{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "F20Na2Sb6",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -130.62364559940724,
  "input_cartesian_polarization_e_A2": [
    5.538504292029913e-11,
    -0.016656867245970413,
    -4.6992775365122366e-11
  ],
  "input_reduced_polarization": [
    1.6134506018741107e-09,
    -1.0081104049908074,
    -3.0987026911426113e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -1.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -1.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -1.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.703340290305871e-15,
      "parent_symmetrization_rmsd_A": 0.6851774991523967,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -120.83784054387257,
      "reduced_polarization": [
        -2.1633264504207786e-15,
        -2.410913737152023e-16,
        -2.9961012873787703e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.1649900867802513e-17,
        -3.983519053311809e-18,
        -4.5436793652839247e-17
      ],
      "ranking_score": 0.6851774991524041
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.2930046765738153e-15,
      "parent_symmetrization_rmsd_A": 0.8510603415358463,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -113.03790330003375,
      "reduced_polarization": [
        -2.0933492666179775e-15,
        -3.4428765482991917e-16,
        -8.701869370836805e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.90383558959743e-17,
        -5.68861677504533e-18,
        -1.3196651417034988e-17
      ],
      "ranking_score": 0.8510603415358509
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 5.326971204772856e-15,
      "parent_symmetrization_rmsd_A": 0.8510603425319884,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -113.0379033148726,
      "reduced_polarization": [
        -3.3088577483497352e-15,
        3.710565064737904e-15,
        -1.9130576358311024e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.1192537815785805e-17,
        6.130914767360076e-17,
        -2.9012104968351614e-17
      ],
      "ranking_score": 0.851060342531999
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.427932652207319e-06,
      "parent_symmetrization_rmsd_A": 0.0009206617151697014,
      "parent_cell_rmsd_A": 0.004294941581115682,
      "energy_eV": -130.61663841732988,
      "reduced_polarization": [
        2.2338479661725283e-13,
        -0.9999955720673478,
        -2.2202642173520057e-12
      ],
      "cartesian_polarization_e_A2": [
        4.6505852341552075e-12,
        -0.016518201458196855,
        -3.947304508792349e-12
      ],
      "ranking_score": 0.502003252975753
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.660523679965577e-15,
      "parent_symmetrization_rmsd_A": 0.6851775269145282,
      "parent_cell_rmsd_A": 0.004294941581115682,
      "energy_eV": -120.79215246713795,
      "reduced_polarization": [
        7.415533520606628e-16,
        3.552228777891417e-15,
        4.772397239335126e-16
      ],
      "cartesian_polarization_e_A2": [
        8.798688545337948e-18,
        5.867669039449603e-17,
        7.230605438248016e-18
      ],
      "ranking_score": 0.6862512623098144
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.921337377112896e-15,
      "parent_symmetrization_rmsd_A": 0.9900195601159567,
      "parent_cell_rmsd_A": 0.004294941581115682,
      "energy_eV": -122.8192440831636,
      "reduced_polarization": [
        -2.369754542360006e-15,
        -5.279627452642536e-15,
        1.0234779697687306e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.041096803533557e-17,
        -8.721033603066307e-17,
        1.5506599614555986e-17
      ],
      "ranking_score": 0.9910932955112475
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00044099784372986234,
      "parent_symmetrization_rmsd_A": 0.05967569980685826,
      "parent_cell_rmsd_A": 0.27467917739002584,
      "energy_eV": -127.20635167162155,
      "reduced_polarization": [
        -3.942715221156975e-12,
        -1.4995590021562701,
        4.074718896377874e-13
      ],
      "cartesian_polarization_e_A2": [
        6.865263514380025e-12,
        -0.025244194318948,
        -7.204879712569684e-12
      ],
      "ranking_score": 0.6292274898418244
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        -1.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0007965166789183293,
      "parent_symmetrization_rmsd_A": 0.06834110168773307,
      "parent_cell_rmsd_A": 0.3974835976306657,
      "energy_eV": -129.44363879344704,
      "reduced_polarization": [
        5.203955478208051e-05,
        -1.0003280829901544,
        -0.4992760578364921
      ],
      "cartesian_polarization_e_A2": [
        0.003981158081794432,
        -0.01612533284144183,
        -0.006891870628754826
      ],
      "ranking_score": 0.6693050344532362
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0002096772443299341,
      "parent_symmetrization_rmsd_A": 0.06833038905910904,
      "parent_cell_rmsd_A": 0.3994313691718949,
      "energy_eV": -129.44060402549164,
      "reduced_polarization": [
        0.4998113590927024,
        -1.0000907866805686,
        1.1701859470642895e-05
      ],
      "cartesian_polarization_e_A2": [
        0.007965130748188855,
        -0.01611955356534527,
        1.2614423792244445e-06
      ],
      "ranking_score": 0.6686075858407426
    },
    {
      "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,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00044608898879145597,
      "parent_symmetrization_rmsd_A": 0.09375688173258774,
      "parent_cell_rmsd_A": 0.4574506759641117,
      "energy_eV": -125.92231647570438,
      "reduced_polarization": [
        -5.0097850480421885e-05,
        -1.4996088008853914,
        -0.4997915561369873
      ],
      "cartesian_polarization_e_A2": [
        0.0040572968886093425,
        -0.024844353435580356,
        -0.00703749432054305
      ],
      "ranking_score": 0.7090117287011986
    },
    {
      "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": [
        0.5,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0004715781404941057,
      "parent_symmetrization_rmsd_A": 0.09375682791711773,
      "parent_cell_rmsd_A": 0.4567073463515792,
      "energy_eV": -125.92229205736034,
      "reduced_polarization": [
        0.49974146164498945,
        -1.499608803227836,
        -5.0089390382012735e-05
      ],
      "cartesian_polarization_e_A2": [
        0.008123297946614904,
        -0.02484435403798936,
        -5.0267756708834765e-06
      ],
      "ranking_score": 0.7088768207860008
    },
    {
      "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,
        -1.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 5.825157495130345e-05,
      "parent_symmetrization_rmsd_A": 0.12622183270796025,
      "parent_cell_rmsd_A": 0.8518984770733757,
      "energy_eV": -125.51220207209755,
      "reduced_polarization": [
        0.4999701031375914,
        -1.000049994231338,
        -0.49999997913469585
      ],
      "cartesian_polarization_e_A2": [
        0.011797177173386323,
        -0.015221600566850924,
        -0.00680178523589968
      ],
      "ranking_score": 0.8393129551262068
    },
    {
