{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "Br12In4Sn4",
  "input_spacegroup": "R3c",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -60.031564792602275,
  "input_cartesian_polarization_e_A2": [
    -1.01838817299376e-10,
    4.794786113048521e-12,
    -0.0023520818492365346
  ],
  "input_reduced_polarization": [
    -0.09082812720249656,
    4.6027369564541323e-10,
    -0.2724844117308448
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "R-3c",
      "spacegroup_number": 167,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.30872148080974e-15,
      "parent_symmetrization_rmsd_A": 0.8892691465835856,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -58.98634589459341,
      "reduced_polarization": [
        4.2892853124625687e-16,
        3.076477441535406e-15,
        -2.9860320939330117e-15
      ],
      "cartesian_polarization_e_A2": [
        2.569843914801275e-17,
        3.2048434340999056e-17,
        -2.5775389662712814e-17
      ],
      "ranking_score": 0.8892691465835942
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "R-3m",
      "spacegroup_number": 166,
      "pointgroup": "-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.354298727362984e-15,
      "parent_symmetrization_rmsd_A": 1.0851488709486015,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -58.248486155916915,
      "reduced_polarization": [
        1.1719001854840533e-15,
        -5.353693797638148e-19,
        6.788038830023492e-16
      ],
      "cartesian_polarization_e_A2": [
        1.7062237069707435e-17,
        -5.577076621429386e-21,
        5.859426167755242e-18
      ],
      "ranking_score": 1.0851488709486041
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00012825557126336357,
      "parent_symmetrization_rmsd_A": 0.06904803214913316,
      "parent_cell_rmsd_A": 0.021049033477438302,
      "energy_eV": -60.148012430792974,
      "reduced_polarization": [
        -4.57324573031135e-05,
        -7.515302069303795e-13,
        -0.5001198250137038
      ],
      "cartesian_polarization_e_A2": [
        0.002999483549456771,
        1.988423116530788e-13,
        -0.0043166411428138
      ],
      "ranking_score": 0.5745668016610195
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999999,
      "parent_symmetrization_rmsd_A": 0.8893004015331838,
      "parent_cell_rmsd_A": 0.021049033477438302,
      "energy_eV": -58.973697450999154,
      "reduced_polarization": [
        -3.363553052625782e-16,
        2.4544713692562067e-15,
        -1.2692646136595582e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.312082016385453e-18,
        2.5504753225101647e-17,
        -1.1094407374055306e-18
      ],
      "ranking_score": 1.8945626599025431
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3c",
      "spacegroup_number": 161,
      "pointgroup": "3m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.27951133616185e-06,
      "parent_symmetrization_rmsd_A": 0.04246972692482424,
      "parent_cell_rmsd_A": 0.013251586532333395,
      "energy_eV": -59.90277946904508,
      "reduced_polarization": [
        1.3533196210125398e-06,
        -1.2787328750074135e-13,
        4.0598944912054355e-06
      ],
      "cartesian_polarization_e_A2": [
        3.9229865125883907e-13,
        -1.3341692014276555e-15,
        3.498468534503624e-08
      ],
      "ranking_score": 0.5457911825805799
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0009748994765176107,
      "parent_symmetrization_rmsd_A": 0.1318416250868139,
      "parent_cell_rmsd_A": 0.06237271198345045,
      "energy_eV": -60.030576363144874,
      "reduced_polarization": [
        -0.49927301800348134,
        4.3989243592027295e-11,
        -0.5006495584392894
      ],
      "cartesian_polarization_e_A2": [
        -0.005948296969096539,
        -1.4784997604689271e-12,
        -0.004299071214260528
      ],
      "ranking_score": 0.6493846020357117
    },
    {
      "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": 1.7690052459494485e-06,
      "parent_symmetrization_rmsd_A": 0.1914628394137005,
      "parent_cell_rmsd_A": 0.07581747210344017,
      "energy_eV": -59.86532126062709,
      "reduced_polarization": [
        -0.4999984459761437,
        -1.2508342975068638e-12,
        -8.452156021878517e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.008981531963772379,
        -1.5285768056216185e-12,
        6.82201816143593e-05
      ],
      "ranking_score": 0.7104207454500524
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.2465316044968366e-05,
      "parent_symmetrization_rmsd_A": 0.13111775861288913,
      "parent_cell_rmsd_A": 0.0794947143340986,
      "energy_eV": -60.019420536909905,
      "reduced_polarization": [
        -3.722130559577879e-07,
        0.5000107878653449,
        -0.5000197021278988
      ],
      "cartesian_polarization_e_A2": [
        0.0029670137417383627,
        0.005157407363395568,
        -0.004293734466744487
      ],
      "ranking_score": 0.6510363678285037
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.457961317501716e-05,
      "parent_symmetrization_rmsd_A": 0.10836216194771653,
      "parent_cell_rmsd_A": 0.07082387240218235,
      "energy_eV": -59.95360602418224,
      "reduced_polarization": [
        2.8093847109727097e-06,
        0.49997826390037264,
        -2.6746943336935016e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.8881681391063304e-05,
        0.005214051662628936,
        2.0137190086480146e-05
      ],
      "ranking_score": 0.6261372892746122
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 5.389287687096629e-05,
      "parent_symmetrization_rmsd_A": 0.174452830851473,
      "parent_cell_rmsd_A": 0.1030660415976119,
      "energy_eV": -59.97550290420229,
      "reduced_polarization": [
        -0.5000028042207075,
        0.4999725033753626,
        -0.5000462656909297
      ],
      "cartesian_polarization_e_A2": [
        -0.005994397274955194,
        0.0052418121006238124,
        -0.00426867207330512
      ],
      "ranking_score": 0.7003271270046179
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0008522160927410094,
      "parent_symmetrization_rmsd_A": 0.23134771649125493,
      "parent_cell_rmsd_A": 0.11819121010087233,
      "energy_eV": -59.868981645403395,
      "reduced_polarization": [
