{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "As4Bi4Cd8O24",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -203.65894085070747,
  "input_cartesian_polarization_e_A2": [
    5.105809729944022e-18,
    -1.8578282716242338e-17,
    0.0021972007493148704
  ],
  "input_reduced_polarization": [
    3.4416703015775998e-16,
    -9.07682026398353e-16,
    0.23677054106336887
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.145839874244573e-16,
      "parent_symmetrization_rmsd_A": 0.5195186358465005,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -190.33429404059865,
      "reduced_polarization": [
        2.4046995428905203e-16,
        1.0812513167127715e-17,
        7.7820586171755375e-16
      ],
      "cartesian_polarization_e_A2": [
        3.5674359388969876e-18,
        2.213086969332943e-19,
        7.221652215718026e-18
      ],
      "ranking_score": 0.5195186358465022
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 6.69374785678107e-15,
      "parent_symmetrization_rmsd_A": 0.6340926852847938,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -192.58243928358178,
      "reduced_polarization": [
        -2.196506777089232e-18,
        3.34391196684434e-15,
        5.7986643551351006e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.258576415413602e-20,
        6.844262648315986e-17,
        5.381087363701356e-17
      ],
      "ranking_score": 0.6340926852848072
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 0.00026191623130050274,
      "parent_symmetrization_rmsd_A": 0.013435873707744576,
      "parent_cell_rmsd_A": 0.00798591666609483,
      "energy_eV": -203.5658786483764,
      "reduced_polarization": [
        1.340989936239567e-15,
        -4.84128902310865e-15,
        -0.00026191623130050274
      ],
      "cartesian_polarization_e_A2": [
        1.987034140602581e-17,
        -9.895737110100931e-17,
        -2.432823842668789e-06
      ],
      "ranking_score": 0.5159561853368693
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4410338660111248e-15,
      "parent_symmetrization_rmsd_A": 0.5195212427006702,
      "parent_cell_rmsd_A": 0.00798591666609483,
      "energy_eV": -190.50389777257962,
      "reduced_polarization": [
        2.5069646165650416e-15,
        1.5853403688328852e-15,
        -1.744287359718912e-15
      ],
      "cartesian_polarization_e_A2": [
        3.715350545794882e-17,
        3.240382511705598e-17,
        -1.620191255852799e-17
      ],
      "ranking_score": 0.5215177218672008
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 6.812071423916492e-15,
      "parent_symmetrization_rmsd_A": 0.6340940543597836,
      "parent_cell_rmsd_A": 0.00798591666609483,
      "energy_eV": -192.43623059130798,
      "reduced_polarization": [
        5.014680688879175e-15,
        6.081693656298586e-16,
        -4.5702762165794e-15
      ],
      "cartesian_polarization_e_A2": [
        7.431814757697803e-17,
        1.2430777738870612e-17,
        -4.245127112614765e-17
      ],
      "ranking_score": 0.636090533526321
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 0.0006434149362481434,
      "parent_symmetrization_rmsd_A": 0.014987608048145702,
      "parent_cell_rmsd_A": 0.008881019320018765,
      "energy_eV": -203.64106969824252,
      "reduced_polarization": [
        -5.626109506009304e-16,
        7.0308362708943746e-15,
        0.49935658506375186
      ],
      "cartesian_polarization_e_A2": [
        -1.533776175820996e-17,
        1.3784765368223588e-16,
        0.00462915033028294
      ],
      "ranking_score": 0.5184946927506466
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0004902195816332542,
      "parent_symmetrization_rmsd_A": 0.09189089481510197,
      "parent_cell_rmsd_A": 0.07198988609606759,
      "energy_eV": -199.9704396933349,
      "reduced_polarization": [
        4.990946097954849e-15,
        -0.5000712753804618,
        0.0004850103693290557
      ],
      "cartesian_polarization_e_A2": [
        -1.2462462329895258e-16,
        -0.010222405892832938,
        0.00011126505907391358
      ],
      "ranking_score": 0.6108688055023854
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.8365645490446123e-06,
      "parent_symmetrization_rmsd_A": 0.06813601180701187,
      "parent_cell_rmsd_A": 0.01633957965925926,
      "energy_eV": -202.31336727684217,
      "reduced_polarization": [
        0.5000006951622492,
        -3.7520117466729875e-15,
        1.6999172891885145e-06
      ],
      "cartesian_polarization_e_A2": [
        0.007410156503212363,
        -1.2143354775822722e-16,
        2.129768138358644e-05
      ],
      "ranking_score": 0.5722245798509248
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.8048040713957118e-05,
      "parent_symmetrization_rmsd_A": 0.09150937858140819,
      "parent_cell_rmsd_A": 0.07217798876701442,
      "energy_eV": -200.50731855379644,
      "reduced_polarization": [
        3.2817487684485705e-15,
        -0.49999203028775147,
        0.5000268919369806
      ],
      "cartesian_polarization_e_A2": [
        -9.965322494593526e-17,
        -0.010299459960052453,
        0.004741938999057941
      ],
      "ranking_score": 0.6096099718545898
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.1142426870487064e-05,
      "parent_symmetrization_rmsd_A": 0.06877484682015335,
      "parent_cell_rmsd_A": 0.01697156994752316,
      "energy_eV": -202.49998541896034,
      "reduced_polarization": [
        0.500000538627037,
        2.3961268785069308e-15,
        0.4999888705994106
      ],
      "cartesian_polarization_e_A2": [