      "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,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 8.720661531971805e-05,
      "parent_symmetrization_rmsd_A": 0.14512202789725506,
      "parent_cell_rmsd_A": 0.8193139841461834,
      "energy_eV": -122.04804814569486,
      "reduced_polarization": [
        0.4999653583020731,
        -1.4999207990748118,
        -0.4999885039150318
      ],
      "cartesian_polarization_e_A2": [
        0.012062324462239211,
        -0.023963974968397615,
        -0.006966666564488987
      ],
      "ranking_score": 0.8501249371644404
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "target_residual": 0.008110404990808149,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.001344528420616905,
            "max_log_strain_component": 0.0008124367067433285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0008127668228382,
              1.0001387941336928,
              1.0001387917756024
            ],
            "cell_volume_ratio": 1.0010905976238917,
            "cell_rmsd_from_input_A": 0.004294941581115682
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.2338479661725283e-13,
              -0.9999955720673478,
              -2.2202642173520057e-12
            ],
            "branch_aligned_reduced_polarization": [
              2.2338479661725283e-13,
              -0.9999955720673478,
              -2.2202642173520057e-12
            ],
            "target_residual": 4.427932652207319e-06,
            "energy_eV": -130.61663841732988
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.427932652207319e-06,
        "parent_symmetrization_rmsd_A": 0.0009206617151697014,
        "parent_cell_rmsd_A": 0.004294941581115682,
        "energy_eV": -130.61663841732988,
        "reduced_polarization": [
          2.2338479661725283e-13,
          -0.9999955720673478,
          -2.2202642173520057e-12
        ],
        "cartesian_polarization_e_A2": [
          4.6505852341552075e-12,
          -0.016518201458196855,
          -3.947304508792349e-12
        ],
        "ranking_score": 0.502003252975753
      },
      "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": [
          -130.62364559940724,
          -130.62283729942038,
          -130.62200962329456,
          -130.62116260242524,
          -130.62029626808686,
          -130.6194106514337,
          -130.61850578350004,
          -130.61758169520033,
          -130.6166384173298
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.5385019562356907e-11,
            -0.016656867245970458,
            -4.6992794845820605e-11
          ],
          [
            4.904175460869927e-11,
            -0.016639543592317788,
            -4.160938021244926e-11
          ],
          [
            4.269907396037846e-11,
            -0.01662221718723967,
            -3.622677076910639e-11
          ],
          [
            3.6356829432291744e-11,
            -0.01660488803934104,
            -3.0844907109210914e-11
          ],
          [
            3.0014674623767095e-11,
            -0.016587556157220074,
            -2.546375628713543e-11
          ],
          [
            2.367311455915257e-11,
            -0.016570221549466826,
            -2.0083457927576883e-11
          ],
          [
            1.7331850460049107e-11,
            -0.016552884224663823,
            -1.4703951833665412e-11
          ],
          [
            1.0991044761088139e-11,
            -0.016535544191385265,
            -9.325195179687944e-12
          ],
          [
            4.650586308582522e-12,
            -0.016518201458196866,
            -3.947320879289601e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.229059621532487e-13,
            -0.9999955720673483,
            -2.221344714922913e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.2290596215324047e-13,
            -0.9999955720673483,
            -2.2213447149229172e-12
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.6134485969487855e-09,
            -0.008110404990810283,
            -3.0987039600915978e-09
          ],
          [
            1.4118406443941467e-09,
            -0.007096880656341398,
            -2.7115391598719896e-09
          ],
          [
            1.2102285840143168e-09,
            -0.0060831182430050035,
            -2.324405723452827e-09
          ],
          [
            1.0086056434488455e-09,
            -0.005069118250567106,
            -1.9372998760758264e-09
          ],
          [
            8.069532819732217e-10,
            -0.004054881178454428,
            -1.5502194528060897e-09
          ],
          [
            6.052958134716846e-10,
            -0.0030404075256718066,
            -1.1631736684947214e-09
          ],
          [
            4.0361802788879686e-10,
            -0.0020256977908430507,
            -7.761585818499839e-10
          ],
          [
            2.0193069438789735e-10,
            -0.0010107524721534311,
            -3.891714173143157e-10
          ],
          [
            2.2293278334473143e-13,
            4.427932651651645e-06,
            -2.2213342276700132e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -130.61663841732985,
          -130.61731188699954,
          -130.61798402584088,
          -130.61865483432427,
          -130.61932431290347,
          -130.6199924620151,
          -130.62065928207917,
          -130.62132477349866,
          -130.62198893665985
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.650582577125499e-12,
            -0.016518201458196855,
            -3.947296944243286e-12
          ],
          [
            2.213999261155288e-12,
            -0.016518843379059237,
            -1.8638920577358173e-12
          ],
          [
            -2.2288949133238705e-13,
            -0.016519485107249498,
            2.1898154023656032e-13
          ],
          [
            -2.6598141248817218e-12,
            -0.016520126637692624,
            2.301579174906262e-12
          ],
          [
            -5.096839977997265e-12,
            -0.016520767965292293,
            4.383836766754272e-12
          ],
          [
            -7.534111158457273e-12,
            -0.016521409084932406,
            6.46575557181281e-12
          ],
          [
            -9.9714197189384e-12,
            -0.016522049991476176,
            8.547430398481397e-12
          ],
          [
            -1.240891975015193e-11,
            -0.01652269067976828,
            1.0628695989075807e-11
          ],
          [
            -1.484640450518257e-11,
            -0.01652333114463314,
            1.2709493952588811e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2348256112078903e-13,
            -0.9999955720673478,
            -2.219764936434322e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2348256112078903e-13,
            -0.9999955720673478,
            -2.219764936434322e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3425848636924539e-09,
          -0.9913256853425673,
          2.5781314520967805e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.008702819780029736
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.229059621532487e-13,
            -0.9999955720673483,
            -2.221344714922913e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.2290596215324047e-13,
