421543e-14,
              -0.21951482183638052,
              -0.08609347421300208
            ],
            "branch_aligned_reduced_polarization": [
              1.1949549646421543e-14,
              -0.2195148218363805,
              -0.08609347421300208
            ],
            "target_residual": 0.29340078641943385,
            "energy_eV": -87.04373710200721,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.003028882339796147,
            "step_scale": 0.7560051780333764,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0087695852836351,
              0.9990452998851208,
              0.9961938697392945
            ],
            "cell_volume_ratio": 1.0039706699792041,
            "cell_rmsd_from_input_A": 0.055849963193776074
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.0371505888757746e-14,
              -0.41386667739736194,
              -0.026402554651671194
            ],
            "branch_aligned_reduced_polarization": [
              3.0371505888757746e-14,
              -0.41386667739736194,
              -0.026402554651671194
            ],
            "target_residual": 0.0900890900981057,
            "energy_eV": -85.56528396285833,
            "max_atomic_step_A": 0.07236644766416793,
            "max_log_strain_component": 0.0017463412911579896,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0115311879743043,
              0.9987195436011197,
              0.9951437328674227
            ],
            "cell_volume_ratio": 1.0053299906722588,
            "cell_rmsd_from_input_A": 0.07283175339861543
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              9.444283946560084e-15,
              -0.4960423738610531,
              -0.003518255264113157
            ],
            "branch_aligned_reduced_polarization": [
              9.444283946560084e-15,
              -0.4960423738610531,
              -0.003518255264113157
            ],
            "target_residual": 0.005295368236405822,
            "energy_eV": -84.70171569002565,
            "max_atomic_step_A": 0.0040031041071443545,
            "max_log_strain_component": 0.00021617947499971,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0117768236842044,
              0.9986749184244532,
              0.9951310572054884
            ],
            "cell_volume_ratio": 1.0055163811087138,
            "cell_rmsd_from_input_A": 0.07396868685617618
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -2.686719485650921e-15,
              -0.49996121629135504,
              -0.00012334163432490387
            ],
            "branch_aligned_reduced_polarization": [
              -2.686719485650921e-15,
              -0.49996121629135504,
              -0.00012334163432490387
            ],
            "target_residual": 0.0001292955328470232,
            "energy_eV": -84.65631274673747
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0001292955328470232,
        "parent_symmetrization_rmsd_A": 0.3018200096840139,
        "parent_cell_rmsd_A": 0.07396868685617618,
        "energy_eV": -84.65631274673747,
        "reduced_polarization": [
          -2.686719485650921e-15,
          -0.49996121629135504,
          -0.00012334163432490387
        ],
        "cartesian_polarization_e_A2": [
          -1.4975505930314512e-15,
          -0.007416630876054548,
          5.645192680813742e-05
        ],
        "ranking_score": 0.820570772463752
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.6062791031767506,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.008308037909732375,
            "step_scale": 0.7325194839741241,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0018374900988891,
              0.999466372443041,
              0.9916087989487595
            ],
            "cell_volume_ratio": 0.9929007482104729,
            "cell_rmsd_from_input_A": 0.03296466865295002
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3558750649425042,
              -5.514043612335656e-15,
              -0.3940400617854093
            ],
            "branch_aligned_reduced_polarization": [
              0.3558750649425042,
              -5.514043612335656e-15,
              -0.3940400617854093
            ],
            "target_residual": 0.1788840557785049,
            "energy_eV": -86.99094755415621,
            "max_atomic_step_A": 0.0534484929293416,
            "max_log_strain_component": 0.004498910356325942,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.002816401469438,
              0.9991775250557308,
              0.9871115282355447
            ],
            "cell_volume_ratio": 0.9890774695304606,
            "cell_rmsd_from_input_A": 0.05051040290370871
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49498800641271523,
              5.676915857227682e-17,
              -0.4946755502557181
            ],
            "branch_aligned_reduced_polarization": [
              0.49498800641271523,
              5.676915857227682e-17,
              -0.4946755502557181
            ],
            "target_residual": 0.007312307761464056,
            "energy_eV": -86.3324293142544,
            "max_atomic_step_A": 0.002328089721763075,
            "max_log_strain_component": 0.00026127065158948107,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0028716370147963,
              0.9991607530376927,
              0.9868525974348156
            ],
            "cell_volume_ratio": 0.9888558885098798,
            "cell_rmsd_from_input_A": 0.05151512534280485
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999870673930821,
              -6.249334490172869e-16,
              -0.49999285169705276
            ],
            "branch_aligned_reduced_polarization": [
              0.4999870673930821,
              -6.249334490172869e-16,
              -0.49999285169705276
            ],
            "target_residual": 1.4776689640072829e-05,
            "energy_eV": -86.2998193374024
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.4776689640072829e-05,
        "parent_symmetrization_rmsd_A": 0.2042769066248739,