        0.0074396891591226675,
        6.297390390976854e-17,
        0.004656344824896038
      ],
      "ranking_score": 0.5730400241607752
    },
    {
      "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": 0.0009039177408527004,
      "parent_symmetrization_rmsd_A": 0.1135873586283874,
      "parent_cell_rmsd_A": 0.07323058810514149,
      "energy_eV": -198.57587086990108,
      "reduced_polarization": [
        0.499773266124618,
        -0.5003444010330906,
        0.0008043922925964679
      ],
      "cartesian_polarization_e_A2": [
        0.007407129885625411,
        -0.010228037295597299,
        0.00013531072538253432
      ],
      "ranking_score": 0.6337028411363782
    },
    {
      "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": 2.7553308796478515e-06,
      "parent_symmetrization_rmsd_A": 0.11336583896162068,
      "parent_cell_rmsd_A": 0.07343332664033034,
      "energy_eV": -199.20383860196483,
      "reduced_polarization": [
        0.4999994316944534,
        -0.49999966170444027,
        0.49999732522278006
      ],
      "cartesian_polarization_e_A2": [
        0.007440364061260706,
        -0.010299822742209004,
        0.004762782505184223
      ],
      "ranking_score": 0.6317296812834625
    }
  ],
  "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": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "target_residual": 0.23677054106336887,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.01768606123790787,
            "max_log_strain_component": 0.0016670944055078747,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.001668484779907,
              0.9997100562067287,
              0.9993549334587121
            ],
            "cell_volume_ratio": 1.0007321017399375,
            "cell_rmsd_from_input_A": 0.00798591666609483
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.340989936239567e-15,
              -4.84128902310865e-15,
              -0.00026191623130050274
            ],
            "branch_aligned_reduced_polarization": [
              1.340989936239567e-15,
              -4.84128902310865e-15,
              -0.00026191623130050274
            ],
            "target_residual": 0.00026191623130050274,
            "energy_eV": -203.5658786483764
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 0.00026191623130050274,
        "parent_symmetrization_rmsd_A": 0.013435873707744576,
        "parent_cell_rmsd_A": 0.00798591666609483,
        "energy_eV": -203.5658786483764,
        "reduced_polarization": [
          1.340989936239567e-15,
          -4.84128902310865e-15,
          -0.00026191623130050274
        ],
        "cartesian_polarization_e_A2": [
          1.987034140602581e-17,
          -9.895737110100931e-17,
          -2.432823842668789e-06
        ],
        "ranking_score": 0.5159561853368693
      },
      "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": [
          -203.65894085070744,
          -203.65263785180576,
          -203.6447622688822,
          -203.63533981181894,
          -203.62439553757102,
          -203.6119538509801,
          -203.5980385066959,
          -203.5826726150537,
          -203.5658786483764
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.9391101842965648e-18,
            1.214868267902242e-17,
            0.002197200749314859
          ],
          [
            2.309068739894552e-18,
            -5.2154194275277995e-17,
            0.001923088732623492
          ],
          [
            -5.606424383459835e-19,
            -4.878381753150715e-17,
            0.0016487111582743988
          ],
          [
            8.04810899552624e-18,
            -3.152783569868751e-17,
            0.0013740806125917774
          ],
          [
            1.8070204323361806e-17,
            -5.403196244119519e-17,
            0.0010992095260558671
          ],
          [
            -1.1237602689243442e-17,
            -3.530005909484445e-17,
            0.000824110370198837
          ],
          [
            -9.6819511023105e-18,
            -5.1088436195023667e-17,
            0.0005487955049400567
          ],
          [
            1.515724198808305e-17,
            -5.254462928789278e-17,
            0.0002732771068497178
          ],
          [
            -2.0124749067950157e-18,
            -1.5254473131614068e-16,
            -2.4328238426767735e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554005e-16,
            -7.46302288018717e-15,
            -0.00026191623130136235
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554008e-16,
            -7.46302288018717e-15,
            -0.00026191623130136094
          ]
        ],
        "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,
            5.551115123125783e-16,
            0.2367705410633676
          ],
          [
            1.1102230246251565e-16,
            -2.55351295663786e-15,
            0.20720798105457539
          ],
          [
            -5.551115123125783e-17,
            -2.3869795029440866e-15,
            0.17762371975415836
          ],
          [
            4.440892098500626e-16,
            -1.5543122344752192e-15,
            0.1480191218121869
          ],
          [
            1.2212453270876722e-15,
            -2.6645352591003757e-15,
            0.11839553445667816
          ],
          [
            -8.326672684688674e-16,
            -1.7763568394002505e-15,
            0.08875430870871215
          ],
          [
            -6.661338147750939e-16,
            -2.4980018054066022e-15,
            0.05909678294040277
          ],
          [