        -0.5000615390654183,
        0.4993804114955757,
        -0.0005818894201989548
      ],
      "cartesian_polarization_e_A2": [
        -0.009010631405234927,
        0.0052992181993275975,
        9.427412888878536e-05
      ],
      "ranking_score": 0.762599951201955
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.24497569593037724,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.07977642170392427,
            "max_log_strain_component": 0.0023032734153837185,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0034557356240186,
              0.9989750807047039,
              0.9976993770834975
            ],
            "cell_volume_ratio": 1.0001210673188092,
            "cell_rmsd_from_input_A": 0.020284548847892825
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0035924423454591196,
              -3.750319855454553e-11,
              -0.4943663829130715
            ],
            "branch_aligned_reduced_polarization": [
              -0.0035924423454591196,
              -3.750319855454553e-11,
              -0.4943663829130715
            ],
            "target_residual": 0.006681562952452111,
            "energy_eV": -60.14573992101794,
            "max_atomic_step_A": 0.0025905242772280546,
            "max_log_strain_component": 8.237203254718309e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0035811996336244,
              0.9989354157433269,
              0.9976180342149965
            ],
            "cell_volume_ratio": 1.0001248516926937,
            "cell_rmsd_from_input_A": 0.021049033477438302
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.57324573031135e-05,
              -7.515302069303795e-13,
              -0.5001198250137038
            ],
            "branch_aligned_reduced_polarization": [
              -4.57324573031135e-05,
              -7.515302069303795e-13,
              -0.5001198250137038
            ],
            "target_residual": 0.00012825557126336357,
            "energy_eV": -60.148012430792974
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00012825557126336357,
        "parent_symmetrization_rmsd_A": 0.06904803214913316,
        "parent_cell_rmsd_A": 0.021049033477438302,
        "energy_eV": -60.148012430792974,
        "reduced_polarization": [
          -4.57324573031135e-05,
          -7.515302069303795e-13,
          -0.5001198250137038
        ],
        "cartesian_polarization_e_A2": [
          0.002999483549456771,
          1.988423116530788e-13,
          -0.0043166411428138
        ],
        "ranking_score": 0.5745668016610195
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.2872237861449108,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.05239155933036923,
            "max_log_strain_component": 0.0018909999910463572,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0008733878779261,
              1.0008733860968988,
              0.9981107868228869
            ],
            "cell_volume_ratio": 0.9998550221330299,
            "cell_rmsd_from_input_A": 0.01344206851744389
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0013475109514488302,
              -1.7365843304435677e-11,
              0.004042564566789527
            ],
            "branch_aligned_reduced_polarization": [
              0.0013475109514488302,
              -1.7365843304435677e-11,
              0.004042564566789527
            ],
            "target_residual": 0.004261233863675723,
            "energy_eV": -59.9010850488452,
            "max_atomic_step_A": 0.0007571704442209913,
            "max_log_strain_component": 2.678296404867373e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0008610125132944,
              1.0008610105785807,
              0.9981375195461965
            ],
            "cell_volume_ratio": 0.9998570753638709,
            "cell_rmsd_from_input_A": 0.013251586532333395
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.3533196210125398e-06,
              -1.2787328750074135e-13,
              4.0598944912054355e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.3533196210125398e-06,
              -1.2787328750074135e-13,
              4.0598944912054355e-06
            ],
            "target_residual": 4.27951133616185e-06,
            "energy_eV": -59.90277946904508
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3c",
        "spacegroup_number": 161,
        "pointgroup": "3m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.27951133616185e-06,
        "parent_symmetrization_rmsd_A": 0.04246972692482424,
        "parent_cell_rmsd_A": 0.013251586532333395,
        "energy_eV": -59.90277946904508,
        "reduced_polarization": [
          1.3533196210125398e-06,
          -1.2787328750074135e-13,
          4.0598944912054355e-06
        ],
        "cartesian_polarization_e_A2": [
          3.9229865125883907e-13,
          -1.3341692014276555e-15,
          3.498468534503624e-08
        ],
        "ranking_score": 0.5457911825805799
      },
      "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": [
          -60.03156479260227,
          -60.014441023773244,
          -59.99752221929084,
          -59.98085338852317,
          -59.96447793161346,
          -59.94844021420325,
          -59.932784214862075,
          -59.9175511880666,
          -59.902779469045086
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0183883838805895e-10,
            4.794797514725382e-12,
            -0.00235208184923651
          ],
          [
            -7.663452722037991e-11,
            4.224175821887481e-12,
            -0.002060814243170037
          ],
          [
            -5.4652095066223745e-11,
            3.644749023158624e-12,
            -0.001768443180542627
          ],
          [
            -3.6001860818750045e-11,
            3.0567358008658462e-12,
            -0.0014751308642836026
          ],
          [
            -2.08452520551409e-11,
            2.4604254423609285e-12,
            -0.001181037196760813
          ],
          [
            -9.503388348829238e-12,
            1.8560897892324412e-12,
            -0.0008863202559330548
          ],
          [
            -2.11310096896437e-12,
            1.2442581428510347e-12,
            -0.0005911354114935569
          ],
          [
            1.2177927780328434e-12,
            6.249709056637536e-13,