            -0.9999955720673483,
            -2.2213447149229172e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.6134485969487855e-09,
            -0.008110404990810283,
            -3.0987039600915978e-09
          ],
          [
            1.4118406443941467e-09,
            -0.007096880656341398,
            -2.7115391598719896e-09
          ],
          [
            1.2102285840143168e-09,
            -0.0060831182430050035,
            -2.324405723452827e-09
          ],
          [
            1.0086056434488455e-09,
            -0.005069118250567106,
            -1.9372998760758264e-09
          ],
          [
            8.069532819732217e-10,
            -0.004054881178454428,
            -1.5502194528060897e-09
          ],
          [
            6.052958134716846e-10,
            -0.0030404075256718066,
            -1.1631736684947214e-09
          ],
          [
            4.0361802788879686e-10,
            -0.0020256977908430507,
            -7.761585818499839e-10
          ],
          [
            2.0193069438789735e-10,
            -0.0010107524721534311,
            -3.891714173143157e-10
          ],
          [
            2.2293278334473143e-13,
            4.427932651651645e-06,
            -2.2213342276700132e-12
          ],
          [
            -5.338235409269032e-11,
            2.6310253087302726e-07,
            1.0300793551465404e-10
          ],
          [
            -1.0700790253892478e-10,
            -3.888571467047797e-06,
            2.081699257416858e-10
          ],
          [
            -1.606291211153632e-10,
            -8.026783449688324e-06,
            3.132835102448439e-10
          ],
          [
            -2.1425183849288487e-10,
            -1.2151226280066041e-05,
            4.183444701766348e-10
          ],
          [
            -2.67884270321872e-10,
            -1.6261591661681507e-05,
            5.233529165593609e-10
          ],
          [
            -3.2151137308034095e-10,
            -2.0357570093221256e-05,
            6.283149556196577e-10
          ],
          [
            -3.751474131341581e-10,
            -2.443885099334686e-05,
            7.332199292164887e-10
          ],
          [
            -4.2878250949840435e-10,
            -2.8505122596778065e-05,
            8.380637295246629e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "target_residual": 0.4918895950091926,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.033098659670393486,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4058965535455105,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              0.9965893873839378,
              0.9965893295401325,
              0.9801986733067553
            ],
            "cell_volume_ratio": 0.9735238628227271,
            "cell_rmsd_from_input_A": 0.10371138025420538
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.544905796217863e-10,
              -1.2042733609390766,
              -1.7990314534775792e-09
            ],
            "branch_aligned_reduced_polarization": [
              9.544905796217863e-10,
              -1.2042733609390766,
              -1.7990314534775792e-09
            ],
            "target_residual": 0.29572663906092345,
            "energy_eV": -130.34575357094315,
            "max_atomic_step_A": 0.03013101386731964,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6287024467907598,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              0.9931904070462924,
              0.9931902917532506,
              0.9607894391523226
            ],
            "cell_volume_ratio": 0.9477487114852841,
            "cell_rmsd_from_input_A": 0.20365028038270122
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.105171586734895e-10,
              -1.383321959517557,
              -6.416083422167989e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.105171586734895e-10,
              -1.383321959517557,
              -6.416083422167989e-10
            ],
            "target_residual": 0.11667804048244301,
            "energy_eV": -128.99795127606254,
            "max_atomic_step_A": 0.01810309569500959,
            "max_log_strain_component": 0.013773491857193777,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              0.9908563588290131,
              0.9908562042005212,
              0.9476467318949587
            ],
            "cell_volume_ratio": 0.9303959324724372,
            "cell_rmsd_from_input_A": 0.27036175797333956
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -4.622432963463066e-11,
              -1.4929607585680695,
              7.093051691633742e-12
            ],
            "branch_aligned_reduced_polarization": [
              -4.622432963463066e-11,
              -1.4929607585680695,
              7.093051691633742e-12
            ],
            "target_residual": 0.007039241431930465,
            "energy_eV": -127.33223571414523,
            "max_atomic_step_A": 0.0010314430534305889,
            "max_log_strain_component": 0.0009035378218691638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              0.9907034376700355,
              0.9907032804676388,
              0.946790883934647
            ],
            "cell_volume_ratio": 0.929268762964953,
            "cell_rmsd_from_input_A": 0.27467917739002584
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.942715221156975e-12,
              -1.4995590021562701,
              4.074718896377874e-13
            ],
            "branch_aligned_reduced_polarization": [
              -3.942715221156975e-12,
              -1.4995590021562701,
              4.074718896377874e-13
            ],
            "target_residual": 0.00044099784372986234,
            "energy_eV": -127.20635167162155
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00044099784372986234,
        "parent_symmetrization_rmsd_A": 0.05967569980685826,
        "parent_cell_rmsd_A": 0.27467917739002584,
        "energy_eV": -127.20635167162155,
        "reduced_polarization": [
          -3.942715221156975e-12,
          -1.4995590021562701,
          4.074718896377874e-13
        ],
        "cartesian_polarization_e_A2": [
          6.865263514380025e-12,
          -0.025244194318948,
          -7.204879712569684e-12
        ],
        "ranking_score": 0.6292274898418244
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026833351194e-09
            ],
            "target_residual": 0.5000657712445556,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.05683270386240978,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5213197746275277,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.023619540464721,
              1.000072353341157,
              0.9774100365487166
            ],
            "cell_volume_ratio": 1.000568401686919,
            "cell_rmsd_from_input_A": 0.19593173733810323
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00013134298148247592,
              -1.0084281179927677,
              -0.25756825104108055
            ],
            "branch_aligned_reduced_polarization": [
              0.00013134298148247592,
              -1.0084281179927677,
              -0.25756825104108055
            ],
            "target_residual": 0.24257824166062245,