            9.992007221626409e-16,
            -2.609024107869118e-15,
            0.029424275158111524
          ],
          [
            -1.1102230246251565e-16,
            -7.438494264988549e-15,
            -0.0002619162313013401
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -203.56587864837644,
          -203.55280516983296,
          -203.53863799469596,
          -203.52338793712408,
          -203.50706545958525,
          -203.48968067938972,
          -203.4712433746699,
          -203.45176299041765,
          -203.4312486446015
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.270888055703265e-18,
            -1.2833497691834024e-16,
            -2.4328238426325906e-06
          ],
          [
            3.6093800873747643e-17,
            -1.0273790387570707e-16,
            -0.0002683724238230718
          ],
          [
            2.3260754588690664e-17,
            -1.5345739225767392e-16,
            -0.0005342559347558076
          ],
          [
            5.2215476780669266e-17,
            -2.464833611797335e-16,
            -0.0008000743811628405
          ],
          [
            1.9161284916836212e-17,
            -2.4689014795886276e-16,
            -0.0010658188868562092
          ],
          [
            3.6013778565508375e-17,
            -2.327412196157589e-16,
            -0.0013314806668481933
          ],
          [
            -9.26960929201832e-18,
            -2.131395150302325e-16,
            -0.0015970510189040478
          ],
          [
            4.443065961393208e-18,
            -2.943485823847925e-16,
            -0.0018625213148565434
          ],
          [
            5.152359796796481e-17,
            -2.673991450261915e-16,
            -0.0021278829917127425
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.253394919874431e-16,
            -6.278573179335018e-15,
            -0.0002619162312966056
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165935e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.253394919874431e-16,
            -6.278573179335018e-15,
            -0.0002619162312966056
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165937e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.020190578425315e-16,
          -1.5499353034135586e-14,
          -0.2372948636749652
        ],
        "actual_opposite_endpoint_branch_residual": 0.00799401011187273
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554005e-16,
            -7.46302288018717e-15,
            -0.00026191623130136235
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165935e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554008e-16,
            -7.46302288018717e-15,
            -0.00026191623130136094
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165937e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "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,
            5.551115123125783e-16,
            0.2367705410633676
          ],
          [
            1.1102230246251565e-16,
            -2.55351295663786e-15,
            0.20720798105457539
          ],
          [
            -5.551115123125783e-17,
            -2.3869795029440866e-15,
            0.17762371975415836
          ],
          [
            4.440892098500626e-16,
            -1.5543122344752192e-15,
            0.1480191218121869
          ],
          [
            1.2212453270876722e-15,
            -2.6645352591003757e-15,
            0.11839553445667816
          ],
          [
            -8.326672684688674e-16,
            -1.7763568394002505e-15,
            0.08875430870871215
          ],
          [
            -6.661338147750939e-16,
            -2.4980018054066022e-15,
            0.05909678294040277
          ],
          [
            9.992007221626409e-16,
            -2.609024107869118e-15,
            0.029424275158111524
          ],
          [
            -1.1102230246251565e-16,
            -7.438494264988549e-15,
            -0.0002619162313013401
          ],
          [
            2.4424906541753444e-15,
            -4.9960036108132044e-15,
            -0.02889617844118192
          ],
          [
            1.5543122344752192e-15,
            -7.494005416219807e-15,
            -0.05753109624018243
          ],
          [
            3.552713678800501e-15,
            -1.2045919817182948e-14,
            -0.08616570205095908
          ],
          [
            1.3322676295501878e-15,
            -1.2045919817182948e-14,
            -0.11479903853830786
          ],
          [
            2.4424906541753444e-15,
            -1.1324274851176597e-14,
            -0.14343015774382817
          ],
          [
            -6.106226635438361e-16,
            -1.0380585280245214e-14,
            -0.17205812018146915
          ],
          [
            3.3306690738754696e-16,
            -1.4377388168895777e-14,
            -0.2006819939067761
          ],
          [
            3.4416913763379853e-15,
            -1.304512053934559e-14,
            -0.2293008535630925
          ]
        ]
      },
      "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": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "target_residual": 0.26322945893663113,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.019662464382039124,
            "max_log_strain_component": 0.0018533908669012811,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.000717640995523,
              1.0003224434930886,
              0.9981483256013588
            ],
            "cell_volume_ratio": 0.9991867151623446,
            "cell_rmsd_from_input_A": 0.008881019320018765