            -0.000295634366381008
          ],
          [
            3.923211484801475e-13,
            -1.3485603512469352e-15,
            3.498468539181632e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240677161e-06,
            -1.2925337481675312e-13,
            4.059894496634159e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240676088e-06,
            -1.2925337481675042e-13,
            4.059894496637184e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.09082812720249678,
            4.602748182591654e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218951,
            4.049223178981265e-10,
            -0.23879296163300223
          ],
          [
            -0.06831969445020186,
            3.48887474466153e-10,
            -0.204959110774801
          ],
          [
            -0.05700051667312456,
            2.921923814014349e-10,
            -0.17100157496019475
          ],
          [
            -0.04564626590772336,
            2.348655714357051e-10,
            -0.13693881939533864
          ],
          [
            -0.0342630320211047,
            1.7693380094385702e-10,
            -0.10278911363105242
          ],
          [
            -0.022856805403495384,
            1.1844847325193086e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158307,
            5.941391822972264e-11,
            -0.03430032617212153
          ],
          [
            1.3533196240311796e-06,
            -1.2922996006636822e-13,
            4.059894496588612e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -59.902779469045086,
          -59.88976979216482,
          -59.87726883254669,
          -59.865307631504926,
          -59.85391440757257,
          -59.84311446796449,
          -59.832930132830704,
          -59.82338067189134,
          -59.81448225249744
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.922760479602593e-13,
            -1.361766971535635e-15,
            3.498468535795999e-08
          ],
          [
            1.5989912668722985e-11,
            -6.880006996974361e-13,
            0.00029361953206999484
          ],
          [
            3.415969182793328e-11,
            -1.3777006326126298e-12,
            0.0005874820568022068
          ],
          [
            5.4997839769943014e-11,
            -2.069880782807893e-12,
            0.0008814812680779212
          ],
          [
            7.859838732127067e-11,
            -2.763891905532968e-12,
            0.0011754784565229733
          ],
          [
            1.0505194817657542e-10,
            -3.459223892668077e-12,
            0.0014693372538285856
          ],
          [
            1.3444494996067837e-10,
            -4.155467205341636e-12,
            0.001762923342389588
          ],
          [
            1.668580505031646e-10,
            -4.8519963522783755e-12,
            0.002056104120815862
          ],
          [
            2.0236544203590162e-10,
            -5.548397480813243e-12,
            0.0023487483315238608
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.3533196202609885e-06,
            -1.3051986772270517e-13,
            4.059894492705208e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.3533196202609885e-06,
            -1.3051986772270517e-13,
            4.059894492705208e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.09083082918703936,
          -4.605336992359574e-10,
          0.272492517555409
        ],
        "actual_opposite_endpoint_branch_residual": 0.0004156140777436355
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240677161e-06,
            -1.2925337481675312e-13,
            4.059894496634159e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240676088e-06,
            -1.2925337481675042e-13,
            4.059894496637184e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.09082812720249678,
            4.602748182591654e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218951,
            4.049223178981265e-10,
            -0.23879296163300223
          ],
          [
            -0.06831969445020186,
            3.48887474466153e-10,
            -0.204959110774801
          ],
          [
            -0.05700051667312456,
            2.921923814014349e-10,
            -0.17100157496019475
          ],
          [
            -0.04564626590772336,
            2.348655714357051e-10,
            -0.13693881939533864
          ],
          [
            -0.0342630320211047,
            1.7693380094385702e-10,
            -0.10278911363105242
          ],
          [
            -0.022856805403495384,
            1.1844847325193086e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158307,
            5.941391822972264e-11,
            -0.03430032617212153
          ],
          [
            1.3533196240311796e-06,
            -1.2922996006636822e-13,
            4.059894496588612e-06
          ],
          [
            0.011355518528318398,
            -6.546269082363665e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556962,
            -1.3125422970716727e-10,
            0.06814664757810107
          ],
          [
            0.0340759707881122,
            -1.9744988977166145e-10,
            0.1022279222680309
          ],
          [
            0.04543142766986852,
            -2.6398777608349633e-10,
            0.13629429496580925
          ],
          [
            0.05677664966397977,
            -3.308189833184372e-10,
            0.17032996233483289
          ],
          [
            0.06810645275558491,
            -3.979042650925635e-10,
            0.20431937231335917
          ],
          [
            0.07941572368065508,
            -4.6518339180678936e-10,
            0.23824718509329956
          ],
          [
            0.09069940547130328,
            -5.32616339921077e-10,
            0.2720982297562562
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.4681719389220974,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037728960174958615,
            "step_scale": 0.85461353012976,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0034589411865202,
              1.0020700955126332,
              0.9945971803585474
            ],
            "cell_volume_ratio": 1.0001034663222346,
            "cell_rmsd_from_input_A": 0.04664048836078739