            "energy_eV": -130.35285281888366,
            "max_atomic_step_A": 0.05301093357094996,
            "max_log_strain_component": 0.01937199549542252,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.047567891251001,
              1.0002975145845268,
              0.9565403258074294
            ],
            "cell_volume_ratio": 1.0023390537941976,
            "cell_rmsd_from_input_A": 0.3870559123463641
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0004048634592822109,
              -1.0063275631992372,
              -0.488482464547227
            ],
            "branch_aligned_reduced_polarization": [
              0.0004048634592822109,
              -1.0063275631992372,
              -0.488482464547227
            ],
            "target_residual": 0.013147455775429947,
            "energy_eV": -129.50783864215984,
            "max_atomic_step_A": 0.002784073827758313,
            "max_log_strain_component": 0.001027765710276421,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.049222284833305,
              1.0004163584562225,
              0.9558100339536642
            ],
            "cell_volume_ratio": 1.0032747357619398,
            "cell_rmsd_from_input_A": 0.3974835976306657
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.203955478208051e-05,
              -1.0003280829901544,
              -0.4992760578364921
            ],
            "branch_aligned_reduced_polarization": [
              5.203955478208051e-05,
              -1.0003280829901544,
              -0.4992760578364921
            ],
            "target_residual": 0.0007965166789183293,
            "energy_eV": -129.44363879344704
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0007965166789183293,
        "parent_symmetrization_rmsd_A": 0.06834110168773307,
        "parent_cell_rmsd_A": 0.3974835976306657,
        "energy_eV": -129.44363879344704,
        "reduced_polarization": [
          5.203955478208051e-05,
          -1.0003280829901544,
          -0.4992760578364921
        ],
        "cartesian_polarization_e_A2": [
          0.003981158081794432,
          -0.01612533284144183,
          -0.006891870628754826
        ],
        "ranking_score": 0.6693050344532362
      },
      "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,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134505953502298e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "target_residual": 0.5000657727296124,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.04921324977740121,
            "max_log_strain_component": 0.02,
            "step_scale": 0.45143215386749674,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0204209964661208,
              1.0000626535482857,
              0.9804085829317403
            ],
            "cell_volume_ratio": 1.000492183597325,
            "cell_rmsd_from_input_A": 0.16960163891904576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.22372400340728968,
              -1.0078809021161794,
              7.996419231304045e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.2237240034072897,
              -1.0078809021161794,
              7.996419231304045e-05
            ],
            "target_residual": 0.2763883885146627,
            "energy_eV": -130.42172248272698,
            "max_atomic_step_A": 0.04785003480700413,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7923557281924585,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.041645606295304,
              1.0002328220379602,
              0.9615524060233803
            ],
            "cell_volume_ratio": 1.001830032774193,
            "cell_rmsd_from_input_A": 0.34037354941199943
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4347695966122163,
              -1.0066023181936252,
              0.00037147098586195543
            ],
            "branch_aligned_reduced_polarization": [
              0.4347695966122163,
              -1.0066023181936252,
              0.00037147098586195543
            ],
            "target_residual": 0.0655647323059905,
            "energy_eV": -129.77432601396043,
            "max_atomic_step_A": 0.014385810481782295,
            "max_log_strain_component": 0.006458136414000222,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0489542380258643,
              1.0003870145392886,
              0.9558620857936556
            ],
            "cell_volume_ratio": 1.0030436281511248,
            "cell_rmsd_from_input_A": 0.3964023529697703
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.496780745511394,
              -1.001560772546686,
              5.642152576597116e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.496780745511394,
              -1.001560772546686,
              5.642152576597116e-05
            ],
            "target_residual": 0.0035780991872037564,
            "energy_eV": -129.45914984728222,
            "max_atomic_step_A": 0.0007810249737726419,
            "max_log_strain_component": 0.00033490249379710416,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.049413965224658,
              1.000416740709264,
              0.9556379471227244
            ],
            "cell_volume_ratio": 1.0032777399166422,
            "cell_rmsd_from_input_A": 0.3994313691718949
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998113590927024,
              -1.0000907866805686,
              1.1701859470642895e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4998113590927024,
              -1.0000907866805686,
              1.1701859470642895e-05
            ],
            "target_residual": 0.0002096772443299341,
            "energy_eV": -129.44060402549164
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0002096772443299341,
        "parent_symmetrization_rmsd_A": 0.06833038905910904,
        "parent_cell_rmsd_A": 0.3994313691718949,
        "energy_eV": -129.44060402549164,
        "reduced_polarization": [
          0.4998113590927024,
          -1.0000907866805686,
          1.1701859470642895e-05
        ],
        "cartesian_polarization_e_A2": [
          0.007965130748188855,
          -0.01611955356534527,
          1.2614423792244445e-06
        ],
        "ranking_score": 0.6686075858407426
      },
      "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,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026833351194e-09
            ],
            "target_residual": 0.7013953026500853,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.06035682720558784,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4058965539046511,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0081268639015784,
              0.9965893474647756,
              0.9689808025742846
            ],
            "cell_volume_ratio": 0.9735238627274855,
            "cell_rmsd_from_input_A": 0.18023078336689116
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0006973909306932012,
              -1.2061382421834188,
              -0.20322452682840925
            ],
            "branch_aligned_reduced_polarization": [
              -0.0006973909306932012,
              -1.2061382421834188,
              -0.20322452682840925
            ],
            "target_residual": 0.41764925540144665,
            "energy_eV": -130.1693276600198,