        "parent_cell_rmsd_A": 0.05151512534280485,
        "energy_eV": -86.2998193374024,
        "reduced_polarization": [
          0.4999870673930821,
          -6.249334490172869e-16,
          -0.49999285169705276
        ],
        "cartesian_polarization_e_A2": [
          0.005380710543254323,
          -1.3631044562867874e-16,
          -0.004347427745174513
        ],
        "ranking_score": 0.7171852413398553
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.944915835165607e-16,
              -3.885780586188048e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.6062791031767512,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004798582392998998,
            "step_scale": 0.42309088337583106,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0009923388533153,
              1.0009550491549002,
              0.993956861352751
            ],
            "cell_volume_ratio": 0.9958934230303377,
            "cell_rmsd_from_input_A": 0.030316243990953676
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.5265671162456955e-14,
              -0.2061958942777082,
              -0.29621110827341135
            ],
            "branch_aligned_reduced_polarization": [
              1.5265671162456955e-14,
              -0.20619589427770824,
              -0.29621110827341135
            ],
            "target_residual": 0.3575622532237245,
            "energy_eV": -87.06085677305664,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005708343254377196,
            "step_scale": 0.6978169777250826,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0021740972968967,
              1.0019180527062885,
              0.9869872238239961
            ],
            "cell_volume_ratio": 0.9910302393646065,
            "cell_rmsd_from_input_A": 0.06437889179982645
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.3461741242683597e-14,
              -0.3929041111971355,
              -0.41970273244221845
            ],
            "branch_aligned_reduced_polarization": [
              3.3461741242683597e-14,
              -0.3929041111971355,
              -0.41970273244221845
            ],
            "target_residual": 0.1338550730294578,
            "energy_eV": -85.42632654147685,
            "max_atomic_step_A": 0.09608209946992571,
            "max_log_strain_component": 0.005563782551331611,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.003327270952276,
              1.0024244938957976,
              0.9806646045483602
            ],
            "cell_volume_ratio": 0.9863130677190333,
            "cell_rmsd_from_input_A": 0.0932895595819139
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.2590225741915053e-14,
              -0.4940179770309584,
              -0.49182708435311967
            ],
            "branch_aligned_reduced_polarization": [
              1.2590225741915053e-14,
              -0.4940179770309584,
              -0.49182708435311967
            ],
            "target_residual": 0.010128235234884831,
            "energy_eV": -83.93182819062528,
            "max_atomic_step_A": 0.007058836948212875,
            "max_log_strain_component": 0.0006697971292046904,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0034661854607736,
              1.0024144885402624,
              0.9799755879112655
            ],
            "cell_volume_ratio": 0.9857467063522111,
            "cell_rmsd_from_input_A": 0.09611175743694833
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.2212291747457983e-15,
              -0.5000897658180384,
              -0.5002751833350974
            ],
            "branch_aligned_reduced_polarization": [
              -1.2212291747457983e-15,
              -0.5000897658180384,
              -0.5002751833350974
            ],
            "target_residual": 0.00028945426236870345,
            "energy_eV": -83.81436026198503
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00028945426236870345,
        "parent_symmetrization_rmsd_A": 0.33425626876673586,
        "parent_cell_rmsd_A": 0.09611175743694833,
        "energy_eV": -83.81436026198503,
        "reduced_polarization": [
          -1.2212291747457983e-15,
          -0.5000897658180384,
          -0.5002751833350974
        ],
        "cartesian_polarization_e_A2": [
          -1.518063352292162e-15,
          -0.007520344003646999,
          -0.004277838815765949
        ],
        "ranking_score": 0.8588631166507104
      },
      "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": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              -3.885780586188048e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.7243501819386637,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0025832936758124077,
            "step_scale": 0.4054813453250786,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0039514331114672,
              0.9996014291414831,
              0.9982634989280657
            ],
            "cell_volume_ratio": 1.0018086194406781,
            "cell_rmsd_from_input_A": 0.02482847599185327
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19820750175018326,
              -0.1979866501888693,
              -0.0915382282126412
            ],
            "branch_aligned_reduced_polarization": [
              0.19820750175018326,
              -0.1979866501888693,
              -0.0915382282126412
            ],
            "target_residual": 0.43665778670294614,
            "energy_eV": -87.01154537495354,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0027473761114821006,
            "step_scale": 0.6283598561690668,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.007947930554376,
              0.9992357118210963,
              0.9963086756860671
            ],
            "cell_volume_ratio": 1.0034597488213908,
            "cell_rmsd_from_input_A": 0.050953103531492565
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.37230254617969744,
              -0.3709337321557214,
              -0.03742730465995438
            ],