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.41813781328717636,
              3.0305194375973013e-10,
              -0.45642986716356726
            ],
            "branch_aligned_reduced_polarization": [
              -0.41813781328717636,
              3.0305194375973013e-10,
              -0.45642986716356726
            ],
            "target_residual": 0.0927349669153421,
            "energy_eV": -60.08726296024404,
            "max_atomic_step_A": 0.031268273897728224,
            "max_log_strain_component": 0.001249809570611647,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0046608099605836,
              1.0027192536416771,
              0.9928044165879273
            ],
            "cell_volume_ratio": 1.000143959055129,
            "cell_rmsd_from_input_A": 0.06237271198345045
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49927301800348134,
              4.3989243592027295e-11,
              -0.5006495584392894
            ],
            "branch_aligned_reduced_polarization": [
              -0.49927301800348134,
              4.3989243592027295e-11,
              -0.5006495584392894
            ],
            "target_residual": 0.0009748994765176107,
            "energy_eV": -60.030576363144874
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0009748994765176107,
        "parent_symmetrization_rmsd_A": 0.1318416250868139,
        "parent_cell_rmsd_A": 0.06237271198345045,
        "energy_eV": -60.030576363144874,
        "reduced_polarization": [
          -0.49927301800348134,
          4.3989243592027295e-11,
          -0.5006495584392894
        ],
        "cartesian_polarization_e_A2": [
          -0.005948296969096539,
          -1.4784997604689271e-12,
          -0.004299071214260528
        ],
        "ranking_score": 0.6493846020357117
      },
      "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": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.4915987958944986,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0038410547168514905,
            "step_scale": 0.5800379898929878,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.003251185912605,
              1.0022203029789352,
              0.9944675091526237
            ],
            "cell_volume_ratio": 0.99991590576278,
            "cell_rmsd_from_input_A": 0.037932721205825956
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3213371572685627,
              1.8601899024134033e-10,
              -0.11622216641049235
            ],
            "branch_aligned_reduced_polarization": [
              -0.3213371572685627,
              1.8601899024134033e-10,
              -0.11622216641049235
            ],
            "target_residual": 0.21313846048525936,
            "energy_eV": -59.979951307615174,
            "max_atomic_step_A": 0.09323797006073428,
            "max_log_strain_component": 0.0034233110917126597,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0059678313550267,
              1.0043636172140176,
              0.9896222968811152
            ],
            "cell_volume_ratio": 0.9998722998265448,
            "cell_rmsd_from_input_A": 0.07262550674050165
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4885991205970456,
              -4.9476318823479025e-11,
              -0.01063838204445087
            ],
            "branch_aligned_reduced_polarization": [
              -0.4885991205970456,
              -4.9476318823479025e-11,
              -0.01063838204445087
            ],
            "target_residual": 0.015593435275281873,
            "energy_eV": -59.882668475278784,
            "max_atomic_step_A": 0.007085645834235583,
            "max_log_strain_component": 0.0003197915773474375,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.006223256447933,
              1.004563258419065,
              0.9891702264016149
            ],
            "cell_volume_ratio": 0.9998680165346115,
            "cell_rmsd_from_input_A": 0.07584702663528495
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5003849460691467,
              -1.306194853935481e-11,
              -0.0013622334307111727
            ],
            "branch_aligned_reduced_polarization": [
              -0.5003849460691467,
              -1.306194853935481e-11,
              -0.0013622334307111727
            ],
            "target_residual": 0.001415578820093978,
            "energy_eV": -59.865162173403526,
            "max_atomic_step_A": 0.0002737133533931664,
            "max_log_strain_component": 1.1188498061430965e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0062286733538686,
              1.0045589109606208,
              0.9891683336025999
            ],
            "cell_volume_ratio": 0.9998671587941401,
            "cell_rmsd_from_input_A": 0.07581747210344017
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999984459761437,
              -1.2508342975068638e-12,
              -8.452156021878517e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999984459761437,
              -1.2508342975068638e-12,
              -8.452156021878517e-07
            ],
            "target_residual": 1.7690052459494485e-06,
            "energy_eV": -59.86532126062709
          }
        ],
        "iterations": 4
      },
      "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": 1.7690052459494485e-06,
        "parent_symmetrization_rmsd_A": 0.1914628394137005,
        "parent_cell_rmsd_A": 0.07581747210344017,
        "energy_eV": -59.86532126062709,
        "reduced_polarization": [
          -0.4999984459761437,
          -1.2508342975068638e-12,
          -8.452156021878517e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.008981531963772379,
          -1.5285768056216185e-12,
          6.82201816143593e-05
        ],
        "ranking_score": 0.7104207454500524
      },
      "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": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027370803614076e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.5567881923463346,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004656260492761097,
            "step_scale": 0.8563529319600116,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.004361573345326,
              1.002884742046705,
              0.9928963427390955
            ],
            "cell_volume_ratio": 1.0001036754258807,