            "max_atomic_step_A": 0.05718519920156656,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6325635338433028,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0155261892478618,
              0.9931903273560561,
              0.9396575192957086
            ],
            "cell_volume_ratio": 0.9477487113043216,
            "cell_rmsd_from_input_A": 0.34515854537050783
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0012534090337988784,
              -1.3857766672483895,
              -0.3858622248737084
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012534090337988784,
              -1.3857766672483895,
              -0.3858622248737084
            ],
            "target_residual": 0.16148056381456885,
            "energy_eV": -128.264523969856,
            "max_atomic_step_A": 0.03582050670363545,
            "max_log_strain_component": 0.013857292551509975,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0202768859519877,
              0.9908420676283985,
              0.9202302172934735
            ],
            "cell_volume_ratio": 0.9302913328105433,
            "cell_rmsd_from_input_A": 0.45156560975540233
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0005664264531670143,
              -1.4933833763535673,
              -0.4948406888269141
            ],
            "branch_aligned_reduced_polarization": [
              -0.0005664264531670143,
              -1.4933833763535673,
              -0.4948406888269141
            ],
            "target_residual": 0.008409461289887014,
            "energy_eV": -126.06997514436189,
            "max_atomic_step_A": 0.0018598644768070649,
            "max_log_strain_component": 0.000887412783464009,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.020452211736325,
              0.9906918757365182,
              0.9191166493696442
            ],
            "cell_volume_ratio": 0.9291843918829125,
            "cell_rmsd_from_input_A": 0.4574506759641117
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -5.0097850480421885e-05,
              -1.4996088008853914,
              -0.4997915561369873
            ],
            "branch_aligned_reduced_polarization": [
              -5.0097850480421885e-05,
              -1.4996088008853914,
              -0.4997915561369873
            ],
            "target_residual": 0.00044608898879145597,
            "energy_eV": -125.92231647570438
          }
        ],
        "iterations": 4
      },
      "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,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00044608898879145597,
        "parent_symmetrization_rmsd_A": 0.09375688173258774,
        "parent_cell_rmsd_A": 0.4574506759641117,
        "energy_eV": -125.92231647570438,
        "reduced_polarization": [
          -5.0097850480421885e-05,
          -1.4996088008853914,
          -0.4997915561369873
        ],
        "cartesian_polarization_e_A2": [
          0.0040572968886093425,
          -0.024844353435580356,
          -0.00703749432054305
        ],
        "ranking_score": 0.7090117287011986
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134505953502298e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "target_residual": 0.7013953037088693,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.060356550368151136,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4058965534509388,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0081268401721886,
              0.9965893407976836,
              0.968980831924321
            ],
            "cell_volume_ratio": 0.973523862787442,
            "cell_rmsd_from_input_A": 0.1802159304414171
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.20252712659805186,
              -1.2061382022848766,
              -0.0006973184772835928
            ],
            "branch_aligned_reduced_polarization": [
              0.20252712659805183,
              -1.2061382022848766,
              -0.0006973184772835928
            ],
            "target_residual": 0.4181451336790067,
            "energy_eV": -130.16932488855332,
            "max_atomic_step_A": 0.057185000600219894,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6325632347323821,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0155261479404583,
              0.9931903143076568,
              0.9396575699753227
            ],
            "cell_volume_ratio": 0.947748711418436,
            "cell_rmsd_from_input_A": 0.34493634706673987
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3846087707655339,
              -1.38577655573658,
              -0.00125323863945252
            ],
            "branch_aligned_reduced_polarization": [
              0.3846087707655339,
              -1.38577655573658,
              -0.00125323863945252
            ],
            "target_residual": 0.16236902909953962,
            "energy_eV": -128.26451256886224,
            "max_atomic_step_A": 0.035820456552412484,
            "max_log_strain_component": 0.013857313256653368,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0202768453278752,
              0.9908420469393939,
              0.9202302477326764
            ],
            "cell_volume_ratio": 0.930291307116673,
            "cell_rmsd_from_input_A": 0.4510109978033025
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4942743026493068,
              -1.4933833872646123,
              -0.0005662965719280352
            ],
            "branch_aligned_reduced_polarization": [
              0.4942743026493068,
              -1.4933833872646123,
              -0.0005662965719280352
            ],
            "target_residual": 0.008768344544394215,
            "energy_eV": -126.06995122855172,
            "max_atomic_step_A": 0.001859861397424398,
            "max_log_strain_component": 0.0008874118877588896,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0204521739790626,
              0.9906918551559265,
              0.9191166781924432
            ],
            "cell_volume_ratio": 0.9291843673382835,
            "cell_rmsd_from_input_A": 0.4567073463515792
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49974146164498945,
              -1.499608803227836,
              -5.0089390382012735e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49974146164498945,
              -1.499608803227836,
              -5.0089390382012735e-05
            ],
            "target_residual": 0.0004715781404941057,
            "energy_eV": -125.92229205736034
          }
        ],
        "iterations": 4
      },
      "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": [
          0.5,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0004715781404941057,
        "parent_symmetrization_rmsd_A": 0.09375682791711773,
        "parent_cell_rmsd_A": 0.4567073463515792,
        "energy_eV": -125.92229205736034,
        "reduced_polarization": [
          0.49974146164498945,
          -1.499608803227836,
          -5.0089390382012735e-05
        ],
        "cartesian_polarization_e_A2": [
          0.008123297946614904,
          -0.02484435403798936,
          -5.0267756708834765e-06
        ],
        "ranking_score": 0.7088768207860008
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -1.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134505953502298e-09,