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.626109506009304e-16,
              7.0308362708943746e-15,
              0.49935658506375186
            ],
            "branch_aligned_reduced_polarization": [
              -5.626109506009304e-16,
              7.0308362708943746e-15,
              0.49935658506375186
            ],
            "target_residual": 0.0006434149362481434,
            "energy_eV": -203.64106969824252
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 0.0006434149362481434,
        "parent_symmetrization_rmsd_A": 0.014987608048145702,
        "parent_cell_rmsd_A": 0.008881019320018765,
        "energy_eV": -203.64106969824252,
        "reduced_polarization": [
          -5.626109506009304e-16,
          7.0308362708943746e-15,
          0.49935658506375186
        ],
        "cartesian_polarization_e_A2": [
          -1.533776175820996e-17,
          1.3784765368223588e-16,
          0.00462915033028294
        ],
        "ranking_score": 0.5184946927506466
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.4416703015775998e-16,
              -8.881784197001252e-16,
              0.23677054106336887
            ],
            "target_residual": 0.5532271586929184,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00946662920622245,
            "step_scale": 0.9088458349848063,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0100391655530387,
              0.9997364823085122,
              0.9909804907431325
            ],
            "cell_volume_ratio": 1.0006653454216645,
            "cell_rmsd_from_input_A": 0.06535113212496185
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.385267155270738e-14,
              -0.45286004831973625,
              0.012352370914739425
            ],
            "branch_aligned_reduced_polarization": [
              3.385267155270738e-14,
              -0.45286004831973625,
              0.012352370914739425
            ],
            "target_residual": 0.04873146941795313,
            "energy_eV": -200.62816014597925,
            "max_atomic_step_A": 0.01237998381458414,
            "max_log_strain_component": 0.0009663015445842422,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0110450763788659,
              0.9997206249109812,
              0.9900498766351851
            ],
            "cell_volume_ratio": 1.0007054028531797,
            "cell_rmsd_from_input_A": 0.07198988609606759
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.990946097954849e-15,
              -0.5000712753804618,
              0.0004850103693290557
            ],
            "branch_aligned_reduced_polarization": [
              4.990946097954849e-15,
              -0.5000712753804618,
              0.0004850103693290557
            ],
            "target_residual": 0.0004902195816332542,
            "energy_eV": -199.9704396933349
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0004902195816332542,
        "parent_symmetrization_rmsd_A": 0.09189089481510197,
        "parent_cell_rmsd_A": 0.07198988609606759,
        "energy_eV": -199.9704396933349,
        "reduced_polarization": [
          4.990946097954849e-15,
          -0.5000712753804618,
          0.0004850103693290557
        ],
        "cartesian_polarization_e_A2": [
          -1.2462462329895258e-16,
          -0.010222405892832938,
          0.00011126505907391358
        ],
        "ranking_score": 0.6108688055023854
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "target_residual": 0.5532271586929189,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.0771227134918616,
            "max_log_strain_component": 0.002870555692716422,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0037282465640969,
              0.9993549334587055,
              0.9976585401951915
            ],
            "cell_volume_ratio": 1.0007321017399153,
            "cell_rmsd_from_input_A": 0.016375136091628634
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.500236588476514,
              2.751957274345499e-15,
              -0.0017982808130119256
            ],
            "branch_aligned_reduced_polarization": [
              0.500236588476514,
              2.751957274345499e-15,
              -0.0017982808130119256
            ],
            "target_residual": 0.0018137772712397838,
            "energy_eV": -202.3106582714692,
            "max_atomic_step_A": 0.0001371070193212114,
            "max_log_strain_component": 1.273182862073594e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0037192955582535,
              0.9993598583431992,
              0.9976569445723055
            ],
            "cell_volume_ratio": 1.0007265085479984,
            "cell_rmsd_from_input_A": 0.01633957965925926
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000006951622492,
              -3.7520117466729875e-15,
              1.6999172891885145e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000006951622492,
              -3.7520117466729875e-15,
              1.6999172891885145e-06
            ],
            "target_residual": 1.8365645490446123e-06,
            "energy_eV": -202.31336727684217
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.8365645490446123e-06,
        "parent_symmetrization_rmsd_A": 0.06813601180701187,
        "parent_cell_rmsd_A": 0.01633957965925926,
        "energy_eV": -202.31336727684217,
        "reduced_polarization": [
          0.5000006951622492,
          -3.7520117466729875e-15,
          1.6999172891885145e-06
        ],
        "cartesian_polarization_e_A2": [
          0.007410156503212363,