            "cell_rmsd_from_input_A": 0.060202686929933226
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.018151774187062368,
              0.40125684837158426,
              -0.45782590715007543
            ],
            "branch_aligned_reduced_polarization": [
              -0.018151774187062368,
              0.40125684837158426,
              -0.45782590715007543
            ],
            "target_residual": 0.10889605597708515,
            "energy_eV": -60.080349552911464,
            "max_atomic_step_A": 0.030259086315789854,
            "max_log_strain_component": 0.0014910297388044563,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.005741797522883,
              1.0038437702495728,
              0.9906250414092549
            ],
            "cell_volume_ratio": 1.0001426081245257,
            "cell_rmsd_from_input_A": 0.07934927705648581
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0004244045313283745,
              0.4991001623936641,
              -0.5010180779815149
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004244045313283745,
              0.4991001623936641,
              -0.5010180779815149
            ],
            "target_residual": 0.0014234850545171715,
            "energy_eV": -60.02008320299056,
            "max_atomic_step_A": 0.0003020788021469055,
            "max_log_strain_component": 1.1785412898451918e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0057575845134512,
              1.0038412591424792,
              0.9906114463232979
            ],
            "cell_volume_ratio": 1.0001420794537161,
            "cell_rmsd_from_input_A": 0.0794947143340986
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.722130559577879e-07,
              0.5000107878653449,
              -0.5000197021278988
            ],
            "branch_aligned_reduced_polarization": [
              -3.722130559577879e-07,
              0.5000107878653449,
              -0.5000197021278988
            ],
            "target_residual": 2.2465316044968366e-05,
            "energy_eV": -60.019420536909905
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.2465316044968366e-05,
        "parent_symmetrization_rmsd_A": 0.13111775861288913,
        "parent_cell_rmsd_A": 0.0794947143340986,
        "energy_eV": -60.019420536909905,
        "reduced_polarization": [
          -3.722130559577879e-07,
          0.5000107878653449,
          -0.5000197021278988
        ],
        "cartesian_polarization_e_A2": [
          0.0029670137417383627,
          0.005157407363395568,
          -0.004293734466744487
        ],
        "ranking_score": 0.6510363678285037
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027370803614076e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.5766259644406795,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005155588597771701,
            "step_scale": 0.948186508512702,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0068224331956286,
              0.9991380245048014,
              0.9939440172820938
            ],
            "cell_volume_ratio": 0.9998625333973095,
            "cell_rmsd_from_input_A": 0.06544838299299369
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.005352413760225016,
              0.4659607162858848,
              -0.020749789494995854
            ],
            "branch_aligned_reduced_polarization": [
              -0.005352413760225016,
              0.4659607162858848,
              -0.020749789494995854
            ],
            "target_residual": 0.0402228160739314,
            "energy_eV": -59.95436677656271,
            "max_atomic_step_A": 0.009183239345413855,
            "max_log_strain_component": 0.0004146222193141988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0073810025960797,
              0.9990476628441809,
              0.993472109988518
            ],
            "cell_volume_ratio": 0.9998518264907085,
            "cell_rmsd_from_input_A": 0.07069835966067295
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.671829242450725e-06,
              0.499198689949203,
              -0.0010698173453040634
            ],
            "branch_aligned_reduced_polarization": [
              4.671829242450725e-06,
              0.499198689949203,
              -0.0010698173453040634
            ],
            "target_residual": 0.00133664833662791,
            "energy_eV": -59.95371826032141,
            "max_atomic_step_A": 0.00032114107582709134,
            "max_log_strain_component": 9.789186576151288e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0073977028066559,
              0.999038639981612,
              0.9934640390901863
            ],
            "cell_volume_ratio": 0.9998512488206923,
            "cell_rmsd_from_input_A": 0.07082387240218235
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.8093847109727097e-06,
              0.49997826390037264,
              -2.6746943336935016e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.8093847109727097e-06,
              0.49997826390037264,
              -2.6746943336935016e-05
            ],
            "target_residual": 3.457961317501716e-05,
            "energy_eV": -59.95360602418224
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.457961317501716e-05,
        "parent_symmetrization_rmsd_A": 0.10836216194771653,
        "parent_cell_rmsd_A": 0.07082387240218235,
        "energy_eV": -59.95360602418224,
        "reduced_polarization": [
          2.8093847109727097e-06,
          0.49997826390037264,
          -2.6746943336935016e-05
        ],
        "cartesian_polarization_e_A2": [
          -2.8881681391063304e-05,
          0.005214051662628936,
          2.0137190086480146e-05
        ],
        "ranking_score": 0.6261372892746122
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027370803614076e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.6849707759706266,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0035924202527294856,
            "step_scale": 0.6606975118369194,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0062939248516458,
              0.9987969754677528,
              0.9950219647605724
            ],
            "cell_volume_ratio": 1.0000799883451985,
            "cell_rmsd_from_input_A": 0.05742098617274227
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3471471400038878,