            "branch_aligned_reduced_polarization": [
              0.37230254617969744,
              -0.3709337321557214,
              -0.03742730465995438
            ],
            "target_residual": 0.18537946040904427,
            "energy_eV": -85.41329768192236,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00260224229162504,
            "step_scale": 0.9728998274966063,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.011808302129156,
              0.9988703566903849,
              0.9944993200499243
            ],
            "cell_volume_ratio": 1.0051059731900072,
            "cell_rmsd_from_input_A": 0.07592455697163875
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48845225486435323,
              -0.4865043644660391,
              -0.005647068338832922
            ],
            "branch_aligned_reduced_polarization": [
              0.48845225486435323,
              -0.4865043644660391,
              -0.005647068338832922
            ],
            "target_residual": 0.018637917721859663,
            "energy_eV": -83.7345787846522,
            "max_atomic_step_A": 0.016300616538010494,
            "max_log_strain_component": 0.00041246062528179956,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0124615748682702,
              0.998791431201658,
              0.9942877963965692
            ],
            "cell_volume_ratio": 1.0054615483637288,
            "cell_rmsd_from_input_A": 0.0797313105329105
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49987979947885464,
              -0.4997894781617964,
              -0.0003652298777250623
            ],
            "branch_aligned_reduced_polarization": [
              0.49987979947885464,
              -0.4997894781617964,
              -0.0003652298777250623
            ],
            "target_residual": 0.00043836112193863157,
            "energy_eV": -83.53980229124247
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00043836112193863157,
        "parent_symmetrization_rmsd_A": 0.37494106173394665,
        "parent_cell_rmsd_A": 0.0797313105329105,
        "energy_eV": -83.53980229124247,
        "reduced_polarization": [
          0.49987979947885464,
          -0.4997894781617964,
          -0.0003652298777250623
        ],
        "cartesian_polarization_e_A2": [
          0.005262491205149638,
          -0.00741443119727881,
          4.854909984765752e-05
        ],
        "ranking_score": 0.8957506116110515
      },
      "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": [
              9.944915835165607e-16,
              -4.074868812973143e-16,
              -0.1571088351257705
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              -3.885780586188048e-16,
              -0.1571088351257705
            ],
            "target_residual": 0.7858589892269507,
            "energy_eV": -87.60571907430932,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00438634811050159,
            "step_scale": 0.3867441975309044,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0011593090868744,
              1.0006632300336744,
              0.9944323891791904
            ],
            "cell_volume_ratio": 0.9962455457189432,
            "cell_rmsd_from_input_A": 0.027964814472284542
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1882695223817534,
              -0.1882459461874196,
              -0.28266353835422736
            ],
            "branch_aligned_reduced_polarization": [
              0.18826952238175343,
              -0.18824594618741963,
              -0.28266353835422736
            ],
            "target_residual": 0.4915298752928267,
            "energy_eV": -87.03330770997613,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005324661701954143,
            "step_scale": 0.5916798629285198,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0024439467478894,
              1.0013717426281137,
              0.9879339259613272
            ],
            "cell_volume_ratio": 0.9917068869616438,
            "cell_rmsd_from_input_A": 0.059564428393835765
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.35754747909096884,
              -0.35549325175308594,
              -0.39267009185094326
            ],
            "branch_aligned_reduced_polarization": [
              0.35754747909096884,
              -0.35549325175308594,
              -0.39267009185094326
            ],
            "target_residual": 0.22955310972740037,
            "energy_eV": -85.31085140885003,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006104735904311462,
            "step_scale": 0.8091931221794366,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0037342764753876,
              1.0019363610946468,
              0.9809589861219474
            ],
            "cell_volume_ratio": 0.9865287422271832,
            "cell_rmsd_from_input_A": 0.09152388073682433
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4674085595378645,
              -0.4639968972148282,
              -0.46857538443540303
            ],
            "branch_aligned_reduced_polarization": [
              0.4674085595378645,
              -0.4639968972148282,
              -0.46857538443540303
            ],
            "target_residual": 0.057844030503927384,
            "energy_eV": -83.33544546554788,
            "max_atomic_step_A": 0.0487252178408959,
            "max_log_strain_component": 0.0031504130611477114,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.770601066124264,
            "cell_principal_stretches": [
              1.0043593787608631,
              1.0021053341596813,
              0.9775386136376035
            ],
            "cell_volume_ratio": 0.9838670919430791,
            "cell_rmsd_from_input_A": 0.10641698399067087
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49973365339633086,
              -0.4996168775577716,
              -0.5001570286199454
            ],
            "branch_aligned_reduced_polarization": [
              0.49973365339633086,
              -0.4996168775577716,
              -0.5001570286199454