          -1.2143354775822722e-16,
          2.129768138358644e-05
        ],
        "ranking_score": 0.5722245798509248
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.4416703015775998e-16,
              -8.881784197001252e-16,
              0.23677054106336887
            ],
            "target_residual": 0.5650572962559378,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00944975734283313,
            "step_scale": 0.9072260480006612,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0090468079139845,
              1.000292524761101,
              0.9900134539808966
            ],
            "cell_volume_ratio": 0.9992621389672101,
            "cell_rmsd_from_input_A": 0.06537621845180631
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.6127961205407477e-14,
              -0.4525752394281255,
              0.4599836913401135
            ],
            "branch_aligned_reduced_polarization": [
              2.6127961205407477e-14,
              -0.4525752394281255,
              0.4599836913401135
            ],
            "target_residual": 0.062051695174772846,
            "energy_eV": -201.06339048041932,
            "max_atomic_step_A": 0.013215555124847568,
            "max_log_strain_component": 0.0009706445961140701,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0099521363557638,
              1.000345076333404,
              0.9889429122713032
            ],
            "cell_volume_ratio": 0.9991296640503614,
            "cell_rmsd_from_input_A": 0.07217798876701442
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.2817487684485705e-15,
              -0.49999203028775147,
              0.5000268919369806
            ],
            "branch_aligned_reduced_polarization": [
              3.2817487684485705e-15,
              -0.49999203028775147,
              0.5000268919369806
            ],
            "target_residual": 2.8048040713957118e-05,
            "energy_eV": -200.50731855379644
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.8048040713957118e-05,
        "parent_symmetrization_rmsd_A": 0.09150937858140819,
        "parent_cell_rmsd_A": 0.07217798876701442,
        "energy_eV": -200.50731855379644,
        "reduced_polarization": [
          3.2817487684485705e-15,
          -0.49999203028775147,
          0.5000268919369806
        ],
        "cartesian_polarization_e_A2": [
          -9.965322494593526e-17,
          -0.010299459960052453,
          0.004741938999057941
        ],
        "ranking_score": 0.6096099718545898
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "target_residual": 0.5650572962559383,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.07748559352720587,
            "max_log_strain_component": 0.002870555692713564,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0023069450541546,
              1.000717640995516,
              0.9961720578321679
            ],
            "cell_volume_ratio": 0.9991867151623229,
            "cell_rmsd_from_input_A": 0.01679570760491922
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49711319622217703,
              6.035973593925113e-15,
              0.4944316995186544
            ],
            "branch_aligned_reduced_polarization": [
              0.49711319622217703,
              6.035973593925113e-15,
              0.4944316995186544
            ],
            "target_residual": 0.006272129327605307,
            "energy_eV": -202.51409394601322,
            "max_atomic_step_A": 0.0005693643369089641,
            "max_log_strain_component": 4.095652384402589e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0023145891056455,
              1.000733505354237,
              0.9961307586959939
            ],
            "cell_volume_ratio": 0.999168750537339,
            "cell_rmsd_from_input_A": 0.01697156994752316
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.500000538627037,
              2.3961268785069308e-15,
              0.4999888705994106
            ],
            "branch_aligned_reduced_polarization": [
              0.500000538627037,
              2.3961268785069308e-15,
              0.4999888705994106
            ],
            "target_residual": 1.1142426870487064e-05,
            "energy_eV": -202.49998541896034
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.1142426870487064e-05,
        "parent_symmetrization_rmsd_A": 0.06877484682015335,
        "parent_cell_rmsd_A": 0.01697156994752316,
        "energy_eV": -202.49998541896034,
        "reduced_polarization": [
          0.500000538627037,
          2.3961268785069308e-15,
          0.4999888705994106
        ],
        "cartesian_polarization_e_A2": [
          0.0074396891591226675,
          6.297390390976854e-17,
          0.004656344824896038
        ],
        "ranking_score": 0.5730400241607752
      },
      "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": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              -8.881784197001252e-16,
              0.23677054106336887
            ],
            "target_residual": 0.7456945011969978,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008216204507843572,
            "step_scale": 0.7887985346927172,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.009023728431409,
              0.9997516184480494,
              0.9918756067552514
            ],
            "cell_volume_ratio": 1.0005774361475568,
            "cell_rmsd_from_input_A": 0.05782930669387822
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.39477126538092766,
              -0.3934303713638145,
              0.04239020593347603
            ],