              0.3169949374295823,
              -0.4202542625717402
            ],
            "branch_aligned_reduced_polarization": [
              -0.3471471400038878,
              0.3169949374295823,
              -0.4202542625717402
            ],
            "target_residual": 0.2514244068768395,
            "energy_eV": -60.10112148715752,
            "max_atomic_step_A": 0.07634805115273478,
            "max_log_strain_component": 0.0023990266974390434,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.010735103034394,
              0.9981477749914928,
              0.991362870064473
            ],
            "cell_volume_ratio": 1.0001493134315305,
            "cell_rmsd_from_input_A": 0.09830099668778694
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4904102086990397,
              0.4824253209944517,
              -0.5022473059774172
            ],
            "branch_aligned_reduced_polarization": [
              -0.4904102086990397,
              0.4824253209944517,
              -0.5022473059774172
            ],
            "target_residual": 0.020146558601909417,
            "energy_eV": -59.997669072444516,
            "max_atomic_step_A": 0.007124189257446281,
            "max_log_strain_component": 0.0003005712097314279,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0112643538927737,
              0.9980294172312935,
              0.990964470563061
            ],
            "cell_volume_ratio": 1.0001522707676087,
            "cell_rmsd_from_input_A": 0.10294965441383787
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5003082908430109,
              0.4990473430648426,
              -0.5014628264841258
            ],
            "branch_aligned_reduced_polarization": [
              -0.5003082908430109,
              0.4990473430648426,
              -0.5014628264841258
            ],
            "target_residual": 0.0017726984522607292,
            "energy_eV": -59.975622332554124,
            "max_atomic_step_A": 0.00039643029530570727,
            "max_log_strain_component": 1.3728839385500378e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0112820250540582,
              0.9980169459036761,
              0.9909587021979113
            ],
            "cell_volume_ratio": 1.0001514278037094,
            "cell_rmsd_from_input_A": 0.1030660415976119
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000028042207075,
              0.4999725033753626,
              -0.5000462656909297
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000028042207075,
              0.4999725033753626,
              -0.5000462656909297
            ],
            "target_residual": 5.389287687096629e-05,
            "energy_eV": -59.97550290420229
          }
        ],
        "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,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 5.389287687096629e-05,
        "parent_symmetrization_rmsd_A": 0.174452830851473,
        "parent_cell_rmsd_A": 0.1030660415976119,
        "energy_eV": -59.97550290420229,
        "reduced_polarization": [
          -0.5000028042207075,
          0.4999725033753626,
          -0.5000462656909297
        ],
        "cartesian_polarization_e_A2": [
          -0.005994397274955194,
          0.0052418121006238124,
          -0.00426867207330512
        ],
        "ranking_score": 0.7003271270046179
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.09082812720249656,
              4.6027369564541323e-10,
              -0.2724844117308448
            ],
            "branch_aligned_reduced_polarization": [
              -0.09082812720249656,
              4.6027370803614076e-10,
              -0.2724844117308448
            ],
            "target_residual": 0.7011913973122084,
            "energy_eV": -60.031564792602275,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003355833581637364,
            "step_scale": 0.506764697738651,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0057332259344982,
              0.9991657336217352,
              0.9950565461776273
            ],
            "cell_volume_ratio": 0.9999265285606067,
            "cell_rmsd_from_input_A": 0.04774731622034996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2921037505554591,
              0.247023976157987,
              -0.1388800427131479
            ],
            "branch_aligned_reduced_polarization": [
              -0.2921037505554591,
              0.247023976157987,
              -0.1388800427131479
            ],
            "target_residual": 0.35567595566193017,
            "energy_eV": -60.00049153871251,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00377538760580056,
            "step_scale": 0.9372365717521125,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0119141070966204,
              0.9985219750907245,
              0.9895646571999819
            ],
            "cell_volume_ratio": 0.9998744097047256,
            "cell_rmsd_from_input_A": 0.10042649117648177
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.46690659323110845,
              0.44839306291496034,
              -0.026788804318119405
            ],
            "branch_aligned_reduced_polarization": [
              -0.46690659323110845,
              0.44839306291496034,
              -0.026788804318119405
            ],
            "target_residual": 0.06690358408684136,
            "energy_eV": -59.92901257297797,
            "max_atomic_step_A": 0.026866453852380914,
            "max_log_strain_component": 0.0010725466934187967,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0138325366311902,
              0.9982038286378696,
              0.987996417875231
            ],
            "cell_volume_ratio": 0.9998637562754118,
            "cell_rmsd_from_input_A": 0.11669502844797096
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5001819564455668,
              0.49309430708202495,
              -0.007064045254814422
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001819564455668,
              0.49309430708202495,
              -0.007064045254814422
            ],
            "target_residual": 0.009880406782492319,
            "energy_eV": -59.87076667093557,
            "max_atomic_step_A": 0.002796427300395257,
            "max_log_strain_component": 0.00012225369546086423,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9770959865976323,