              -1.0081104049908074,
              -3.0987026833351194e-09
            ],
            "target_residual": 0.7071532888680937,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.05978455614911042,
            "max_log_strain_component": 0.02,
            "step_scale": 0.30092473473187464,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0235070913841695,
              1.000041764567376,
              0.9773125116386456
            ],
            "cell_volume_ratio": 1.0003280626846214,
            "cell_rmsd_from_input_A": 0.21450506748288875
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1488153039578984,
              -1.0101879368153577,
              -0.1485972468106484
            ],
            "branch_aligned_reduced_polarization": [
              0.14881530395789844,
              -1.0101879368153577,
              -0.1485972468106484
            ],
            "target_residual": 0.49690882437303663,
            "energy_eV": -130.35428641796477,
            "max_atomic_step_A": 0.0580295805618653,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4119658003323638,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0479938897577115,
              1.0001958924776784,
              0.9554859168636439
            ],
            "cell_volume_ratio": 1.00153955826279,
            "cell_rmsd_from_input_A": 0.43071043320714747
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.2868643367362165,
              -1.012824322503979,
              -0.2862249731434476
            ],
            "branch_aligned_reduced_polarization": [
              0.2868643367362165,
              -1.012824322503979,
              -0.2862249731434476
            ],
            "target_residual": 0.3021440654887974,
            "energy_eV": -129.4711628131216,
            "max_atomic_step_A": 0.05316929074934698,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.6176729683807278,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0736582100634793,
              1.000494581384563,
              0.9345569440147218
            ],
            "cell_volume_ratio": 1.0038909960708937,
            "cell_rmsd_from_input_A": 0.65070279082763
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.40607117519712077,
              -1.0150128768068334,
              -0.40571378886508336
            ],
            "branch_aligned_reduced_polarization": [
              0.40607117519712077,
              -1.0150128768068334,
              -0.40571378886508336
            ],
            "target_residual": 0.13393244643866256,
            "energy_eV": -127.82969911890123,
            "max_atomic_step_A": 0.03636444385365723,
            "max_log_strain_component": 0.015982155096937643,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0954845983155457,
              1.0009486309407396,
              0.9187896661673921
            ],
            "cell_volume_ratio": 1.0074747443243899,
            "cell_rmsd_from_input_A": 0.8314867586583867
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4863531483378884,
              -1.010112555579577,
              -0.48632414264104734
            ],
            "branch_aligned_reduced_polarization": [
              0.4863531483378884,
              -1.010112555579577,
              -0.48632414264104734
            ],
            "target_residual": 0.02180663695162851,
            "energy_eV": -125.91833006402337,
            "max_atomic_step_A": 0.0066800938826872625,
            "max_log_strain_component": 0.001937593952455171,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 7.812443328659031,
            "cell_principal_stretches": [
              1.0977433059160095,
              1.0012776494717277,
              0.9164575284627534
            ],
            "cell_volume_ratio": 1.0073204772621267,
            "cell_rmsd_from_input_A": 0.8518984770733757
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999701031375914,
              -1.000049994231338,
              -0.49999997913469585
            ],
            "branch_aligned_reduced_polarization": [
              0.4999701031375914,
              -1.000049994231338,
              -0.49999997913469585
            ],
            "target_residual": 5.825157495130345e-05,
            "energy_eV": -125.51220207209755
          }
        ],
        "iterations": 5
      },
      "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 5.825157495130345e-05,
        "parent_symmetrization_rmsd_A": 0.12622183270796025,
        "parent_cell_rmsd_A": 0.8518984770733757,
        "energy_eV": -125.51220207209755,
        "reduced_polarization": [
          0.4999701031375914,
          -1.000049994231338,
          -0.49999997913469585
        ],
        "cartesian_polarization_e_A2": [
          0.011797177173386323,
          -0.015221600566850924,
          -0.00680178523589968
        ],
        "ranking_score": 0.8393129551262068
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.6134506018741107e-09,
              -1.0081104049908074,
              -3.0987026911426113e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.6134505953502298e-09,
              -1.0081104049908074,
              -3.0987026833351194e-09
            ],
            "target_residual": 0.8613683120281093,
            "energy_eV": -130.62364559940724,
            "max_atomic_step_A": 0.06920696465728263,
            "max_log_strain_component": 0.02,
            "step_scale": 0.30092473474919984,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.015332043499114,
              0.997470270899065,
              0.9679486469949174
            ],
            "cell_volume_ratio": 0.9803030871195269,
            "cell_rmsd_from_input_A": 0.22314586345634813
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.14917059830951507,
              -1.1577644977890782,
              -0.1502452255210968
            ],
            "branch_aligned_reduced_polarization": [
              0.14917059830951507,
              -1.1577644977890782,
              -0.15024522552109676
            ],
            "target_residual": 0.6021086366552584,
            "energy_eV": -130.22411370534465,
            "max_atomic_step_A": 0.06726636303014276,
            "max_log_strain_component": 0.02,
            "step_scale": 0.41305386057580706,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0309173696303706,
              0.9949557721252498,
              0.936965028987401
            ],
            "cell_volume_ratio": 0.9610611343168611,
            "cell_rmsd_from_input_A": 0.4368927857205402
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.28739009531231074,
              -1.2986316947513565,
              -0.28981676462722594
            ],
            "branch_aligned_reduced_polarization": [
              0.28739009531231074,
              -1.2986316947513565,
              -0.28981676462722594
            ],
            "target_residual": 0.3604568744826295,
            "energy_eV": -128.59256933299596,
            "max_atomic_step_A": 0.060629643198409466,
            "max_log_strain_component": 0.02,
            "step_scale": 0.615527979525433,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.04698825216171,