            "branch_aligned_reduced_polarization": [
              0.39477126538092766,
              -0.3934303713638145,
              0.04239020593347603
            ],
            "target_residual": 0.15565057627991022,
            "energy_eV": -200.54898667025728,
            "max_atomic_step_A": 0.032353523544818984,
            "max_log_strain_component": 0.0021911137316764774,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0114255812961936,
              0.999694537016366,
              0.9897078882601007
            ],
            "cell_volume_ratio": 1.0007101029006924,
            "cell_rmsd_from_input_A": 0.07323058810514149
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.499773266124618,
              -0.5003444010330906,
              0.0008043922925964679
            ],
            "branch_aligned_reduced_polarization": [
              0.499773266124618,
              -0.5003444010330906,
              0.0008043922925964679
            ],
            "target_residual": 0.0009039177408527004,
            "energy_eV": -198.57587086990108
          }
        ],
        "iterations": 2
      },
      "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": 0.0009039177408527004,
        "parent_symmetrization_rmsd_A": 0.1135873586283874,
        "parent_cell_rmsd_A": 0.07323058810514149,
        "energy_eV": -198.57587086990108,
        "reduced_polarization": [
          0.499773266124618,
          -0.5003444010330906,
          0.0008043922925964679
        ],
        "cartesian_polarization_e_A2": [
          0.007407129885625411,
          -0.010228037295597299,
          0.00013531072538253432
        ],
        "ranking_score": 0.6337028411363782
      },
      "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": [
              3.4416703015775998e-16,
              -9.07682026398353e-16,
              0.23677054106336887
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              -8.881784197001252e-16,
              0.23677054106336887
            ],
            "target_residual": 0.7545129210636955,
            "energy_eV": -203.65894085070747,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.008205166846226478,
            "step_scale": 0.7877388615427479,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0081448032048117,
              1.0002758105862875,
              0.9910121319539626
            ],
            "cell_volume_ratio": 0.9993592886118347,
            "cell_rmsd_from_input_A": 0.057862097230081594
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.39240081847197106,
              -0.3932607691886269,
              0.43065030262380305
            ],
            "branch_aligned_reduced_polarization": [
              0.39240081847197106,
              -0.3932607691886269,
              0.43065030262380305
            ],
            "target_residual": 0.16667401652889813,
            "energy_eV": -200.91700354744853,
            "max_atomic_step_A": 0.03352001473472668,
            "max_log_strain_component": 0.002188798245894638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.010299021193818,
              1.0003784121454307,
              0.9885628188013152
            ],
            "cell_volume_ratio": 0.9991219851015951,
            "cell_rmsd_from_input_A": 0.07342289258728643
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4993592571067152,
              -0.5000000646538726,
              0.4988418976408764
            ],
            "branch_aligned_reduced_polarization": [
              0.4993592571067152,
              -0.5000000646538726,
              0.4988418976408764
            ],
            "target_residual": 0.0013235378852465042,
            "energy_eV": -199.20655188661192,
            "max_atomic_step_A": 0.00012413552058546156,
            "max_log_strain_component": 8.783539926937297e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.358345477924767,
            "cell_principal_stretches": [
              1.0102981489764193,
              1.000380144694242,
              0.9885581484152381
            ],
            "cell_volume_ratio": 0.999118132628827,
            "cell_rmsd_from_input_A": 0.07343332664033034
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999994316944534,
              -0.49999966170444027,
              0.49999732522278006
            ],
            "branch_aligned_reduced_polarization": [
              0.4999994316944534,
              -0.49999966170444027,
              0.49999732522278006
            ],
            "target_residual": 2.7553308796478515e-06,
            "energy_eV": -199.20383860196483
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 2.7553308796478515e-06,
        "parent_symmetrization_rmsd_A": 0.11336583896162068,
        "parent_cell_rmsd_A": 0.07343332664033034,
        "energy_eV": -199.20383860196483,
        "reduced_polarization": [
          0.4999994316944534,
          -0.49999966170444027,
          0.49999732522278006
        ],
        "cartesian_polarization_e_A2": [
          0.007440364061260706,
          -0.010299822742209004,
          0.004762782505184223
        ],
        "ranking_score": 0.6317296812834625
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.013435873707744576,
        "minimum_distance_A_by_image": [
          1.7261085099694062,
          1.7251307207041482,
          1.724155506540762,
          1.7231828761984354,
          1.7222128384082047,
          1.721245401912866,
          1.720280575466874,
          1.7193183678362467,
          1.7183587877984683
        ],
        "minimum_distance_A": 1.7183587877984683,