            "cell_principal_stretches": [
              1.0140375138299338,
              0.9981091621776383,
              0.9878858837657088
            ],
            "cell_volume_ratio": 0.9998591924070768,
            "cell_rmsd_from_input_A": 0.11819121010087233
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000615390654183,
              0.4993804114955757,
              -0.0005818894201989548
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000615390654183,
              0.4993804114955757,
              -0.0005818894201989548
            ],
            "target_residual": 0.0008522160927410094,
            "energy_eV": -59.868981645403395
          }
        ],
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0008522160927410094,
        "parent_symmetrization_rmsd_A": 0.23134771649125493,
        "parent_cell_rmsd_A": 0.11819121010087233,
        "energy_eV": -59.868981645403395,
        "reduced_polarization": [
          -0.5000615390654183,
          0.4993804114955757,
          -0.0005818894201989548
        ],
        "cartesian_polarization_e_A2": [
          -0.009010631405234927,
          0.0052992181993275975,
          9.427412888878536e-05
        ],
        "ranking_score": 0.762599951201955
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "bec_projection_01",
      "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
        ],
        "endpoint_rmsd_A": 0.04246972692482424,
        "minimum_distance_A_by_image": [
          2.873975670473563,
          2.8811595979064557,
          2.8883549520106926,
          2.895561608223707,
          2.902779443126623,
          2.910008334434847,
          2.9172481609886587,
          2.924498802743833,
          2.9317601407622966
        ],
        "minimum_distance_A": 2.873975670473563,
        "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": [
          785.0751468186472,
          785.0611201190792,
          785.047093670122,
          785.033067471771,
          785.0190415240219,
          785.0050158268715,
          784.9909903803119,
          784.9769651843421,
          784.9629402389543
        ],
        "cell_deformation_log_strain_norm": 0.002226367285334031
      },
      "parent_reduced_polarization": [
        1.3533196240677161e-06,
        -1.2925337481675312e-13,
        4.059894496634159e-06
      ],
      "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": [
          -60.03156479260227,
          -60.014441023773244,
          -59.99752221929084,
          -59.98085338852317,
          -59.96447793161346,
          -59.94844021420325,
          -59.932784214862075,
          -59.9175511880666,
          -59.902779469045086
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0183883838805895e-10,
            4.794797514725382e-12,
            -0.00235208184923651
          ],
          [
            -7.663452722037991e-11,
            4.224175821887481e-12,
            -0.002060814243170037
          ],
          [
            -5.4652095066223745e-11,
            3.644749023158624e-12,
            -0.001768443180542627
          ],
          [
            -3.6001860818750045e-11,
            3.0567358008658462e-12,
            -0.0014751308642836026
          ],
          [
            -2.08452520551409e-11,
            2.4604254423609285e-12,
            -0.001181037196760813
          ],
          [
            -9.503388348829238e-12,
            1.8560897892324412e-12,
            -0.0008863202559330548
          ],
          [
            -2.11310096896437e-12,
            1.2442581428510347e-12,
            -0.0005911354114935569
          ],
          [
            1.2177927780328434e-12,
            6.249709056637536e-13,
            -0.000295634366381008
          ],
          [
            3.923211484801475e-13,
            -1.3485603512469352e-15,
            3.498468539181632e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240677161e-06,
            -1.2925337481675312e-13,
            4.059894496634159e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240676088e-06,
            -1.2925337481675042e-13,
            4.059894496637184e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.09082812720249678,
            4.602748182591654e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218951,
            4.049223178981265e-10,
            -0.23879296163300223
          ],
          [
            -0.06831969445020186,
            3.48887474466153e-10,
            -0.204959110774801
          ],
          [
            -0.05700051667312456,
            2.921923814014349e-10,
            -0.17100157496019475
          ],
          [
            -0.04564626590772336,
            2.348655714357051e-10,
            -0.13693881939533864
          ],
          [
            -0.0342630320211047,
            1.7693380094385702e-10,
            -0.10278911363105242
          ],
          [
            -0.022856805403495384,
            1.1844847325193086e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158307,
            5.941391822972264e-11,
            -0.03430032617212153
          ],
          [
            1.3533196240311796e-06,
            -1.2922996006636822e-13,
            4.059894496588612e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -59.902779469045086,
          -59.88976979216482,
          -59.87726883254669,
          -59.865307631504926,
          -59.85391440757257,
          -59.84311446796449,
          -59.832930132830704,
          -59.82338067189134,
          -59.81448225249744
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.922760479602593e-13,
            -1.361766971535635e-15,
            3.498468535795999e-08
          ],
          [
            1.5989912668722985e-11,
            -6.880006996974361e-13,
            0.00029361953206999484
          ],
          [
            3.415969182793328e-11,
            -1.3777006326126298e-12,
            0.0005874820568022068
          ],
          [
            5.4997839769943014e-11,
            -2.069880782807893e-12,
            0.0008814812680779212
          ],
          [
            7.859838732127067e-11,
            -2.763891905532968e-12,
            0.0011754784565229733
          ],
          [
            1.0505194817657542e-10,