            ],
            "target_residual": 0.0004923223603565801,
            "energy_eV": -82.52040885149133
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0004923223603565801,
        "parent_symmetrization_rmsd_A": 0.4054127797035002,
        "parent_cell_rmsd_A": 0.10641698399067087,
        "energy_eV": -82.52040885149133,
        "reduced_polarization": [
          0.49973365339633086,
          -0.4996168775577716,
          -0.5001570286199454
        ],
        "cartesian_polarization_e_A2": [
          0.005413456982146232,
          -0.00752377114519341,
          -0.004281554778494484
        ],
        "ranking_score": 0.9330016704218811
      },
      "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": 0.09376468264994407,
        "minimum_distance_A_by_image": [
          2.2626285427188355,
          2.2622051722518264,
          2.2618381870788804,
          2.2615276146494527,
          2.261273478207405,
          2.261075796782318,
          2.260934585182371,
          2.260849853988798,
          2.260821609551927
        ],
        "minimum_distance_A": 2.260821609551927,
        "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": [
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242,
          853.157544988242
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.3763603144080763e-16,
        -1.712863195814681e-16,
        -5.145351575277259e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -87.6057190743093,
          -87.6029837860686,
          -87.60053165954716,
          -87.59839265613607,
          -87.59659509253554,
          -87.59516504929374,
          -87.59412526897901,
          -87.59349367154717,
          -87.59328180660079
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3663762135192518e-18,
            1.968232402807494e-18,
            -0.001365869648369417
          ],
          [
            1.4639745144849128e-18,
            -6.270690837043709e-18,
            -0.0011967205899841792
          ],
          [
            2.895416261981272e-18,
            -4.896181431777319e-18,
            -0.0010269680705681029
          ],
          [
            -6.783081917113429e-18,
            9.751696904818946e-18,
            -0.0008566813147777593
          ],
          [
            -4.22925970851197e-19,
            9.938760315003129e-18,
            -0.0006859330224712133
          ],
          [
            5.514304004559838e-18,
            1.677064138259939e-17,
            -0.0005148014240218703
          ],
          [
            4.2780588589948005e-18,
            7.254807038447456e-18,
            -0.00034337199620328813
          ],
          [
            -7.759064926770037e-18,
            4.22925970851197e-19,
            -0.00017173811304328562
          ],
          [
            -3.5786043687408975e-18,
            -2.553822208601459e-18,
            -4.4732554609261225e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.205788292908023e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413384e-16,
            -0.09853956678766877
          ],
          [
            -3.990244007936818e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330238e-16,
            2.836588731922402e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.2057882929080235e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413383e-16,
            -0.09853956678766877
          ],
          [
            -3.9902440079368156e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330239e-16,
            2.8365887319224e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.134781488891349e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.15710883512577112
          ],
          [
            1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.13765250445962673
          ],
          [
            2.220446049250313e-16,
            -3.3306690738754696e-16,
            -0.1181267608303112
          ],
          [
            -6.661338147750939e-16,
            6.661338147750939e-16,
            -0.09853956678766879
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            -0.07889928461577833
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-15,
            -0.059214912744945336
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.03949628312094883
          ],
          [
            -7.216449660063518e-16,
            0.0,
            -0.019754136069382144
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -4.996003610813204e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.59328180660079,
          -87.59349367154715,
          -87.59412526897904,
          -87.5951650492937,
          -87.59659509253554,
          -87.59839265613604,
          -87.60053165954714,
          -87.60298378606865,
          -87.60571907430929
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.5786043687408975e-18,
            -2.553822208601459e-18,
            -4.4732554609261225e-18
          ],
          [
            -3.643669902718005e-18,
            6.360155946262232e-18,
            0.00017173811304329803
          ],
          [
            7.970527912195636e-18,
            1.655104520542665e-17,
            0.0003433719962032995
          ],
          [
            3.611137135729451e-18,
            1.9096734222280973e-17,
            0.0005148014240218664
          ],
          [
            4.749783980328828e-18,
            4.0543960859484945e-17,
            0.0006859330224711977
          ],
          [
            -2.9442154124641023e-18,
            1.5640127729747152e-17,
            0.000856681314777754
          ],
          [
            3.05808009692404e-18,
            2.5033964197692007e-17,
            0.001026968070568089
          ],
          [
            3.9527311891092646e-18,
            2.404171480454112e-17,
            0.0011967205899841755
          ],
          [
            -8.165724514126957e-18,
            9.564633494634763e-18,
            0.0013658696483693968