              0.992519005966069,
              0.9072069760394823
            ],
            "cell_volume_ratio": 0.9427293358787033,
            "cell_rmsd_from_input_A": 0.6423926085079016
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4069614098660673,
              -1.4181353268172352,
              -0.41019253026902647
            ],
            "branch_aligned_reduced_polarization": [
              0.4069614098660673,
              -1.4181353268172352,
              -0.41019253026902647
            ],
            "target_residual": 0.15304700450812664,
            "energy_eV": -125.60397202780989,
            "max_atomic_step_A": 0.0393218027681106,
            "max_log_strain_component": 0.016155032558525503,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.305837794123548,
            "cell_principal_stretches": [
              1.0602870327803529,
              0.9906040910720048,
              0.8840488222416106
            ],
            "cell_volume_ratio": 0.9285382895913326,
            "cell_rmsd_from_input_A": 0.803022823719554
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4882822897390252,
              -1.4934036947427494,
              -0.4916214891093339
            ],
            "branch_aligned_reduced_polarization": [
              0.4882822897390252,
              -1.4934036947427494,
              -0.4916214891093339
            ],
            "target_residual": 0.015843466210144694,
            "energy_eV": -122.45633801903183,
            "max_atomic_step_A": 0.004715958032421791,
            "max_log_strain_component": 0.0018371938016809545,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 7.629071977633066,
            "cell_principal_stretches": [
              1.0610006510191619,
              0.9907282718096412,
              0.8812786669353143
            ],
            "cell_volume_ratio": 0.9263678282165724,
            "cell_rmsd_from_input_A": 0.8193139841461834
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999653583020731,
              -1.4999207990748118,
              -0.4999885039150318
            ],
            "branch_aligned_reduced_polarization": [
              0.4999653583020731,
              -1.4999207990748118,
              -0.4999885039150318
            ],
            "target_residual": 8.720661531971805e-05,
            "energy_eV": -122.04804814569486
          }
        ],
        "iterations": 5
      },
      "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,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 8.720661531971805e-05,
        "parent_symmetrization_rmsd_A": 0.14512202789725506,
        "parent_cell_rmsd_A": 0.8193139841461834,
        "energy_eV": -122.04804814569486,
        "reduced_polarization": [
          0.4999653583020731,
          -1.4999207990748118,
          -0.4999885039150318
        ],
        "cartesian_polarization_e_A2": [
          0.012062324462239211,
          -0.023963974968397615,
          -0.006966666564488987
        ],
        "ranking_score": 0.8501249371644404
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.0009206617151697014,
        "minimum_distance_A_by_image": [
          1.9654885299541285,
          1.9659392824036184,
          1.9663901113280222,
          1.9668410167367054,
          1.9672919986390505,
          1.9677430570444292,
          1.9681941919622212,
          1.968645403401802,
          1.9690966913725587
        ],
        "minimum_distance_A": 1.9654885299541285,
        "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": [
          477.3880505157203,
          477.45309926912773,
          477.51815688605853,
          477.5832233677208,
          477.6482987153224,
          477.7133829300711,
          477.7784760131763,
          477.8435779658452,
          477.90868878928717
        ],
        "cell_deformation_log_strain_norm": 0.0008358080068973829
      },
      "parent_reduced_polarization": [
        2.229059621532487e-13,
        -0.9999955720673483,
        -2.221344714922913e-12
      ],
      "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": [
          -130.62364559940724,
          -130.62283729942038,
          -130.62200962329456,
          -130.62116260242524,
          -130.62029626808686,
          -130.6194106514337,
          -130.61850578350004,
          -130.61758169520033,
          -130.6166384173298
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.5385019562356907e-11,
            -0.016656867245970458,
            -4.6992794845820605e-11
          ],
          [
            4.904175460869927e-11,
            -0.016639543592317788,
            -4.160938021244926e-11
          ],
          [
            4.269907396037846e-11,
            -0.01662221718723967,
            -3.622677076910639e-11
          ],
          [
            3.6356829432291744e-11,
            -0.01660488803934104,
            -3.0844907109210914e-11
          ],
          [
            3.0014674623767095e-11,
            -0.016587556157220074,
            -2.546375628713543e-11
          ],
          [
            2.367311455915257e-11,
            -0.016570221549466826,
            -2.0083457927576883e-11
          ],
          [
            1.7331850460049107e-11,
            -0.016552884224663823,
            -1.4703951833665412e-11
          ],
          [
            1.0991044761088139e-11,
            -0.016535544191385265,
            -9.325195179687944e-12
          ],
          [
            4.650586308582522e-12,
            -0.016518201458196866,
            -3.947320879289601e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.229059621532487e-13,
            -0.9999955720673483,
            -2.221344714922913e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.2290596215324047e-13,
            -0.9999955720673483,
            -2.2213447149229172e-12
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.6134485969487855e-09,
            -0.008110404990810283,
            -3.0987039600915978e-09
          ],
          [
            1.4118406443941467e-09,
            -0.007096880656341398,
            -2.7115391598719896e-09
          ],
          [
            1.2102285840143168e-09,
            -0.0060831182430050035,
            -2.324405723452827e-09
          ],
          [
            1.0086056434488455e-09,
            -0.005069118250567106,
            -1.9372998760758264e-09
          ],
          [
            8.069532819732217e-10,
            -0.004054881178454428,
            -1.5502194528060897e-09
          ],
          [
            6.052958134716846e-10,
            -0.0030404075256718066,
            -1.1631736684947214e-09
          ],
          [
            4.0361802788879686e-10,
            -0.0020256977908430507,
            -7.761585818499839e-10
          ],
          [
            2.0193069438789735e-10,
            -0.0010107524721534311,
            -3.891714173143157e-10
          ],
          [
            2.2293278334473143e-13,
            4.427932651651645e-06,
            -2.2213342276700132e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -130.61663841732985,
          -130.61731188699954,
          -130.61798402584088,
          -130.61865483432427,
          -130.61932431290347,