            -3.459223892668077e-12,
            0.0014693372538285856
          ],
          [
            1.3444494996067837e-10,
            -4.155467205341636e-12,
            0.001762923342389588
          ],
          [
            1.668580505031646e-10,
            -4.8519963522783755e-12,
            0.002056104120815862
          ],
          [
            2.0236544203590162e-10,
            -5.548397480813243e-12,
            0.0023487483315238608
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.3533196202609885e-06,
            -1.3051986772270517e-13,
            4.059894492705208e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.3533196202609885e-06,
            -1.3051986772270517e-13,
            4.059894492705208e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.09083082918703936,
          -4.605336992359574e-10,
          0.272492517555409
        ],
        "actual_opposite_endpoint_branch_residual": 0.0004156140777436355
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240677161e-06,
            -1.2925337481675312e-13,
            4.059894496634159e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.09082812720249676,
            4.602747901451097e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218952,
            4.0492234373382635e-10,
            -0.2387929616330022
          ],
          [
            -0.06831969445020186,
            3.488875293233335e-10,
            -0.20495911077480103
          ],
          [
            -0.057000516673124536,
            2.921923861685582e-10,
            -0.17100157496019477
          ],
          [
            -0.04564626590772338,
            2.348655544038993e-10,
            -0.13693881939533864
          ],
          [
            -0.03426303202110468,
            1.7693382598249288e-10,
            -0.10278911363105243
          ],
          [
            -0.022856805403495366,
            1.1844851896990778e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158317,
            5.94138836465948e-11,
            -0.034300326172121545
          ],
          [
            1.3533196240676088e-06,
            -1.2925337481675042e-13,
            4.059894496637184e-06
          ],
          [
            0.011355518528318448,
            -6.546268796304793e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556993,
            -1.312542277203511e-10,
            0.06814664757810106
          ],
          [
            0.03407597078811215,
            -1.9744990802846605e-10,
            0.1022279222680309
          ],
          [
            0.0454314276698685,
            -2.639877544958965e-10,
            0.1362942949658093
          ],
          [
            0.056776649663979745,
            -3.308189696646005e-10,
            0.1703299623348329
          ],
          [
            0.06810645275558495,
            -3.979042432044742e-10,
            0.20431937231335914
          ],
          [
            0.0794157236806551,
            -4.6518338012252386e-10,
            0.23824718509329953
          ],
          [
            0.09069940547130323,
            -5.326163364104515e-10,
            0.27209822975625614
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.09082812720249678,
            4.602748182591654e-10,
            -0.2724844117308419
          ],
          [
            -0.07959764416218951,
            4.049223178981265e-10,
            -0.23879296163300223
          ],
          [
            -0.06831969445020186,
            3.48887474466153e-10,
            -0.204959110774801
          ],
          [
            -0.05700051667312456,
            2.921923814014349e-10,
            -0.17100157496019475
          ],
          [
            -0.04564626590772336,
            2.348655714357051e-10,
            -0.13693881939533864
          ],
          [
            -0.0342630320211047,
            1.7693380094385702e-10,
            -0.10278911363105242
          ],
          [
            -0.022856805403495384,
            1.1844847325193086e-10,
            -0.06857042881830511
          ],
          [
            -0.011433439798158307,
            5.941391822972264e-11,
            -0.03430032617212153
          ],
          [
            1.3533196240311796e-06,
            -1.2922996006636822e-13,
            4.059894496588612e-06
          ],
          [
            0.011355518528318398,
            -6.546269082363665e-11,
            0.03406655945921688
          ],
          [
            0.022715546791556962,
            -1.3125422970716727e-10,
            0.06814664757810107
          ],
          [
            0.0340759707881122,
            -1.9744988977166145e-10,
            0.1022279222680309
          ],
          [
            0.04543142766986852,
            -2.6398777608349633e-10,
            0.13629429496580925
          ],
          [
            0.05677664966397977,
            -3.308189833184372e-10,
            0.17032996233483289
          ],
          [
            0.06810645275558491,
            -3.979042650925635e-10,
            0.20431937231335917
          ],
          [
            0.07941572368065508,
            -4.6518339180678936e-10,
            0.23824718509329956
          ],
          [
            0.09069940547130328,
            -5.32616339921077e-10,
            0.2720982297562562
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3c",
        "spacegroup_number": 161,
        "pointgroup": "3m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.27951133616185e-06,
        "parent_symmetrization_rmsd_A": 0.04246972692482424,
        "parent_cell_rmsd_A": 0.013251586532333395,
        "energy_eV": -59.90277946904508,
        "reduced_polarization": [
          1.3533196210125398e-06,
          -1.2787328750074135e-13,
          4.0598944912054355e-06
        ],
        "cartesian_polarization_e_A2": [
          3.9229865125883907e-13,
          -1.3341692014276555e-15,
          3.498468534503624e-08
        ],
        "ranking_score": 0.5457911825805799
      }
    }
  ],
  "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": 58,
      "full_response": 25,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 83,
      "full_response": 50,
      "energy_polarization": 33
    },
    "elapsed_seconds": 160.02355755498866
  }
}