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.885253359585084e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809125e-16,
            0.15710883512576881
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.8852533595850833e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809126e-16,
            0.15710883512576881
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.04187638522651e-16,
          -4.745831147639403e-16,
          0.15710883512577012
        ],
        "actual_opposite_endpoint_branch_residual": 1.7171328917433152e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.205788292908023e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413384e-16,
            -0.09853956678766877
          ],
          [
            -3.990244007936818e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330238e-16,
            2.836588731922402e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.145351575277259e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.885253359585084e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809125e-16,
            0.15710883512576881
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2891557564103563e-16,
            1.320104756010041e-16,
            -0.15710883512577115
          ],
          [
            1.3812383104396675e-16,
            -4.2057882929080235e-16,
            -0.13765250445962673
          ],
          [
            2.7317824362028987e-16,
            -3.283896955033242e-16,
            -0.1181267608303112
          ],
          [
            -6.399737505037127e-16,
            6.540519018413383e-16,
            -0.09853956678766877
          ],
          [
            -3.9902440079368156e-17,
            6.665983520017645e-16,
            -0.07889928461577835
          ],
          [
            5.202664302656082e-16,
            1.1248165317738449e-15,
            -0.05921491274494536
          ],
          [
            4.0362852849514737e-16,
            4.865840670913043e-16,
            -0.03949628312094882
          ],
          [
            -7.320563045330239e-16,
            2.8365887319224e-17,
            -0.019754136069382144
          ],
          [
            -3.3763603144080763e-16,
            -1.712863195814681e-16,
            -5.134781488891349e-16
          ],
          [
            -3.437748683760951e-16,
            4.265793054544843e-16,
            0.01975413606938357
          ],
          [
            7.52007524572708e-16,
            1.1100880902811707e-15,
            0.03949628312095014
          ],
          [
            3.407054499084513e-16,
            1.280828912029577e-15,
            0.059214912744944906
          ],
          [
            4.481350962759811e-16,
            2.719306697814072e-15,
            0.07889928461577655
          ],
          [
            -2.777823713217554e-16,
            1.0489923329782269e-15,
            0.09853956678766816
          ],
          [
            2.8852533595850833e-16,
            1.679042330164837e-15,
            0.11812676083030961
          ],
          [
            3.729343438187103e-16,
            1.6124915945312733e-15,
            0.13765250445962632
          ],
          [
            -7.704240353785701e-16,
            6.415054516809126e-16,
            0.15710883512576881
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.15710883512577112
          ],
          [
            1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.13765250445962673
          ],
          [
            2.220446049250313e-16,
            -3.3306690738754696e-16,
            -0.1181267608303112
          ],
          [
            -6.661338147750939e-16,
            6.661338147750939e-16,
            -0.09853956678766879
          ],
          [
            -5.551115123125783e-17,
            6.661338147750939e-16,
            -0.07889928461577833
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-15,
            -0.059214912744945336
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.03949628312094883
          ],
          [
            -7.216449660063518e-16,
            0.0,
            -0.019754136069382144
          ],
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -4.996003610813204e-16
          ],
          [
            -3.3306690738754696e-16,
            4.440892098500626e-16,
            0.019754136069383588
          ],
          [
            7.771561172376096e-16,
            1.1102230246251565e-15,
            0.039496283120950104
          ],
          [
            3.3306690738754696e-16,
            1.3322676295501878e-15,
            0.05921491274494495
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            0.07889928461577655
          ],
          [
            -2.7755575615628914e-16,
            9.992007221626409e-16,
            0.09853956678766818
          ],
          [
            3.3306690738754696e-16,
            1.6653345369377348e-15,
            0.1181267608303096
          ],
          [
            3.3306690738754696e-16,
            1.6653345369377348e-15,
            0.1376525044596263
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.1571088351257688
          ]
        ]
      },
      "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": 6.251762457853436e-16,
        "parent_symmetrization_rmsd_A": 0.09376468264994407,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -87.5932818066008,
        "reduced_polarization": [
          -1.4733208644689787e-16,
          5.804096943779684e-16,
          -1.7961954590058792e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.5615728154505735e-18,
          8.653716018955262e-18,
          -1.5615728154505735e-18
        ],
        "ranking_score": 0.09376468264994532
      }
    }
  ],
  "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": 62,
      "full_response": 26,
      "energy_polarization": 36
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 87,
      "full_response": 51,
      "energy_polarization": 36
    },
    "elapsed_seconds": 217.1901229780051
  }
}