          -130.6199924620151,
          -130.62065928207917,
          -130.62132477349866,
          -130.62198893665985
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.650582577125499e-12,
            -0.016518201458196855,
            -3.947296944243286e-12
          ],
          [
            2.213999261155288e-12,
            -0.016518843379059237,
            -1.8638920577358173e-12
          ],
          [
            -2.2288949133238705e-13,
            -0.016519485107249498,
            2.1898154023656032e-13
          ],
          [
            -2.6598141248817218e-12,
            -0.016520126637692624,
            2.301579174906262e-12
          ],
          [
            -5.096839977997265e-12,
            -0.016520767965292293,
            4.383836766754272e-12
          ],
          [
            -7.534111158457273e-12,
            -0.016521409084932406,
            6.46575557181281e-12
          ],
          [
            -9.9714197189384e-12,
            -0.016522049991476176,
            8.547430398481397e-12
          ],
          [
            -1.240891975015193e-11,
            -0.01652269067976828,
            1.0628695989075807e-11
          ],
          [
            -1.484640450518257e-11,
            -0.01652333114463314,
            1.2709493952588811e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2348256112078903e-13,
            -0.9999955720673478,
            -2.219764936434322e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2348256112078903e-13,
            -0.9999955720673478,
            -2.219764936434322e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3425848636924539e-09,
          -0.9913256853425673,
          2.5781314520967805e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.008702819780029736
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.229059621532487e-13,
            -0.9999955720673483,
            -2.221344714922913e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.6134486257239119e-09,
            -1.0081104049908103,
            -3.098703975699473e-09
          ],
          [
            1.4118406985131217e-09,
            -1.0070968806563414,
            -2.711539141021481e-09
          ],
          [
            1.2102285316849832e-09,
            -1.006083118243005,
            -2.3244057385197234e-09
          ],
          [
            1.0086056302032946e-09,
            -1.005069118250567,
            -1.937299884464114e-09
          ],
          [
            8.069532984482933e-10,
            -1.0040548811784544,
            -1.550219438867926e-09
          ],
          [
            6.052957889868038e-10,
            -1.0030404075256718,
            -1.1631736467037543e-09
          ],
          [
            4.036180242214709e-10,
            -1.002025697790843,
            -7.761585716342195e-10
          ],
          [
            2.0193070596887772e-10,
            -1.0010107524721534,
            -3.8917142178297073e-10
          ],
          [
            2.2290596215324047e-13,
            -0.9999955720673483,
            -2.2213447149229172e-12
          ],
          [
            -5.338237082123089e-11,
            -0.9999997368974691,
            1.0300792489015507e-10
          ],
          [
            -1.0700791871619164e-10,
            -1.000003888571467,
            2.0816996454822847e-10
          ],
          [
            -1.606291296139767e-10,
            -1.0000080267834497,
            3.13283561122071e-10
          ],
          [
            -2.1425184977043e-10,
            -1.00001215122628,
            4.183445005920534e-10
          ],
          [
            -2.6788426758066277e-10,
            -1.0000162615916617,
            5.233528807479298e-10
          ],
          [
            -3.2151137327539727e-10,
            -1.0000203575700932,
            6.283149696851728e-10
          ],
          [
            -3.751474165352001e-10,
            -1.0000244388509933,
            7.332198817706392e-10
          ],
          [
            -4.287825110045193e-10,
            -1.0000285051225968,
            8.380637833784419e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.6134485969487855e-09,
            -0.008110404990810283,
            -3.0987039600915978e-09
          ],
          [
            1.4118406443941467e-09,
            -0.007096880656341398,
            -2.7115391598719896e-09
          ],
          [
            1.2102285840143168e-09,
            -0.0060831182430050035,
            -2.324405723452827e-09
          ],
          [
            1.0086056434488455e-09,
            -0.005069118250567106,
            -1.9372998760758264e-09
          ],
          [
            8.069532819732217e-10,
            -0.004054881178454428,
            -1.5502194528060897e-09
          ],
          [
            6.052958134716846e-10,
            -0.0030404075256718066,
            -1.1631736684947214e-09
          ],
          [
            4.0361802788879686e-10,
            -0.0020256977908430507,
            -7.761585818499839e-10
          ],
          [
            2.0193069438789735e-10,
            -0.0010107524721534311,
            -3.891714173143157e-10
          ],
          [
            2.2293278334473143e-13,
            4.427932651651645e-06,
            -2.2213342276700132e-12
          ],
          [
            -5.338235409269032e-11,
            2.6310253087302726e-07,
            1.0300793551465404e-10
          ],
          [
            -1.0700790253892478e-10,
            -3.888571467047797e-06,
            2.081699257416858e-10
          ],
          [
            -1.606291211153632e-10,
            -8.026783449688324e-06,
            3.132835102448439e-10
          ],
          [
            -2.1425183849288487e-10,
            -1.2151226280066041e-05,
            4.183444701766348e-10
          ],
          [
            -2.67884270321872e-10,
            -1.6261591661681507e-05,
            5.233529165593609e-10
          ],
          [
            -3.2151137308034095e-10,
            -2.0357570093221256e-05,
            6.283149556196577e-10
          ],
          [
            -3.751474131341581e-10,
            -2.443885099334686e-05,
            7.332199292164887e-10
          ],
          [
            -4.2878250949840435e-10,
            -2.8505122596778065e-05,
            8.380637295246629e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.427932652207319e-06,
        "parent_symmetrization_rmsd_A": 0.0009206617151697014,
        "parent_cell_rmsd_A": 0.004294941581115682,
        "energy_eV": -130.61663841732988,
        "reduced_polarization": [
          2.2338479661725283e-13,
          -0.9999955720673478,
          -2.2202642173520057e-12
        ],
        "cartesian_polarization_e_A2": [
          4.6505852341552075e-12,
          -0.016518201458196855,
          -3.947304508792349e-12
        ],
        "ranking_score": 0.502003252975753
      }
    }
  ],
  "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": 90,
      "full_response": 31,
      "energy_polarization": 59
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 115,
      "full_response": 56,
      "energy_polarization": 59
    },
    "elapsed_seconds": 771.0410449620103
  }
}