        "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": [
          595.7243705337777,
          595.7788694364973,
          595.833373324963,
          595.8878821996307,
          595.9423960609568,
          595.9969149093977,
          596.0514387454089,
          596.105967569447,
          596.1605013819685
        ],
        "cell_deformation_log_strain_norm": 0.0018109872893308252
      },
      "parent_reduced_polarization": [
        -1.3557184523554005e-16,
        -7.46302288018717e-15,
        -0.00026191623130136235
      ],
      "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": [
          -203.65894085070744,
          -203.65263785180576,
          -203.6447622688822,
          -203.63533981181894,
          -203.62439553757102,
          -203.6119538509801,
          -203.5980385066959,
          -203.5826726150537,
          -203.5658786483764
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.9391101842965648e-18,
            1.214868267902242e-17,
            0.002197200749314859
          ],
          [
            2.309068739894552e-18,
            -5.2154194275277995e-17,
            0.001923088732623492
          ],
          [
            -5.606424383459835e-19,
            -4.878381753150715e-17,
            0.0016487111582743988
          ],
          [
            8.04810899552624e-18,
            -3.152783569868751e-17,
            0.0013740806125917774
          ],
          [
            1.8070204323361806e-17,
            -5.403196244119519e-17,
            0.0010992095260558671
          ],
          [
            -1.1237602689243442e-17,
            -3.530005909484445e-17,
            0.000824110370198837
          ],
          [
            -9.6819511023105e-18,
            -5.1088436195023667e-17,
            0.0005487955049400567
          ],
          [
            1.515724198808305e-17,
            -5.254462928789278e-17,
            0.0002732771068497178
          ],
          [
            -2.0124749067950157e-18,
            -1.5254473131614068e-16,
            -2.4328238426767735e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554005e-16,
            -7.46302288018717e-15,
            -0.00026191623130136235
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554008e-16,
            -7.46302288018717e-15,
            -0.00026191623130136094
          ]
        ],
        "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,
            5.551115123125783e-16,
            0.2367705410633676
          ],
          [
            1.1102230246251565e-16,
            -2.55351295663786e-15,
            0.20720798105457539
          ],
          [
            -5.551115123125783e-17,
            -2.3869795029440866e-15,
            0.17762371975415836
          ],
          [
            4.440892098500626e-16,
            -1.5543122344752192e-15,
            0.1480191218121869
          ],
          [
            1.2212453270876722e-15,
            -2.6645352591003757e-15,
            0.11839553445667816
          ],
          [
            -8.326672684688674e-16,
            -1.7763568394002505e-15,
            0.08875430870871215
          ],
          [
            -6.661338147750939e-16,
            -2.4980018054066022e-15,
            0.05909678294040277
          ],
          [
            9.992007221626409e-16,
            -2.609024107869118e-15,
            0.029424275158111524
          ],
          [
            -1.1102230246251565e-16,
            -7.438494264988549e-15,
            -0.0002619162313013401
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -203.56587864837644,
          -203.55280516983296,
          -203.53863799469596,
          -203.52338793712408,
          -203.50706545958525,
          -203.48968067938972,
          -203.4712433746699,
          -203.45176299041765,
          -203.4312486446015
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.270888055703265e-18,
            -1.2833497691834024e-16,
            -2.4328238426325906e-06
          ],
          [
            3.6093800873747643e-17,
            -1.0273790387570707e-16,
            -0.0002683724238230718
          ],
          [
            2.3260754588690664e-17,
            -1.5345739225767392e-16,
            -0.0005342559347558076
          ],
          [
            5.2215476780669266e-17,
            -2.464833611797335e-16,
            -0.0008000743811628405
          ],
          [
            1.9161284916836212e-17,
            -2.4689014795886276e-16,
            -0.0010658188868562092
          ],
          [
            3.6013778565508375e-17,
            -2.327412196157589e-16,
            -0.0013314806668481933
          ],
          [
            -9.26960929201832e-18,
            -2.131395150302325e-16,
            -0.0015970510189040478
          ],
          [
            4.443065961393208e-18,
            -2.943485823847925e-16,
            -0.0018625213148565434
          ],
          [
            5.152359796796481e-17,
            -2.673991450261915e-16,
            -0.0021278829917127425
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.253394919874431e-16,
            -6.278573179335018e-15,
            -0.0002619162312966056
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165935e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.253394919874431e-16,
            -6.278573179335018e-15,
            -0.0002619162312966056
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165937e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.020190578425315e-16,
          -1.5499353034135586e-14,
          -0.2372948636749652
        ],
        "actual_opposite_endpoint_branch_residual": 0.00799401011187273
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554005e-16,
            -7.46302288018717e-15,
            -0.00026191623130136235
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165935e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.307094914571625e-16,
            5.935500649112741e-16,
            0.23677054106336765
          ],
          [
            1.3374802367304533e-16,
            -2.5610249612490597e-15,
            0.20720798105457536
          ],
          [
            -7.538465976200538e-17,
            -2.4056599503685583e-15,
            0.1776237197541584
          ],
          [
            4.957210407145629e-16,
            -1.5679106853225705e-15,
            0.14801912181218696
          ],
          [
            1.1685642994086985e-15,
            -2.670203919170221e-15,
            0.11839553445667812
          ],
          [
            -8.049429260931331e-16,
            -1.7528906663147081e-15,
            0.08875430870871218
          ],
          [
            -6.906627140154966e-16,
            -2.519987859893462e-15,
            0.05909678294040274
          ],
          [
            1.0008131077138845e-15,
            -2.582693273322153e-15,
            0.02942427515811152
          ],
          [
            -1.3557184523554008e-16,
            -7.46302288018717e-15,
            -0.00026191623130136094
          ],
          [
            2.456561911523189e-15,
            -5.013339485107626e-15,
            -0.028896178441181936
          ],
          [
            1.6056757378535585e-15,
            -7.484432461283368e-15,
            -0.057531096240182454
          ],
          [
            3.567530964538239e-15,
            -1.202687982006043e-14,
            -0.0861657020509591
          ],
          [
            1.3408567920532752e-15,
            -1.2042987714221356e-14,
            -0.11479903853830788
          ],
          [
            2.4740377803344568e-15,
            -1.1351022194063695e-14,
            -0.14343015774382814
          ],
          [
            -5.885894984165937e-16,
            -1.039624571637379e-14,
            -0.17205812018146913
          ],
          [
            3.2076053933905566e-16,
            -1.4371422173049724e-14,
            -0.2006819939067761
          ],
          [
            3.4730482790378597e-15,
            -1.3064361304092158e-14,
            -0.22930085356309246
          ]
        ],
        "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,
            5.551115123125783e-16,
            0.2367705410633676
          ],
          [
            1.1102230246251565e-16,
            -2.55351295663786e-15,
            0.20720798105457539
          ],
          [
            -5.551115123125783e-17,
            -2.3869795029440866e-15,
            0.17762371975415836
          ],
          [
            4.440892098500626e-16,
            -1.5543122344752192e-15,
            0.1480191218121869
          ],
          [
            1.2212453270876722e-15,
            -2.6645352591003757e-15,
            0.11839553445667816
          ],
          [
            -8.326672684688674e-16,
            -1.7763568394002505e-15,
            0.08875430870871215
          ],
          [
            -6.661338147750939e-16,
            -2.4980018054066022e-15,
            0.05909678294040277
          ],
          [
            9.992007221626409e-16,
            -2.609024107869118e-15,
            0.029424275158111524
          ],
          [
            -1.1102230246251565e-16,
            -7.438494264988549e-15,
            -0.0002619162313013401
          ],
          [
            2.4424906541753444e-15,
            -4.9960036108132044e-15,
            -0.02889617844118192
          ],
          [
            1.5543122344752192e-15,
            -7.494005416219807e-15,
            -0.05753109624018243
          ],
          [
            3.552713678800501e-15,
            -1.2045919817182948e-14,
            -0.08616570205095908
          ],
          [
            1.3322676295501878e-15,
            -1.2045919817182948e-14,
            -0.11479903853830786
          ],
          [
            2.4424906541753444e-15,
            -1.1324274851176597e-14,
            -0.14343015774382817
          ],
          [
            -6.106226635438361e-16,
            -1.0380585280245214e-14,
            -0.17205812018146915
          ],
          [
            3.3306690738754696e-16,
            -1.4377388168895777e-14,
            -0.2006819939067761
          ],
          [
            3.4416913763379853e-15,
            -1.304512053934559e-14,
            -0.2293008535630925
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 0.00026191623130050274,
        "parent_symmetrization_rmsd_A": 0.013435873707744576,
        "parent_cell_rmsd_A": 0.00798591666609483,
        "energy_eV": -203.5658786483764,
        "reduced_polarization": [
          1.340989936239567e-15,
          -4.84128902310865e-15,
          -0.00026191623130050274
        ],
        "cartesian_polarization_e_A2": [
          1.987034140602581e-17,
          -9.895737110100931e-17,
          -2.432823842668789e-06
        ],
        "ranking_score": 0.5159561853368693
      }
    }
  ],
  "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": 50,
      "full_response": 16,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 41,
      "energy_polarization": 34
    },
    "elapsed_seconds": 732.8007157359971
  }
}